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. 2023 Feb 2;122(11):2301–2310. doi: 10.1016/j.bpj.2023.01.041

PDK1:PKCα heterodimer association-dissociation dynamics in single-molecule diffusion tracks on a target membrane

Moshe T Gordon 1, Brian P Ziemba 1, Joseph J Falke 1,∗
PMCID: PMC10257113  PMID: 36733254

Abstract

Previous studies have documented the formation of a heterodimer between the two protein kinases PDK1 and PKCα on a lipid bilayer containing their target lipids. This work investigates the association-dissociation kinetics of this PDK1:PKCα heterodimer. The approach monitors the two-dimensional diffusion of single, membrane-associated PDK1 molecules for diffusivity changes as PKCα molecules bind and unbind. In the absence of PKCα, a membrane-associated PDK1 molecule exhibits high diffusivity (or large diffusion constant, D) because its membrane-contacting PH domain binds the target PIP3 lipid headgroup with little bilayer penetration, yielding minimal frictional drag against the bilayer. In contrast, membrane-associated PKCα contacts the bilayer via its C1A, C1B, and C2 domains, which each bind at least one target lipid with significant bilayer insertion, yielding a large frictional drag and low diffusivity. The present findings reveal that individual fluor-PDK1 molecules freely diffusing on the membrane surface undergo reversible switching between distinct high and low diffusivity states, corresponding to the PDK1 monomer and the PDK1:PKCα heterodimer, respectively. The observed single-molecule diffusion trajectories are converted to step length time courses, then subjected to two-state, hidden Markov modeling and dwell time analysis. The findings reveal that both the PDK1 monomer state and the PDK1:PKCα heterodimer state decay via simple exponential kinetics, yielding estimates of rate constants for state switching in both directions. Notably, the PDK1:PKCα heterodimer has been shown to competitively inhibit PDK1 phosphoactivation of AKT1, and is believed to play a tumor suppressor role by limiting excess activation of the highly oncogenic PDK1/AKT1/mTOR pathway. Thus, the present elucidation of the PDK1:PKCα association-dissociation kinetics has important biological and medical implications. More broadly, the findings illustrate the power of single-molecule diffusion measurements to reveal the kinetics of association-dissociation events in membrane signaling reactions that yield a large change in diffusive mobility.

Significance

This work investigates a membrane signaling reaction of biological and medical significance in which the master kinases PDK1 and PKCα associate to form a PDK1:PKCα heterodimer on their target membrane surface. Single-molecule TIRFM is employed to monitor the 2D diffusion of single, membrane-bound PDK1 molecules in the presence of PKCα molecules, revealing diffusivity changes due to heterodimer formation and dissociation events in real time. Two-state, hidden Markov modeling and dwell time analysis provide, to our knowledge, the first estimates of PDK1 rate constants for switching between the monomer and heterodimer states. The findings have regulatory significance given the demonstrated ability of PDK1:PKCα formation to competitively inhibit PDK1 phosphoactivation of AKT1 in the highly oncogenic PDK1/AKT1/mTOR cell growth pathway.

Introduction

Analysis of single-membrane protein molecules bound to their target lipids while they diffuse and interact on the bilayer surface can provide fundamental insights into their molecular behaviors and mechanisms. Previous single-molecule studies have recorded the two-dimensional (2D) diffusion tracks of individual peripheral membrane proteins to analyze their target lipid specificities, membrane densities, 2D diffusion constants (D), protein-lipid interactions, protein-protein interactions, enzyme activities, and regulatory mechanisms (1,2,3,4,5,6,7,8,9). Typically, such studies quantify the overall parameters of the individual diffusion tracks in a diffusing population, yielding key parameters for each track, including its average diffusion constant D, average brightness, and total bound state lifetime. If the population is composed of multiple subpopulations differing substantially in their frictional drags against the membrane, the subpopulations can be resolved by deconvolution of the ensemble Rayleigh step size distribution into its individual subpopulation components. In principle, if sufficiently large diffusivity differences exist between two interconverting states, kinetic information about transitions between those states can become accessible via monitoring diffusivity changes within individual diffusion tracks as a function of time. Since the diffusivities of membrane-bound proteins are dominated by their frictional drag against the lipid bilayer, this approach detects switching between states possessing different bilayer contacts. Such switching may arise from the formation or dissociation of a complex between two membrane-bound proteins that each contribute bilayer drag to the complex, or a conformational change within a single protein that alters its membrane contacts.

This study investigates whether diffusivity changes can be used to analyze the binding and dissociation kinetics of individual, membrane-bound master kinase molecules diffusing on the surface of their target membrane. The study monitors single molecules of phosphoinositide-dependent kinase isoform 1 (PDK1) (3,10,11,12,13,14,15,16,17) as they bind and unbind single molecules of protein kinase C isoform α (PKCα). The PKCα enzyme, like other AGC kinases phospho-activated by PDK1, possesses a tethered PDK1-interacting fragment (PIF motif) that can bind to the PIF pocket of PDK1, thereby stabilizing the PDK1:PKCα heterodimer (3,15,18,19,20,21). Our previous single-molecule diffusion studies of the PDK1 and PKCα monomers found that they exhibit greatly different 2D diffusivities (quantified as their average diffusion constants D) due to their contrasting interactions with the target lipid bilayer. PDK1 contacts the bilayer primarily by engulfing the aqueous headgroup of its target PIP3 lipid with little protein penetration into the bilayer. In contrast, PKCα exhibits more extensive bilayer contacts, including bilayer insertion and multi-lipid binding by its C1A, C1B, and C2 domains. The greater frictional drag of the PKCα monomer against the bilayer accounts for the large difference between the diffusion constants of the PDK1 and PKCα monomers (1,2,3,22,23,24,25). Most recently, our single-molecule 2D diffusion analysis of Alexa Fluor 555-labeled PDK1 (fluor-PDK1) in the presence of unlabeled, dark PKCα monomers yielded direct detection of PDK1:PKCα heterodimers on the surface of a target membrane (3). These studies revealed that association with PKCα to form the heterodimer reduced the diffusivity of the PDK1 monomer by approximately fivefold, in good agreement with the predicted heterodimer diffusion constant based on the known additivity of multivalent frictional drags on supported lipid bilayers (22,23,26). In addition, the studies measured the nanomolar equilibrium binding affinity of the two master kinases for each other, and confirmed that the heterodimer was stabilized by a PIF interaction (3). Fig. 1 presents schematic membrane docking models of the PDK1 and PKCα monomers and their PDK1:PKCα heterodimer.

Figure 1.

Figure 1

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Schematic models showing the reversible association-dissociation reaction of fluor-labeled PDK1 with dark PKCα on their target membrane surface. PDK1 binds the membrane via its PH domain that primarily contacts the aqueous headgroup of its target lipid PI(3,4,5)P3 (red headgroup). In contrast, PKCα has multiple, bilayer-penetrating domains and exhibits greater protein frictional drag against the bilayer, which adds to the frictional drag of its bound target lipids phosphatidylserine (cyan headgroup), PI(4,5)P2 (blue headgroup), and phorbol ester (lacks headgroup). The PDK1:PKCα heterodimer is stabilized by the binding of the PKCα tethered PIF motif to the PIF pocket of the PDK1 kinase domain. When PDK1 associates with PKCα to form the heterodimer, the PDK1 diffusivity decreases dramatically due to the increased, additive frictional drag of PKCα in the complex (3,22,23,26,27,28). To see this figure in color, go online.

This study addresses the kinetics of PDK1:PKCα heterodimer formation and dissociation. The approach monitors the single-molecule diffusion tracks of individual, fluor-labeled PDK1 molecules and analyzes the changes in diffusivity that occur as the high diffusivity fluor-PDK1 monomer encounters a dark PKCα molecule, forms a low diffusivity fluor-PDK1:PKC heterodimer, and then returns to the high diffusivity monomer state after heterodimer dissociation. For a given diffusion track, the timecourse of transitions between the monomer and heterodimer states is analyzed by boxcar averaging and a published hidden Markov model algorithm, yielding the dwell times in the two states and ultimately the rate constants of heterodimer formation and dissociation. The findings place limits on the kinetics of the PDK1:PKCα association and dissociation reactions. The resulting information provides new molecular insights into a crucial membrane protein interaction with biological and medical significance.

Materials and methods

Reagents

Synthetic DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine), DOPS (1,2-dioleoyl-sn-glycero-3-phospho-L-serine), and DOPIP3 (1,2-dioleoyl-sn-glycero-3-phospho-1′-myo-inositol-3′,4′,5′-trisphosphate) were from Avanti Polar Lipids (Alabaster, AL). PMA (phorbol-12-myristate-13-acetate) was from MilliporeSigma, Burlington, MA. Alexa Fluor 555 C2 Maleimide and CoverWell 9 mm perfusion chambers were from Invitrogen (Carlsbad, CA). Anti-HA agarose affinity resin and HA peptide were from Thermo Scientific (Rockford, IL). Talon metal affinity resin was from Takara Bio (Mountain View, CA). All other chemicals were from MilliporeSigma.

The protein constructs employed, which are the same as those utilized in our previous publication (3), were expressed in eukaryotic tissue culture cells and purified via affinity chromatography as follows. HA-tagged PKCα was expressed in HEK293 cells, and purified using anti-HA agarose affinity resin as described previously (1,25). PKCα protein was active as demonstrated by its Ca2+- and lipid-regulated target membrane binding and enzymatic activities (1,3,25). 6His-tagged PDK1 was expressed in Sf9 cells, purified using metal affinity resin as detailed previously (3,29,30,31), and then, where indicated, labeled on a ybbr-labeling tag by the enzyme Sfp as described previously (1,3,4,12,22). The isolated PDK1 construct was active as demonstrated by its lipid-regulated target membrane binding and enzymatic activities (3). Fig. 2 shows the locations of labeling and affinity tags and the domain structures of each construct.

Figure 2.

Figure 2

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Domain structures of the PDK1 and PKCα constructs used in this study. Also shown are the N- or C-terminal affinity tags employed for protein purification and the ybbr-labeling tag used to attach Alexa Fluor 555 to PDK1 via Sfp enzymatic labeling. PKCα was unlabeled in the present study and was used as a dark binding partner. The AGC segment of PKCα contains the unstructured, tethered PIF motif that binds to the PIF pocket of the PDK1 kinase domain, as shown in Fig. 1.

Preparation of supported lipid bilayers for single-molecule TIRFM

Previously described protocols (1,2,3,4,12,26,32) were employed to generate a homogenous supported lipid bilayer on ultraclean glass. In brief, lipids were dissolved in chloroform (DOPS, DOPC), 20:9:1 chloroform/methanol/water (PIP3), or DMSO (PMA) and mixed to yield the desired molar ratio. Lipids were dried in a speed vac to remove solvent and rehydrated in lipid buffer containing 25 mM HEPES, 140 mM KCl, 15 mM NaCl, 0.5 mM MgCl2 (pH adjusted to 7.4). The lipid mixture was vortexed for 1 min and subjected to three freeze-thaw cycles by freezing in liquid N2 followed by thawing at 37°C and a 1-min vortex. After three freeze-thaw cycles the lipid mixtures were aliquoted into 2 mL amber screw-top tubes (300 μL per tube), snap frozen in liquid N2, and stored at −80°C until use. On the day of an experiment a lipid aliquot was thawed on ice and sonicated with a Misonix XL2020 probe sonicator with a micro tip for a total of 4 min during which 0.6-s pulses were alternated with 0.6-s pauses. The SUVs were mixed with 1 volume of lipid buffer containing 1 M NaCl, then 50–60 μL was deposited for 30 min onto an ultraclean glass surface in the 30-μL imaging chamber, where the excess addition volume forms a bead at the addition port and prevents sample drying. After lipid deposition the resulting supported lipid bilayer was rinsed with deionized H2O and then with imaging buffer, composed of lipid buffer supplemented with 26 μM CaCl2, 20 μM EGTA, 5 mM reduced L-glutathione, and 0.1 mg/mL BSA.

Single-molecule TIRFM measurements

TIRFM was carried out at 22.0 ± 0.5°C on a home-built, objective-based TIRFM instrument, as described previously (4,5). The instrument utilized a Nikon (Melville, NY) TE2000U inverted TIRF microscope; a Nikon Apochromat 60×, NA 1.49 TIRF oil immersion objective; and a 532-nm, diode-pumped solid-state laser (CNI-Laser model MGLIII 532-300 mW). The laser power was reduced with two N.D. filters totaling 0.8 absorbance. Sample fluorescence emerging from the 600-nm long-pass emission filter was captured by a Photometrics Evolve 512 electron-multiplying charge-coupled device camera (Tucson, AZ).

Single-molecule diffusion tracking and analysis

Single-molecule diffusion movies were collected at a 20-ms frame rate and analyzed as described previously (23,25,26,32). The single-molecule trajectories of fluor-labeled proteins were tracked using the ImageJ (NIH, Bethesda, MD) plugin Particle Tracker (33). The software extracts position and brightness for each trajectory in every frame it is present. These data are then imported into Mathematica for analysis. Particles were filtered on the basis of brightness to remove dim contaminants and excessively bright aggregates/contaminants. Additional filtering was done on the basis of diffusivity to remove immobile particles trapped in sparse membrane defects, as well as rapidly dissociating and excessively mobile particles characteristic of transiently bound contaminants. All filtering has been described and validated previously (23,25,26,32). Analysis of the single-molecule tracks for a diffusing population to determine a step size distribution, followed by best fitting of one or two Rayleigh distributions to the step size distribution to determine the number of subpopulations, their relative proportions, and their diffusion constants (D) was carried out as detailed previously ((26) Eqs. 1 and 2).

Analysis of single-molecule diffusion tracks to elucidate the kinetics of transitions between the PDK1 monomer and PDK1:PKCα heterodimer states

A simple approach was developed to extract the dwell times of fluor-PDK1 molecules in the monomer and heterodimer states based on their different diffusivities, and to place limits on the rate constants for switching between these states. The approach was applied to single-molecule diffusion tracks in which fluor-PDK1 spends roughly equal amounts of time in the monomer and heterodimer states, obtained in the presence of half-saturating dark PKCα ([PKCα] ∼ K1/2). We found that a set of single-molecule tracks together comprising a set of >5000 single-molecule steps yielded an adequate number of monomer and heterodimer dwell times to define both the monomer-to-heterodimer and the heterodimer-to-monomer transition rate constants in this half-saturating PKCα regime.

To analyze how the oligomeric state of a given, membrane-bound fluor-PDK1 molecule changed with time, its 2D diffusion track was analyzed (see above) to determine the length of each diffusional step taken between consecutive 20-ms video frames. The resulting step lengths were plotted versus time, yielding a step length time course for the full diffusion track. Due to the broad distribution of step lengths produced by standard 2D diffusion (see Fig. 3), the range of step lengths observed for the pure monomer and predominant heterodimer step length time courses exhibited considerable overlap (see raw data in Fig. 4). Such overlap prevented the use of raw step length to rigorously assign individual fluor-PDK1 steps to the monomer or heterodimer states. To remedy this issue, each raw step length time course was converted to a moving or boxcar average time course, which largely eliminated the overlap between the pure monomer and heterodimer step length ranges (see overlaid raw and averaged data in Figs. 4 and S1). In addition, such averaging minimized effects due to random localization errors arising from diffusion during each 20-ms video frame. Of course, boxcar averaging also reduced the time resolution of the analysis, yet it was necessary to largely eliminate the assignment ambiguity inherent in the analysis of raw step lengths. For the present data, a boxcar length of five averaged steps was operationally chosen because this averaging was sufficient to reveal clear switching events between the monomer and heterodimer states, and also enabled dwell time analysis by a two-state hidden Markov model (HMM) (see below). To calculate each boxcar-averaged step length, the mean of five adjacent steps was calculated—the two previous steps, the current step, and the two subsequent steps. Then the boxcar window was moved to the next step in the trajectory and a new mean was calculated. This procedure was repeated until the window reached the end of the trajectory.

Figure 3.

Figure 3

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Fluor-PDK1 step length distributions acquired for sets of single-molecule diffusion tracks in the absence of PKCα, in the presence of half-saturating PKCα, and in the presence of near-saturating PKCα. Relative to the fluor-PDK1 monomer, the fluor-PDK1:PKCα heterodimer possesses a substantially lower diffusion constant. Thus, when the PKCα concentration is increased, the distribution shifts toward smaller step lengths. (A) In the absence of PKCα, a homogeneous fluor-PDK1 monomer population is observed that is best-fit by a single Rayleigh function (100% monomer, D = 1.22 ± 0.05 μm2 s−1). (B) At half-saturating PKCα, a mixture of monomers and heterodimers is observed that is best fit by the sum of two Rayleigh functions of similar weights (proportions 46 ± 5% monomer with D = 1.13 ± 0.02 μm2 s−1; and 54 ± 5% heterodimer with D = 0.26 ± 0.05 μm2 s−1). (C) At near-saturating PKCα, a predominantly fluor-PDK1:PKCα heterodimer population is observed that is best fit by the sum of two Rayleigh functions with contrasting weights (proportions 24 ± 4% monomer with D = 1.14 ± 0.07 μm2 s−1; and 76 ± 4% heterodimer with D = 0.27 ± 0.01 μm2 s−1). In each case, the membrane-bound monomers and heterodimers are diffusing in two dimensions on a target supported lipid bilayer composed of DOPC/DOPS/DOPIP3/PMA (mol %, 72:24:2:2) at 22.0 ± 0.5°C in a physiological imaging buffer (materials and methods). Each distribution was generated by combining >50 tracks from 3 movies, yielding >5000 individual steps. The indicated error bars on data points are standard deviations, and the indicated uncertainties on best fit parameters are 95% confidence intervals from the nonlinear least-squares best fits. The R2 values for the nonlinear least-squares best fits were (A) 0.995, (B) 0.987, and (C) 0.992.

Figure 4.

Figure 4

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Representative step length time courses and diffusion tracks for individual fluor-PDK1 molecules at three PKCα concentrations, shown both without (gray line) and with (black line) boxcar averaging. Each step length is measured between consecutive, 20 ms video frames. The five-step boxcar average presents each step as the mean of the two previous steps, the present step, and the two subsequent steps. In a given row, step length time courses are shown for three representative fluor-PDK1 molecules, as well as a representative two-dimensional diffusion track for the same experimental conditions. Different rows provide data for membrane-bound fluor-PDK1 diffusing under contrasting conditions: (A) in the absence of PKCα; (B) in the presence of half-saturating PKCα; and (C) in the presence of near-saturating PKCα. In the presence of half-saturating PKCα (B), the boxcar-averaged time course (black line) reveals multiple transitions between high diffusivity and low diffusivity states corresponding to the fluor-PDK1 monomer and the fluor-PDK1:PKCα heterodimer, respectively. Also shown for this condition is an idealized trace (blue line) generated by hidden Markov modeling of the boxcar-averaged data. The idealized trace highlights the transitions of the observed fluor-PDK1 molecule between its monomer state, which displays greater diffusivity and larger average step lengths, and its heterodimer state exhibiting decreased diffusivity due to the associated dark PKCα molecule. The R2 values for the idealized traces are (left) 0.870, (middle) 0.857, and (right) 0.701. Note these R2 values are not expected to approach 1.0 since the hidden Markov model does not attempt to reproduce the fluctuations away from the mean step length that are inherent to random diffusion. To see this figure in color, go online.

A two-state HMM package (QUB Express: https://qub.mandelics.com, SUNY Research Foundation (34,35,36,37)) was employed to generate a maximum likelihood idealized time course depicting the transitions between the high diffusivity, large step length monomer state, and the low diffusivity, smaller step length heterodimer state. QUB was originally developed to analyze the switching of single ion channels between multiple current states, such as open and closed, and subsequently has been applied to a variety of other systems (34,35,36). To our knowledge, the is the first application of QUB to analyze switching between different diffusivity states. The QUB analysis began by inputting, for each of the two states, the mean step length and its standard deviation as measured for the representative set of boxcar-averaged step length time courses. Next an individual boxcar-averaged, step length time course for a single fluor-PDK1 molecule was imported into QUB Express. The QUB analysis employs the Viterbi algorithm (37) to generate a maximum likelihood idealized trace describing the time course of switching between the monomer and heterodimer diffusion states. The resulting idealized trace yielded a set of dwell times for the tracked PDK molecule in each of its two diffusion states. At least 165 dwell times were acquired for each diffusion state by analyzing multiple PDK1 diffusion tracks, then the dwell times were binned to yield a frequency distribution defining the probability that a PDK1 molecule remains in the starting diffusion state as a function of time. The resulting exponential decays, one for each state, were each subjected to nonlinear least-squares best-fit analysis to determine the first-order rate constants for transitions to the other state at a half-saturating PKC concentration.

Buffer and lipid compositions

The standard imaging buffer for smTIRFM was 25 mM HEPES, 140 mM KCl, 15 mM NaCl, 0.5 mM MgCl2, 20 μM EGTA, 26 μM Ca2+, 5 mM reduced glutathione, 0.1 mg/mL BSA (pH 7.4), except where indicated otherwise. The lipid composition for this study was 72:24:2:2 mol % DOPC/DOPS/DOPIP3/PMA.

Statistics

Best-fit Rayleigh distributions were determined by analyzing sets of single-molecule diffusion tracks providing a total of >5000 individual steps. Similarly, QUB Express modeling of two-state switching by a single fluor-PDK1 molecule between contrasting monomer and heterodimer diffusivities was carried out on sets of single-molecule diffusion tracks totaling >5000 steps. Best-fit exponential decays for the monomer state and the heterodimer state were each defined by >165 individual dwell times. In the figures, the indicated error bars on data points are standard deviations, and the indicated uncertainties on best fit parameters are 95% confidence intervals from the nonlinear least-squares best fits. Further details and R-squared values for the nonlinear least-squares best fits are provided in the figure legends.

Results

Preparation of full-length master kinases and a target membrane for single-molecule studies

This study employed previously described, full-length human PDK1 and PKCα constructs (Fig. 2) expressed in eukaryotic tissue culture cells and purified by affinity chromatography (3,25). The PDK1 construct was subsequently labeled on its N-terminal ybbr tag with Alexa Fluor 555 via a gentle enzymatic procedure, as detailed previously (3). The PKCα construct was unlabeled (dark). Both isolated enzymes were fully active, as assessed by native target lipid binding and protein kinase activity (1,3,25).

The target membrane employed was a supported lipid bilayer that included the key plasma membrane target and background lipids required by each kinase at levels similar to those found in the plasma membrane cytoplasmic leaflet. Specifically, to drive efficient membrane recruitment and activity of PDK1, the lipids DOPS and DOPIP3 were included at 24 and 2 mol % each, respectively. To drive efficient membrane recruitment and activity of PKC, the lipids DOPS and PMA (a diacylglycerol analog) were included at 24 and 2 mol % each, respectively.

Our previous single-molecule studies (3) defined the affinity of the PDK1:PKCα heterodimer by titrating fluor-PDK1 with an increasing concentration of dark PKCα. The titration yielded a simple, hyperbolic binding curve. The resulting, best-fit K1/2 = 3.8 ± 0.4 nM defined the total PKCα concentration required to achieve 50% occupancy of the fluor-PDK1 population with bound PKCα on the same membranes employed herein (DOPC/DOPS/DOPIP3/PMA, mol % 72:24:2:2). Increasing the total PKCα concentration to 28 nM yielded ∼88% occupancy of the fluor-PDK1 population with bound PKCα (3). Notably, these previous studies found that increasing the PKCα concentration through this range had no effect on the diffusion constants of fluor-labeled phospholipid or a fluor-labeled PH domain that does not bind to PDK1 or PKCα. The latter controls indicated that the observed effects of titrating PKCα on fluor-PDK1 diffusion were due to specific PDK1:PKCα heterodimer formation, not due to the formation of lipid domains or increased protein-protein collisions as the density of membrane-bound PKCα increased (3). In the present study, PKCα concentrations [PKCα] ∼ K1/2 are termed half-saturating, while concentrations [PKCα] ∼ 28 nM are termed near-saturating.

Analysis of fluor-PDK1 population step length distributions in the absence and presence of dark PKCα

Fig. 3 plots step length frequency distributions observed for populations of diffusing fluor-PDK1 populations in the absence of PKC, in the presence of half-saturating PKCα, and in the presence of near-saturating PKCα. For a homogeneous population of diffusing molecules adequately described by a single diffusion constant D, the shape of the step length distribution is characterized by a simple Rayleigh function. If multiple, distinct subpopulations are present with different diffusion constants, then the shape is a sum of Rayleigh functions.

In the absence of PKC, the fluor-PDK1 population exhibits a step length frequency distribution whose shape is well fit by a single Rayleigh function as expected for a homogeneous monomer population (Fig. 3 A). This monomer population exhibits a Rayleigh best-fit diffusion constant (D = 1.22 ± 0.05 μm2 s−1) consistent with the D value obtained by a Rayleigh best fit of previous data for PDK1 monomers diffusing on the same target membrane (3).

In the presence of dark PKCα at an approximately half-saturating concentration (total [PKCα] ∼ 4 nM), both fluor-PDK1 monomers and fluor-PDK1:PKCα heterodimers are present in roughly equal proportions as shown previously (3). Under these conditions, the step length distribution shifts toward shorter step lengths, and can no longer be adequately fit by a single Rayleigh distribution. Instead, the distribution is well fit by the sum of two Rayleigh distributions with similar weights (Fig. 3 B) and distinct diffusivities. The results confirm the existence of two nearly equal subpopulations identifiable by their best-fit Rayleigh D values: 1) a fluor-PDK1 monomer subpopulation comprises 46 ± 5% of the total population and exhibits D = 1.13 ± 0.02 μm2 s−1, while 2) a fluor-PDK1:PKCα heterodimer subpopulation comprises 54 ± 5% of the total with D = 0.26 ± 0.05 μm2 s−1.

Addition of sufficient dark PKCα (total [PKCα] ∼ 28 nM) to saturate most of the fluor-PDK1 population with bound PKCα (3) yields a step length distribution well fit by the sum of two Rayleigh distributions, where one is dominant and the other is minor (Fig. 3 C). The two subpopulations are once again identifiable by their best-fit Rayleigh D values: 1) the fluor-PDK1 monomer subpopulation comprises 24 ± 4% of the total population and exhibits D = 1.14 ± 0.07 μm2 s−1, while 2) the fluor-PDK:PKCα heterodimer subpopulation comprises 76 ± 4% of the total with D = 0.27 ± 0.01 μm2 s−1. Thus, most fluor-PDK1 molecules form fluor-PDK1:PKCα heterodimers under these conditions.

Analysis of single fluor-PDK1 diffusion tracks reveals transitions between a high diffusivity monomer state and a low diffusivity heterodimer state

To determine if PDK1-PKCα association-dissociation events can be detected in the 2D diffusion tracks of individual fluor-PDK molecules, we examined the step length time courses of individual fluor-PDK1 diffusion molecules under the same three conditions as above (no PKCα, half-saturating PKCα, and near-saturating PKCα). Fig. 4 presents raw step length time courses for three representative fluor-PDK molecules under each condition, as well as overlays of the same time courses subjected to a five-step moving (boxcar) average. Additional representative step length time courses are provided in Fig. S1.

In the presence of half-saturating PKCα, the fluor-PDK1 single-molecule trajectories show transitions between distinct high and low diffusivity states corresponding to fluor-PDK1 monomers and fluor-PDK1:PKCα heterodimers, respectively (Fig. 4 B). These transitions are reversible and multiple transitions occur during a single trajectory. The high diffusivity state is similar to that observed in fluor-PDK1 monomer tracks in the absence of PKCα (Fig. 4 A), and the low diffusivity state is similar to that observed in fluor-PDK1:PKCα heterodimer tracks in the presence of near-saturating PKCα (Fig. 4 C). Notably, for the raw step length time courses, the large step length fluctuations produced by random diffusion cause the step length ranges observed for the monomer and heterodimer states to overlap significantly, preventing unambiguous assignment of a given step to a given oligomeric state based on its raw step length. For the overlaid five-step boxcar-averaged time courses, the averaging reduces the step length ranges considerably, thereby facilitating the assignment of a given step to the monomer or heterodimer state based on its average step length. To a first approximation, average step lengths longer or shorter than 0.18 μm are indicative of the monomer or heterodimer state, respectively.

Determining dwell times and rate constants for fluor-PDK1 transitions between the monomer and heterodimer states in the presence of half-saturating PKCα

A set of five-step, boxcar-averaged step length time courses together totaling >5000 steps was determined for a representative group of membrane-bound fluor-PDK1 molecules in the presence of half-saturating PKCα (3). Each boxcar-averaged step length time course was subjected to two-state HMM (see materials and methods) to determine a best-fit, idealized trace depicting the switching between the high diffusivity monomer state and the low diffusivity heterodimer state. Figs. 4 B and S1 display the resulting HMM idealized traces superimposed on their corresponding step length time courses. Subsequently, the full set of HMM traces were analyzed to quantify the dwell times of all monomer and heterodimer events, and the measured dwell times were binned to yield two frequency distributions presenting the fraction of the population remaining in the starting monomer or heterodimer as a function of time, respectively. Fig. 5 displays the resulting, normalized frequency versus time plots for the fluor-PDK1 monomer and heterodimer states. Each plot is well approximated by a single exponential decay yielding the best-fit rate constant for transition to the other state. As expected for the half-saturating regime, where a given fluor-PDK1 molecule spends half its time in each state, the best-fit rate constants were similar for the monomer-to-dimer transition (km–>d = 3.3 ± 0.9 s−1) and the dimer-to-monomer transition (kd–>m = 7 ± 1 s−1).

Figure 5.

Figure 5

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Decay time courses showing the fraction of the population remaining in the fluor-PDK1 monomer state or fluor-PDK1:PKCα heterodimer state as a function of time. Single-molecule fluor-PDK1 step length time courses were obtained in the presence of half-saturating PKCα and subjected to five-step moving (boxcar) averaging and hidden Markov modeling (Figs. 4 and S1). The best-fit, idealized trace of the hidden Markov model was employed to define the monomer and heterodimer events and their dwell times (materials and methods). The resulting dwell times were binned in 100 ms intervals, then best fit with a single exponential decay and normalized to 1.0 at t = 0. Shown are the decay time courses for the monomer state (solid circles, based on 167 dwell times) and the heterodimer state (solid triangles, based on 172 dwell times), with the solid curve illustrating the best-fit single exponential function. The resulting best-fit monomer-to-dimer rate constant was km–>d = 3.3 ± 0.9 s−1. The best-fit heterodimer-to-monomer transition rate constant was kd–>m = 7 ± 1 s−1. The indicated error ranges are 95% confidence intervals of the best-fit analysis. The R2 values for the nonlinear least-squares best fits were 0.939 for the monomer and 0.977 for the heterodimer.

Discussion

To our knowledge, this study describes the first use of single-molecule diffusivity changes to analyze the kinetics of master kinase association and dissociation events on a target membrane surface. The 2D single-molecule diffusion tracks of membrane-bound fluor-PDK1 molecules in the presence of half-saturating PKCα reveal the existence of two fluor-PDK1 diffusion states: 1) a high diffusivity fluor-PDK1 monomer (DPDK1 = 1.2 ± 0.1 μm2 s−1) and 2) a low diffusivity fluor-PDK1:PKCα heterodimer (DHeterodimer = 0.27 ± 0.01 μm2 s−1). The latter low diffusivity fluor-PDK1 state is observed exclusively in the presence of PKCα, and its diffusion constant is within error of the value predicted for the heterodimer based on the known additivity of multivalent frictional drags on supported lipid bilayers (D = [DPDK1−1 + DPKCα−1]−1 = 0.3 μm2 s−1, where DPKCα = 0.40 ± 0.07 μm2 s−1 (25)) (22,23,26,27,28).

Reversible transitions between the monomer and heterodimer diffusion states can be detected in the step length time courses for single-molecule fluor-PDK1 diffusion tracks in the presence of half-saturating PKCα (Fig. 4 B). These transitions become evident when raw step length time courses are subjected to five-step, moving (boxcar) averaging (Fig. 4 B, overlay) to reduce the contributions of random step length fluctuations in diffusion data. Analysis of each boxcar-averaged step length time course by two-state HMM generates an idealized trace describing the switching of the observed PDK1 molecule between the monomer and heterodimer states as a function of time. The resulting trace defines the dwell time of the molecule in each monomer or heterodimer event. When the monomer and heterodimer dwell times from all time courses are pooled and binned to generate normalized frequency distributions, both the monomer and heterodimer distributions are well approximated by single exponential decays (Fig. 5). The monomer exponential decay yields the best-fit rate constant for the monomer-to-dimer transition under half-saturating PKCα conditions (km–>d = 3.3 ± 0.9 s−1), while the heterodimer exponential decay yields the best-fit rate constant for the heterodimer-to-monomer transition (kd–>m = 7 ± 1 s−1). As expected for the presence of half-saturating PKCα, where a given fluor-PDK1 molecule spends half its time in each state, the rate constants for the opposing reactions are similar. Fig. 6 presents a schematic molecular model for the monomer and heterodimer states, including the estimated apparent transition rate constants for fluor-PDK1 monomer-to-heterodimer interconversion in the presence of half-saturating PKCα.

Figure 6.

Figure 6

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Schematic molecular models for the two diffusion states observed in these studies, with the apparent rate constants for transitions between the fluor-PDK1 monomer and fluor-PDK1:PKCα heterodimer states. (Upper) Fluor-PDK1 monomer and a dark PKCα monomer, the latter possessing a tethered PIF motif. (Lower) Fluor-PDK1:PKCα heterodimer stabilized by the binding of the PKCα PIF motif to the PDK1 PIF pocket. The indicated apparent rate constants (from Fig. 5) describe the kinetics of transitions between the monomer and heterodimer states, as determined in the presence of half-saturating PKCα. To see this figure in color, go online.

The observed rate constant for heterodimer-to-monomer conversion (kd–>m) provides the apparent koff for PKCα dissociation from membrane-bound fluor-PDK1, since the continued detection of fluor-PDK1 confirms its continuing membrane association after heterodimer dissociation. The membrane-bound PKCα molecule, although not directly visualized here, has been shown to exhibit an even longer membrane-bound dwell time in previous single-molecule diffusion studies (25), thus it will also typically remain membrane bound upon heterodimer dissociation. The apparent koff for PKCα dissociation from membrane-bound fluor-PDK1 may represent a lower limit for the true koff for dissociation of the heterodimer-stabilizing PIF interaction, since the decreased time resolution of the present boxcar averaging analysis may hide multiple PIF dissociation and rebinding events likely to occur before the adjacent fluor-PDK1 and PKCα molecules become fully independent monomers. In that case, the observed koff is best viewed as the rate constant for the diffusion of previously associated fluor-PDK1 and PKCα molecules away from each other to reach membrane locations outside the range of the long PIF tether.

In principle, the rate constant for monomer to heterodimer conversion (km–>d), together with the half-saturating bulk PKCα concentration, can be converted to an apparent on-rate constant kon for the heterodimer association reaction. However, use of the bulk PKCα concentration in the calculation fails to capture the true 2D collision and association kinetics of fluor-PDK1 and PKCα molecules diffusing on the membrane surface. Further studies measuring the apparent kon as a function of the membrane-bound densities of fluor-PDK1 and PKCα molecules are needed to define these 2D association kinetics, but the present approach using bulk protein concentrations is more easily extended to calculations relevant to cellular conditions, where only bulk concentrations are typically known.

The protein concentrations, lipid densities, and ionic conditions employed in these experiments are within their physiological ranges (3,25), thus the findings provide a window into the biophysical parameters of PDK1:PKCα interactions in crucial intracellular signaling pathways. Among its many functions, PKCα is proposed to act as a tumor suppressor by forming the PDK1:PKCα heterodimer, thereby competitively inhibiting the formation of PDK1:AKT1 heterodimers and concomitantly blocking PDK1 phosphoactivation of AKT1 (3,38,39,40,41). The measured biophysical parameters of the PDK1:PKCα interaction are well suited for this proposed regulation in three ways. First, the nanomolar affinity of the PDK1:PKCα association reaction measured in a previous single-molecule study indicates that intracellular levels of PKCα during a Ca2+/DAG signaling event are sufficient to trap a large fraction of the PDK1 population in PDK1:PKCα heterodimers and inhibit AKT1 phosphoactivation (3). Second, the present findings indicate that fluor-PDK1:PKCα heterodimer association-dissociation reactions occur on a timescale of ∼200 ms under physiological conditions, ensuring that these transitions will be rapid on the timescales of signaling reactions in chemotaxis, cell growth, and oncogenesis as required for effective regulation. Third, the observed heterodimer dissociation kinetics are within the range expected for the known affinity of the PIF interaction that stabilizes the heterodimer (3,15,17,18,19,20,42).

Overall, the findings show that single-molecule diffusion tracks in the fluor-PDK1/PKCα system contain key information about distinct oligomeric states and the transitions between them that can be extracted by careful analysis. The success of the present approach opens the door to single-molecule kinetic studies of other time-dependent protein-protein and protein-lipid interactions that occur on membrane surfaces, with implications for a deeper mechanistic understanding of membrane-based signaling reactions central to biology and medicine. An advantage of the approach is that only one component of the complex is labeled with fluor, minimizing perturbations and eliminating complications arising from incomplete labeling of the binding partner in dual fluor studies. Several modifications of the initial analysis methods presented here may yield further enhancements. To optimize the boxcar averaging length for different systems, and to ascertain the relationship between boxcar length and the extracted kinetic parameters, the effects of shorter and longer boxcar lengths can be tested. To determine whether HMM can extract state transitions from raw diffusion data without boxcar averaging, a more advanced HMM algorithm can be developed employing Rayleigh functions to describe the step length distributions of the pure monomer and oligomer states used to train the starting algorithm. (The QUB package uses Gaussian rather than Rayleigh functions, and is thus not fully optimized for diffusional analysis.) The time resolution of the single-molecule diffusion tracks may be increased by high-speed tracking methods that monitor the surface diffusion of proteins labeled with gold nanoparticles (43). Finally, label-free tracking may be possible using mass photometry to track protein diffusion on supported bilayers; for example, the PDK1:PKCα heterodimer likely possesses sufficient mass for detection by mass photometry (141 kDa), although it is unclear whether the masses of PDK1 and PKCα monomers (64 and 77 kDa, respectively) are large enough to detect (44). For all of these approaches, some combination of boxcar averaging and HMM may well be useful when extracting kinetic information.

Author contributions

Conception, J.J.F., M.T.G., and B.P.Z.; experimental design, M.T.G. and J.J.F.; data collection, M.T.G. and B.P.Z.; data analysis, M.T.G.; data interpretation, M.T.G. and J.J.F.; writing of manuscript, M.T.G. and J.J.F.

Acknowledgments

The authors gratefully acknowledge funding by NIH grants R01 GM063235 and R35 GM144346 (to J.J.F.) and NIH Molecular Biophysics Traineeship T32 GM065103 (to M.T.G.).

Declaration of interests

The authors declare no competing interests.

Editor: Ilya Levental.

Footnotes

Supporting material can be found online at https://doi.org/10.1016/j.bpj.2023.01.041.

Supporting material

Document S1. Figure S1
mmc1.pdf (987.4KB, pdf)
Document S2. Article plus supporting material
mmc2.pdf (2.2MB, pdf)

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Associated Data

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Supplementary Materials

Document S1. Figure S1
mmc1.pdf (987.4KB, pdf)
Document S2. Article plus supporting material
mmc2.pdf (2.2MB, pdf)

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