Supporting Information for Sensing Cooperativity in …...1 Supporting Information for Sensing...

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1 Supporting Information for Sensing Cooperativity in ATP Hydrolysis for Single Multi-Subunit Enzymes in Solution Yan Jiang 1,3 , Nicholai R. Douglas 2 , Nicholas R. Conley 1 , Erik J. Miller 2 , Judith Frydman 2 , and W. E. Moerner 1* 1 Department of Chemistry, 2 Department of Biology and 3 Department of Applied Physics, Stanford University, Stanford, California 94305 Table of Contents I. Methods a. Experimental/Optical Configuration of the ABEL Trap b. Labeling, Biochemical Protocols, and Controls c. Data Analysis II. Discussion: Binding and Hydrolysis Models for Cooperativity I. Methods a. Experimental/Optical Configuration of the ABEL Trap The basic configuration of the hardware-based rotating-beam ABEL trap is shown in Figure S1; for full details, see 1, 2 . A focused CW 532 nm laser beam (CL532-025-L; CrystaLaser, Reno, NV) is diffracted by a pair of acousto-optic deflectors (AOD, AOBD 45100-5-6.5DEG-.51; NEOS Technologies, Melbourne, FL) which are controlled by a function-generating data acquisition board (PCIe-6259, National Instruments, Austin, TX) to scan around a small cone angle at 40 kHz. The beam is then collimated and coupled into the 100x oil-immersion objective (NA 1.0, S Fluor; Nikon, Japan) of an inverted microscope (TE300; Nikon, Japan) so that in the sample plane the scanning laser beam is focused to a revolving spot. The collection path is similar to a typical confocal setup but with a slightly larger spot size and a larger pinhole – 200m in aperture diameter – to collect all the fluorescent light emitted from molecules in the uniform central disk of the scanning pattern. The arrivals of the individual photons emitted by the fluorescent object are recorded by a Si avalanche photodiode detector (SPCM-CD2801; PerkinElmer, Waltham, MA). When the fluorescent object is in the center of the rotation its emission is not modulated, but when the object moves off-center, the emission becomes modulated at 40 kHz. In this way, the arrival times of the fluorescent photons relative to the

Transcript of Supporting Information for Sensing Cooperativity in …...1 Supporting Information for Sensing...

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Supporting Information for

Sensing Cooperativity in ATP Hydrolysis for Single Multi-Subunit Enzymes in Solution

Yan Jiang1,3, Nicholai R. Douglas2, Nicholas R. Conley1, Erik J. Miller2, Judith Frydman2, and W. E. Moerner1*

1Department of Chemistry, 2Department of Biology and 3Department of Applied Physics, Stanford University, Stanford, California 94305

Table of Contents

I. Methods

a. Experimental/Optical Configuration of the ABEL Trap

b. Labeling, Biochemical Protocols, and Controls

c. Data Analysis

II. Discussion: Binding and Hydrolysis Models for Cooperativity

I. Methods

a. Experimental/Optical Configuration of the ABEL Trap

The basic configuration of the hardware-based rotating-beam ABEL trap is shown in Figure S1; for full details, see 1, 2. A focused CW 532 nm laser beam (CL532-025-L; CrystaLaser, Reno, NV) is diffracted by a pair of acousto-optic deflectors (AOD, AOBD 45100-5-6.5DEG-.51; NEOS Technologies, Melbourne, FL) which are controlled by a function-generating data acquisition board (PCIe-6259, National Instruments, Austin, TX) to scan around a small cone angle at 40 kHz. The beam is then collimated and coupled into the 100x oil-immersion objective (NA 1.0, S Fluor; Nikon, Japan) of an inverted microscope (TE300; Nikon, Japan) so that in the sample plane the scanning laser beam is focused to a revolving spot. The collection path is similar to a typical confocal setup but with a slightly larger spot size and a larger pinhole – 200m in aperture diameter – to collect all the fluorescent light emitted from molecules in the uniform central disk of the scanning pattern. The arrivals of the individual photons emitted by the fluorescent object are recorded by a Si avalanche photodiode detector (SPCM-CD2801; PerkinElmer, Waltham, MA). When the fluorescent object is in the center of the rotation its emission is not modulated, but when the object moves off-center, the emission becomes modulated at 40 kHz. In this way, the arrival times of the fluorescent photons relative to the

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instantaneous laser spot location contain information about the X and Y direction of the displacement. The signal from the APD and the reference signal, which is a copy of the AOD control signal, are analyzed by a home-made lock-in circuit to determine the direction of the displacement of the fluorescent object. The correct feedback control voltages are then generated by the circuit and are amplified by a four high-voltage amplifiers (PA83; Apex Microtechnology, Tucson, AZ) and applied to the two pairs of electrodes positioned at the ends of the four microfluidic channels. The corresponding electrokinetic forces are then applied to the target object in the microfluidic cell in order to cancel the molecule’s displacement relative to the center of the revolving beam. This feedback loop cycles every 25s so that the fluorescent object is always kept within the excitation volume until it becomes nonfluorescent.

In the chaperonin measurements, the radius of the circle through which the laser focal spot revolves is further modulated by a square wave which takes on one of two values alternately to be able to capture molecules that attempt to escape from the trap as a result of a rare but large Brownian displacement. Taken together, the beam motion produces a uniformly illuminated 1m-radius disk if averaged at a rate slower than 20 kHz, radically different from the nonuniform illumination in FCS measurements, for example. With this uniform illumination, the emission signal from the trapped object can be directly measured to obtain a fluorescent intensity trace at constant excitation. To realize this measurement, one copy of the signal from the APD is sent to a pulse counting data acquisition board (the same one that generates the functions for modulating the AODs) and binned on 1 ms scale.

To calibrate the probability distributions, it is necessary to count all TRiC, whether Cy3-ADP·AlFx is present or not, and for this reason, TRiC is covalently labeled with the red dye Atto647 as described below. To perform the calibration, the 532nm laser beam or the 638nm laser beam (FTEC2 635-20; Blue Sky Research, Milpitas, CA) is focused at the sample plane without any modulation (trap off). The intensity trace in each case shows spikes corresponding to the individual TRiC molecules with Cy3-ADP·AlFx or Atto647 freely diffusing through the 532nm/638nm laser focus. By counting the number of spikes in the Cy3 channel divided by the number in the Atto647 channel for equal counting times, the percentage of all TRiC with at least one ADP·AlFx is determined, a measurement which allows the proper calibration of the “0 ADP·AlFx” bin in Figure 3.

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Figure S1. Schematic of the ABEL trap. The optical system for trapping (the path along the green 532nm excitation beam and the orange fluorescence beam) is very similar to a typical confocal fluorescence microscopy setup. The modulated fluorescent signals are collected by an avalanche photodiode detector (APD) and analyzed by a home-built analog circuit to generate feedback voltages. Then the required electrokinetic restoring forces are applied by four electrodes via a microfluidic geometry (the channels sketched on the blue transparent slide) to drift the object back to the center. In addition to the 532nm beam used for trapping and counting the number of Cy3 on each chaperonin, a confocal 638nm beam (red) is used separately for counting the total number of chaperonins in a fixed time interval. The long pass filter below the objective is switched between 550nm long pass for 532nm excitation and 655nm long pass for 638nm excitation.

b. Labeling, Biochemical Protocols, and Controls

TRiC labeled by Atto647 on surface-exposed lysines Atto647-TRiC was prepared by coupling 11M Atto647-NHS (ATTO-TEC GmbH) with

1.7M TRiC (purified from bovine testes as described3) and 2 mM ATP in HKM buffer (25 mM HEPES (pH 7.4), 100 mM KCl, 5 mM MgCl2) at room temperature for 2 hours and purified with P30 size-exclusion columns (Bio-Rad). The high concentration of ATP present serves to ensure closed TRiC complexes during the labeling. The average number of Atto647 per TRiC was 0.59.

Cy3 labeled ATP Cy3-ATP (Figure S2) was prepared by coupling 1.6 mM Cy3-NHS (GE BioSciences)

with 7 mM N6-([6-Aminohexyl]carbamoylmethyl) adenosine 5’-triphosphate lithium salt (Sigma-Aldrich) in 20 mM sodium bicarbonate (pH 8.5) at room temperature for one hour (4) and purified by reverse phase HPLC (Shimadzu) using the Prosphere 300Å C18 column (Grace). The pooled factions were dried, resuspended in MQ-A buffer (20 mM HEPES-KOH (pH 7.4), 50 mM KCl, 5 mM MgCl2, 0.1 mM EDTA, 10% (v/v) glycerol, 1 mM DTT, 0.1 mM PMSF) and stored at -80C until use.

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Figure S2. Structure of Cy3-ATP used in this work.

Actin folding assay to test activity of Cy3-ATP A standard actin-folding assay to test for TRiC activity was carried out as described5 to

validate the Cy3-ATP construct used. Briefly, 0.25 M TRiC was incubated in trapping buffer (20 mM Hepes-KOH (pH 7.4), 50 mM sodium chloride, 5 mM MgCl2, 1 mM DTT, and 5 % (v:v) glycerol). The chaperonin was rapidly added to [35S]-actin, previously denatured in 6 M guanidine/HCl, diluted 1:100 to a final concentration of ~0.1 M in the reaction mix. The chaperonin was incubated with [35S]-actin for 30 minutes at 30ºC, then added to 1mM Cy3-ATP or 1mM ATP and incubated 90 additional minutes at 30ºC. After incubation, the reaction was incubated with 1mg/ml DNase I to bind native actin, then centrifuged at 19,000 x g for 10 minutes at 4ºC and loaded on a 4% non-denaturing poly-acrylamide gel. The gel was exposed on a phosphor storage screen (Kodak, USA), and then scanned in a Typhoon 9410 fluorescence imager (GE Healthcare, USA). The radioactive signal was quantified using Image Quant 5.2 (Molecular Dynamics). The percent actin reported is normalized to the native actin produced with ATP (Figure S3). The assay proved that the Cy3 labeled ATP retains 75% of the activity of normal ATP.

Figure S3. Cy3-ATP retains 75% of normal ATP activity in an actin folding assay.

TRiC/ATP complexes For the first type of sample, TRiC (0.17 M), MgCl2 (10 mM) and Cy3-ATP (200M)

are rapidly mixed together in trapping buffer (20 mM HEPES (pH 7.5), 50 mM NaCl, 5 mM

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MgCl2, 5% (v/v) glycerol) and incubated at 25°C for 45 minutes to form TRiC/Cy3-ADP complexes that will dissociate on a 10-30 minute timescale. For the second type of sample with hydrolyzed ATP locked onto TRiC, Atto647-TRiC (0.17 M), MgCl2 (10 mM), Cy3-ATP ( 5M to 1.5 mM), Al(NO3)3 (1 mM) and NaF (6 mM) are rapidly mixed together in TRiC trapping buffer (20 mM HEPES (pH 7.5), 50 mM NaCl, 5 mM MgCl2, 5% (v/v) glycerol) and incubated at room temperature for 45 minutes to form stable Atto647-TRiC/Cy3-ADP·AlFx complexes (Figure 3 in the paper). For both cases, the 30L reaction mixture is then filtered with P30 columns (Bio-Rad, exchanged into TRiC buffer) twice to remove the free Cy3-ATP. The final sample is further diluted with trapping buffer (20 mM HEPES (pH 7.5), 50 mM NaCl, 5 mM MgCl2, 10% (v/v) glycerol) to a concentration near 1 nM as needed right before loading into the microfluidic cell.

Proteinase K digestion assay Purified TRiC (0.25 M) was preincubated in TRiC ATPase buffer (50 mM Tris-HCl

(pH 7.4), 50 mM KCl, 5 mM MgCl2, 1 mM EGTA), which was supplemented with ATP (0 to 1.5 mM) and AlFx (Al(NO3)3 (1 mM) and NaF (6 mM)). The reactions were incubated for 45 min at 25°C. After addition of 20 mg/ml proteinase K and further incubation for 5 min at 25°C, PMSF was added to a final concentration of 5 mM to inhibit protease activity. The reaction was then analyzed by SDS-PAGE. As shown in Figure S4, as the ATP concentration increases, more and more TRiC are protected from the proteinase K digestion (lanes 2-11,with lane 1 lacking proteinase K, and boxes 12-22 used as background). For ATP concentration higher than 1mM, almost all the TRiC (>85%) are protected, which means both cavities are fully closed. Meanwhile, the single-molecule measurements indicate for the same ATP concentrations, every TRiC has ~eight ADP·AlFx locked on it. The symmetry of the TRiC conformation with both cavities closed therefore implies symmetry in the distribution of the eight ADP·AlFx, i.e. there are four nucleotides on each of the two rings.

Figure S4. Protection level of TRiC in a proteinase K digestion assay vs. ATP concentration. The error bars indicate 95% confidence intervals.

TRiC ATPase assay The ATP hydrolysis rate by native TRiC enzymes was measured at 25 ºC at 200M ATP.

After 5 minutes of pre-incubation at 25 ºC, the reaction was started by mixing 2l of -[32P]-ATP (0.01 Ci/l) solution with 18 l of 1.1-fold concentrated reaction mix to achieve a final

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concentration of 0.25 M TRiC, 200 M ATP and 1x trapping buffer. At the indicated time points (Figure S5), 2 l samples were taken and transferred onto PEI-cellulose TLC plastic sheets (Macherey-Nagel Inc.). The plates were developed in a solvent system containing 1 M LiCl and 0.5 M formic acid in H2O, air-dried, and exposed to a phosphor screen (Kodak). After scanning the screen in a Typhoon 9410 imager, the amount of -[32P]-ADP was quantified using Image Quant 5.2. The linear increase of ADP concentration over time (Figure S5) yields the ATP hydrolysis rate of TRiC to be 0.75±0.07 M ATP/M TRiC/min, which is consistent with the ADP release rate measured in the ABEL trap.

Figure S5. ADP concentration vs. time in the TRiC ATPase measurement. The slope of the linear fit is 0.19 M ADP/min.

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c. Data Analysis

Data analysis to extract ADP or ADP·AlFx number distributions Since from the point of view of the analysis of the fluorescence time traces, the same

approach was used for counting ADP (as in Fig. 2 of the paper) as for counting ADP·AlFx (Fig. 3 of the paper), therefore in the first part of this section we will refer to the fluorescent molecule involved as “Cy3-ADP”. Fluorescent intensity traces binned to 1 ms were recorded from the trapped TRiC/Cy3-ADP complexes taking advantage of the uniformity of the pumping intensity in the central trap region. First of all, the traces were manually divided into individual events. The events were identified manually because occasional blinking and the temporary loss of trapping made it difficult to automatically separate individual events. The maximum likelihood estimation method was then used to find the intensity change points in each event as described in6, 7. Because the data was noisy, many steps in brightness could not be clearly resolved and became a source of error in counting the intensity change steps. In addition, sometimes two or more dyes photobleached within 1ms and sometimes the complexes left the trap before complete photobleaching, which also made the detected number of steps deviates from the actual number of Cy3 dyes present. On the other hand, the sizes of the steps in the clearly resolved traces were conserved well between molecules with variation similar to Poisson noise (Figure S6a).

Figure S6. Intermediate results in data analysis. a) Distribution histogram of the photobleaching step sizes, which measure the intensities of individual Cy3 fluorophores, fitted by a Poisson distribution ( = 12.74 ± 0.6, red curve). b) Distribution histogram of the initial intensities of individual chaperonins as they enter the trap at a specific

a) b)

c) d)

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incubation [ATP]. c) ADP number distribution histogram, obtained by dividing the initial intensities by the average intensity of a single dye and binning to the nearest rounded integer number. d) The colored areas are the probability distributions of the actual ADP numbers for the chaperonins grouped in each grey bar, considering the measurement uncertainty. The red curve is the sum of all the colored areas and is therefore the probability distribution of the actual ADP numbers in all the TRiCs. The error bar is the uncertainty of the measured probability of TRiC with no ADP.

After examining various methods on simulated data, we developed a method better than

the direct step counting method: instead of counting the apparent number of steps from each trace, the initial intensity of each event, calculated by averaging the intensity trace before the first photobleach happens, was divided by the average intensity of one Cy3 dye to estimate the total number of dyes in that trapped molecule (Figure S6bc). The average intensity of one dye is calculated from a collection of about 20 events with well-resolved photobleaching steps (Figure S6a). The total dye numbers (not necessarily integers) from 100 detected events were binned in integral bins to build a histogram of ADP number distribution (Figure S6c), with the binning criterion that dye numbers in the range k ±0.5 were binned with integer k (i.e., round to nearest integer). This method of estimating the number of dyes introduces uncertainties from two major sources: first, the error of determining the initial intensity, which can be estimated as the error of finding the true intensity level of the initial intensity traces by fitting the measured signal to normal distributions; second, the error of determining the average intensity of a single dye, which can be estimated as the error of finding the center value of the single dye intensity distribution. Thus for each event, the probability distribution for the actual Cy3-ADP number can be represented by a normal distribution centered at the initial intensity divided by the single dye intensity, with a width determined from the above error estimation.

To generate the final ADP number distributions (as in Figure S6d), several quantities are plotted. First, the initial intensity divided by the single dye intensity, rounded to the nearest integer, is presented in the gray histogram in the background. Then for each event placed into the integral bins, all the normal distributions for individual events are summed and plotted as a new type of histogram intended to represent the uncertainty inherent in the determination of integral number (the colored areas in the distribution figures). The red curve is the sum of all the distributions and is therefore the probability distribution of the actual hydrolyzed ATP (ADP or ADP·AlFx) number for all the events we detected.

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Figure S7. Without AlFx locking the Cy3-ADP on TRiC, the ADP number distribution varies with time after the removal of free Cy3-ATP. These are the original distributions before the spurious events are removed, and these distributions provide the data in Figure 2 of the paper.

Figure S8. ADP·AlFx number distributions in Figure 3 of the paper before removing spurious events.

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Figure S9. ADP·AlFx number distribution for incubation [ATP] = 1.5 mM.

Spurious events from trapped impurities The small fraction of TRiC with one, two and three Cy3-ADPs shown in the ADP or

ADP·AlFx number distributions (Figure S7, Figure S8, Figure S9) most likely arose from impurities rather than real TRiC. To verify this idea, the TRiC buffer alone, in which all the counting experiments are conducted, was loaded into the microfluidic cell and trapped with the same feedback gain settings as for the TRiC/Cy3-ADP or TRiC/Cy3-ADP·AlFx samples. Although there were no expected fluorescent objects in the buffer, some impurities appeared to be fluorescent and were localized by the trap for duration comparable to trapped TRiC molecules. These events were counted and analyzed using the single Cy3 dye intensity measured with the TRiC/Cy3-ADP samples to build an apparent Cy3-ADP number distribution (Figure S10). In Figure S10 the total population of the impurities is assumed to be 10% of an imaginary sample, in order to provide an easy comparison with the real ADP number distributions. To quantify this, the numbers, fractions, and densities of the events with 1, 2 and 3 Cy3-ADP·AlFx are listed in Table 1 for various ATP loading concentrations. It is observed that the frequency of detecting these low intensity events is within the range of 1±0.6 /minute for both the pure buffer and the TRiC/Cy3-ADP·AlFx samples, essentially independent of ATP concentration. Therefore we believe a major source of the events with 1, 2 or 3 ADP detected in the TRiC/Cy3-ADP samples are trapped impurities. In addition, these events count for less than 15% of the total detected events. Thus we delete these low intensity events in Figures 2, 3, 5 and 6 in the paper for simplicity. The full distributions are shown in Figure S7 and S8.

Figure S10. Apparent ADP number distribution for pure buffer, showing transiently trapped impurities as a possible source for the spikes near zero in the ADP number distributions of Figure S7, Figure S8 and Figure S9. For ease of comparison with Figure S7, Figure S8 and Figure S9, the percentage of the total detected events is set to 10%.

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Table 1. Statistics of the detected events with 1, 2, and 3 ADP·AlFx.

Incubation ATP Concentration (M) 10 25 50 200 1000 Number of events with 0 < ADP·AlFx number ≤ 3

12 11 6 13 7

Percentage of the above events in the total detected events

12% 11% 6% 13% 7%

Total detection time for 100 events (min) 12.77 8.53 11.89 10.65 5.62 Density of the above events (/min) 0.94 1.29 0.50 1.22 1.24

Average number of hydrolyzed ATP per TRiC vs. incubation ATP concentration

For each ATP incubation concentration, the average number of hydrolyzed ATP (present specifically as ADP·AlFx as described in the main text) on each TRiC can be calculated from the distribution by direct ensemble averaging of the distribution to yield the points shown in Figure S11. We fit the transition part of the curve (1% to 99% saturation) with the Hill equation

log1

log log (1)

where Y is the average number of hydrolyzed ATP, K is a constant parameter and the incubation [ATP] has the unit of micromolar. The Hill coefficient h is calculated to be 1.67±0.36, which reveals positive cooperativity; log 7.2 1.49.

Figure S11. The average number of hydrolyzed ATP per TRiC versus incubation ATP concentration, calculated by ensemble averaging the single-molecule measurements. The blue, green, red and magenta circles indicate data taken with different batches of Cy3-ATP. The error bars indicate 95% confidence intervals. The data was fit to the Hill equation as shown by the brown curve. Inset: expansion of the plot.

II. Discussion: Binding and Hydrolysis Models for Cooperativity

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Cooperative ATP Binding Trial Model I

For trial model I, positive cooperativity is assumed between the eight subunits within one ring of TRiC, simulated by MWC, and negative cooperativity is assumed between the two rings, simulated by KNF; while only four of the eight dissociation constants KR for the relaxed state subunits are lower than the saturating ATP concentration (Fig. 5). Compared to the convention MWC/KNF model described in the main text, the only difference is that instead of all subunits binding ATP with equal probability, only four of the eight in each ring can bind ATP. We further assume that all complexes with a specific number of ATP bound proceed to the hydrolyzed state with equal probability. Based on these assumptions, after hydrolysis and loading into the trap, each TRiC would have only four ADPs occupying one of the two rings at intermediate ATP loading concentration; ultimately when the ATP loading concentration is high enough to overcome the negative cooperativity, each TRiC in the trap has in total eight ADPs – four in each ring – bound.

As illustrated in Fig. 5a, trial model I assumes the subunits in the same ring change their conformations in a synchronized fashion (MWC model) while the two rings change conformation sequentially (KNF model); in addition, four of the subunits (white) have higher affinity to ATP than the other four (gray); meanwhile the hydrolysis rate is the same for TRiC with any number of ATP bound. There are two equilibrium constants between the three unligated states of the complexes called allosteric constants, / and / , where TT, TR and RR are the unligated both-ring-tense, one-ring-tense-and-one-ring-relaxed and both-ring-relaxed state of TRiC. This gives : : : : 1. The dissociation constants of ATP to the 8 subunits are , 1,2, ,8 in relaxed states and are

,⁄ 1 in tense states. The concentration of the TT state chaperonin with ATP bound in specific subunits indicated by , can be calculated by

,

0 , 0 (2)

where each , is a configuration of ATP occupancy in TRiC’s 16 subunits, and 1,2, … ,8 are 16 Boolean logic numbers that indicate whether each subunit has ATP

bound (1 for true and 0 for false), 0 , 0 is the TT state chaperonin with no ATP bound, and is the concentration of ATP. Similarly, the concentration of the TR state chaperonin with ATP bound in subunits indicated by , can be calculated by

,

0 , 0 (3)

Finally, the concentration of the RR state chaperonin with ATP bound in subunits indicated by , can be calculated by

,

0 , 0 (4)

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After normalizing to the total concentration of chaperonin ∑ ,,

, , , the fraction of chaperonin with each configuration of ATP binding is obtained:

,

∏ ∏ ∏ ∏

∏ 1 ∏ 1 ∏ 1 ∏ 1 (5)

From the percentages of the 216 configurations, the fractions of TRiC with certain numbers n of ATP bound can be calculated as

,∑

(6)

Again, with the final assumptions that (a) any complex with a specific number of ATP proceeds to the hydrolyzed state, and that (b) the distribution of nucleotides that reach hydrolysis is the same as the ADP·AlFx form we measure, the expected ADP·AlFx number distribution is obtained in Fig. 5c in the orange shading as follows. In order to provide a fair comparison of the theoretical calculation and the experimental data, measurement uncertainty is artificially added to the theoretical calculation. Specifically, for each ATP binding configuration calculated, the relative uncertainty in the ADP·AlFx number counting is calculated by combining the following two sources: first, the ratio of the shot noise to the corresponding intensity level (assuming the same brightness per dye as in the experiment); second, the relative uncertainty of determining the average intensity per dye from the analysis of the experimental data. Then a Gaussian distribution with the amplitude calculated from equation (6) and the width corresponding to the relative uncertainty in counting the number of ADP·AlFx is created for each ATP binding configuration. Finally all the Gaussian distributions are summed and shown as orange areas in Fig. 5c. The parameters used to generate the result shown are:

50, 2000, 0.01

10, 10, 20, 50, 10 , 10 , 2 10 , 2 10 , 1,2, ,8

where the dissociation constants are chosen to mimic the behavior observed by Stefanie Reissmann (http://edoc.ub.uni-muenchen.de/7319/).

Compared to the observed distributions in Figs. 2 and 3, we must conclude that 200M ATP is already in the high concentration regime where each TRiC has both rings closed and occupied by four ATPs each. No matter how the 11 parameters are varied, the negative inter-ring cooperativity ensures a finite fraction of TRiC with only one ring occupied by four ATP at intermediate [ATP], shown as a peak at four in the calculated ADP·AlFx number distributions (Fig. 5c). However in the experimental data (Fig. 3 and red in Fig. 5c), the peak at zero directly converts to the peak at eight hydrolyzed ATP as [ATP] increases. In fact, the probability of 4 ADP·AlFx is never dominant in the experimentally measured distributions. In short, trial model I does not match our data.

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On the other hand, the parameters can be adjusted, such as those listed above, to easily match the model-predicted average number of ADP·AlFx per TRiC with that calculated from experimental data (Fig. 5b). Thus the ensemble average result is clearly limited in its ability to constrain models for this system.

Cooperative ATP Binding Trial Model II

For trial model II (Figure S12), positive cooperativity is assumed between four of the subunits in each ring, simulated by MWC, and negative cooperativity is assumed between these four subunits and the other four in the same ring. Further, the two rings behave independently, but have the same parameters since the same 8 subunits are present in both. According to the data, even at the highest ATP concentration in our experiments, the negative cooperativity has not been overcome because only four subunits are observed to be occupied in each ring even at the highest ATP concentration. Thus compared to the trial model I, this model avoids the negative cooperativity effect in the intermediate ATP concentration regime. However, a calculation of expected ADP·AlFx number distributions based on trial model II still does not mimic the experimental data, as will now be described. As shown in Figure S12a, trial model II assumes in both of the rings, four of the eight different subunits change their conformations in a synchronized fashion (MWC model) while all the other four change conformation in a separate step (KNF model); meanwhile the hydrolysis rate is the same for TRiC with any number of ATP bound. Again there are two equilibrium constants between the three unliganded states called allosteric constants, / and / , where TT, TR and RR are the unligated all-subunit-tense, half-ring-tense-and-half-ring-relaxed and all-subunit-relaxed state of TRiC. This gives : : : : 1 . The dissociation constants of ATP to the subunits in relaxed states are , 1,2, ,8 and are ,⁄ 1 in tense states. The fraction of each configuration of ATP binding is calculated by

,

∏ ∏ ∏ ∏

∏ 1 ∏ 1 ∏ 1 ∏ 1

(7)

where subunits 1-4 in each ring are the four subunits that change to relaxed state first. After a similar calculation as for the first trial model, the broadened theoretical distributions are shown as the orange areas in Figure S12c. The parameters used to generate the result shown are:

100, 1 10 , 0.001

20, 50, 60, 60, 1 10 , 1 10 , 1 10 , 1 10 , 1,2, ,8

According to the calculation, the ADP·AlFx distribution peak moves from 0 to 8 gradually while the height of the peak increases. In contrast, in the experiment, the peak of the ADP·AlFx number distribution starts at ~5 containing only 1.5% of the total population and quickly moves to 8 as the ATP concentration increases above 5M. Therefore the trial model II does not fully explain the single-molecule distributions either. (Parenthetically, there is an alternative to this model: instead of assuming any negative cooperativity, we can just make the other four subunits have very low affinity to bind any ATP even at 1.5mM concentration. For the

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ATP concentration range we studied, this new assumption gives the same behavior as trial model II.)

Figure S12. Second trial model and comparison with experimental data. a) Scheme for the second trial model. The squares and circles signify subunits of TRiC in tense/relaxed states, respectively; the L2 transition is not reached. b) Comparison between model and experiment for ensemble data. Circles: experimental data; solid curve: calculated from the model. c) Comparison between model and experiment for single-molecule data. The orange areas show the ADP·AlFx number distributions calculated from the model, which are broadened by an amount effectively equal to 1 nucleotide to approximate the counting uncertainty in experimental measurement. The experimental data of Fig. 3 are shown in the red curves.

On the other hand, as trial model I, the average number of ADP·AlFx per TRiC calculated from the model with the above parameter does match the average number of ADP·AlFx per TRiC calculated from the experimental data (Figure S12b), showing the limited power of ensemble-averaged measurements in distinguishing models.

Failure of Allosteric Binding Models As mentioned in the main text, not only the above two trial models but all allosteric ATP

binding-only models would fail in mimicking the observed hydrolyzed ATP number distributions at low ATP concentrations. More specifically, in ATP binding-only models, the rightward shift and the growth of a peak representing a uniform population are always highly correlated, and the growth scales with powers of [ATP] greater than 1, whereas in our experimental data, the peak amplitude gradually grows larger over a wide range without significant shift of the peak position. For example, we may focus on the 5M case, which contains a single peak centered at 5 ADP·AlFx representing 1.5% of the total population, and the 50M case, which contains a single peak centered at 7 ADP·AlFx representing 42% of the total population. Assume there is an

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allosteric binding model that produces these two distributions at the corresponding [ATP]. The conformation of TRiC that is responsible for the peak is called A, while all the other conformations (present but with no ATP bound) are called B. The population of each conformation can be calculated as in Table 2. Detailed calculation of ATP binding equilibrium”. For any allosteric binding model, the ratios between the unligandeded conformations are constant at equilibrium. Thus we simply write the ratio between all the other conformations (B) and the conformation A with 0 ATP bound to also be a constant L. In the calculation of the populations of conformation A with a certain number of ATP bound (a ’s), K , m 1,2, … ,16 are the ATP binding affinities of the 16 subunits at conformation A and K K K ; n are integers between 1 and 16, and within each equation, n n if i j; S is the [ATP]

concentration. The symbol “b” denotes the population of species B, and “c” denotes the total population.

Table 2. Detailed calculation of ATP binding equilibrium with all possibilities enumerated

Unnormalized populations

Other conformations (B)

b S L b S L

In total,

c S

1S

KL

(Normalization

factor)

Conformation A with 0 ATP bound

a S 1 a S 1

Conformation A with 1 ATP bound a S

SK

Sum of all A conformations with

≥1 ATP,

a S

1S

K1

Conformation A with 2 ATP bound a S

SK

Conformation A with 3 ATP bound a S

SK

Conformation A with 4 ATP bound a S

SK

Conformation A with 5 ATP bound a S

SK

… … Conformation A

with 16 ATP bound a SS

K

Since the peak is centered at 5 when S 5µM, we must have a a for any k 5,

which requires K S 12µM. This can be proved by considering the following scenario: if

K is constrained to be no smaller than a certain value, the best you can do to let more ATP bind to TRiC is to make the other K ’s as small as possible, i.e. K K K K K

K , in which case, knowing that a a yields S /K 5/12 . Meanwhile since

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conformation B and conformation A with no ATP bound represent 98.5% of the population and

conformation A with at least 1 ATP bound represents 1.5% population, we have µM

µM

L

. %

. %.

When S increases by a factor of 10, given K 12 for 1 m 5 , µM

µM

/

/782. Thus

µM

L

. %

. %782 12. Thus the fraction

of TRiC with ATP bound at S 50µM should be µM

µM92%. However the peak

we observed at 50M in experiments only represents 42% of the total population. Therefore our original assumption is false, i.e. this general allosteric ATP binding model alone cannot fully match the single-molecule distributions. Subunit-Occupancy-Dependent Cooperative Hydrolysis Model

As Figure 6a in the paper shows, this model contains cooperativity in two parts, ATP binding and ATP hydrolysis, which will be described in sequence.

The ATP binding process is described with the MWC model. Because we have no direct measurement of the binding distribution, the parameters of the MWC model are chosen so that the Hill coefficient is about 1, which indicates neither positive nor negative cooperativity; if the MWC binding process has a different Hill coefficient, the parameters of the subunit-dependent cooperativity need to be adjusted accordingly. According to the MWC model, the TRiC subunits can be in either tense (low affinity to ATP) or relaxed (high affinity to ATP) state and all sixteen subunits change their conformation simultaneously. The allosteric constant between the all-tense and all-relaxed conformations is set to / 10 . . Meanwhile the ratio of the relaxed state dissociation constant to the tense state dissociation constant is / 0.1. With these parameters, the relaxed state dominates over the ATP concentration range we measured and therefore the system is similar to a one-state system with no cooperativity. Nevertheless, the eight different subunits have eight different binding affinities to ATP to capture the previous experimentally observed behavior. The relative order of the binding affinities is CCT5, 4, 2, 1 > 7, 8 >> 3, 6, following the results of the Reissmann TRiC/ATP crosslinking study (http://edoc.ub.uni-muenchen.de/7319/) described in the main text. Similar to the trial models, the fraction of each ATP binding configuration can be calculated as

,∏ ∏

∏ 1 ∏ 1 (8)

For the hydrolysis process, TRiC molecules with different ATP binding configurations have different hydrolysis probabilities. Given the cavities of TRiC are in the open form before hydrolysis and are in the closed form after hydrolysis, the equation for this process is expressed as

;

;; (9)

where ; is the hydrolysis probability for the corresponding ATP binding configuration,

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indicated by two sets of 8 Boolean logic numbers and ( 1, 2, , 8; 1 means the subunit has ATP bound; 0 means no ATP bound) for the two rings. The hydrolysis probability is

modeled as ; ∑ , , , ∑ , , , , where is the base hydrolysis probability for TRiC with no ATP bound, and are dimensionless parameters ( 1, 1). Based on these assumptions, the hydrolysis probability increases when subunits CCT1 ,2, 4, 5 bind ATP and decreases when subunits CCT3, 6, 7, 8 bind ATP. Since CCT1, 2, 4, 5 have higher affinities to ATP than the other four subunits, they are more likely to bind ATP. Therefore the TRiC with 4 ATP bound in each ring has the highest hydrolysis probability on average than TRiC with other numbers of bound ATP. As a result, our observed distributions of hydrolyzed ATP (sensed as ADP·AlFx) numbers peak around 8 as shown in Fig. 6b.

To fit the data with this model, , the ATP binding affinities of the subunits and the hydrolysis parameters , and , in total eleven parameters, are optimized by nonlinear least square regression using Matlab. At first, the dissociation constants of CCT5, CCT1, CCT2, CCT4, CCT7, CCT8, CCT3, CCT6 are optimized to be 1.09, 13.9, 13.9, 14.0, 3.6210 , 3.70 10 , 1.39 10 , 3.29 10 respectively. However, the confidence intervals of these parameters cannot be satisfactorily estimated because the data is insufficient for extracting so many parameters. Thus in order to reduce the number of parameters, some constraints are set on the dissociation constants based on the above optimization result: the dissociation constants of CCT1, CCT2 and CCT4 are set to be the same, i.e. ; the dissociation constants of the four low-affinity subunits are set to increase each by a factor of 4, i.e. /4 /4

/4 . Finally, since CCT7, 8 , 3 and 6 have much lower affinities to ATP so that they do not bind ATP much for [ATP]≤1.5mM, the exact ratios between their binding/dissociation constants are not critical. Thus we simply set /4 /4 /4 . These constraints are also consistent with the crosslinking study results, where the binding affinities of CCT5, 1, 2, 4 are much larger than CCT7, 8, 3, 6. The nonlinear regression is performed again on the new set of six parameters to yield the optimized parameters and their confidence intervals as 4.950.21 , 116 17 , /10 /100 /1000 1.531.25 10 , 1.15 0.41 10 , 5.14 0.38 and 0.138 0.44.

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