Measurement and Analysis of in vitro Actin Polymerization

Summary

The polymerization of actin underlies force generation in numerous cellular processes. While actin polymerization can occur spontaneously, cells maintain control over this important process by preventing actin filament nucleation and then allowing stimulated polymerization and elongation by several regulated factors. Actin polymerization, regulated nucleation and controlled elongation activities can be reconstituted in vitro, and used to probe the signaling cascades cells use to control when and where actin polymerization occurs. Introducing a pyrene fluorophore allows detection of filament formation by an increase in pyrene fluorescence. This method has been used for many years and continues to be broadly used, owing to its simplicity and flexibility. Here we describe how to perform and analyze these in vitro actin polymerization assays, with an emphasis on extracting useful descriptive parameters from kinetic data.

1. Introduction

Dynamic rearrangements of the actin cytoskeleton underlie key aspects of many cellular functions, including aspects of cell motility, vesicle trafficking, and cytokinesis (1–3). Many of these rearrangements rely on control of when and where actin polymerization occurs. This is regulated at the level of nucleation of new filaments (4–6), elongation of these filaments (5,6), crosslinking of filaments into higher order structures, arrest of filament growth and disassembly of filaments (2). Given the broad cellular importance of these processes, great effort has been put into studying the mechanisms of how these processes are regulated at the biochemical level.

Here we describe a widely used biochemical assay for actin polymerization (7,8) that can be used to answer many important biochemical questions. Although more complex assays are possible (9–12), for questions regarding the activity of actin filament nucleation factors (13–16), often the most direct way to analyze activity is through the use of a bulk kinetic assay. Further, in order to interpret the results from filament mesh reconstitution and bead motility assays, an understanding of the underlying biochemistry is of great utility.

Actin will polymerize into filaments whenever its concentration is greater than its critical concentration. The critical concentration of actin can be modified by type of actin, bound nucleotides (17) and numerous solution conditions (18,19). Thus, purified actin can be maintained as monomers by removing almost all salts present, storing it under mildly alkaline conditions and by including calcium ions rather than magnesium ions (20). This solution can then be induced to form filaments by adding a concentrated buffer mix that alters pH, switches divalent cations, and increases salt concentrations into the physiological range. The polymerization of actin can be tracked in bulk solution by following a variety of observables, including tracking the increase in light scatter or solution viscosity as the polymers grow. Owing to greater flexibility, it is far more common to introduce the environmentally sensitive fluorophore, pyrene, onto an existing cysteine in actin, and follow the increase in fluorescence intensity as the polymers form (8,7).

Part of the great power of the pyrene detected method is that the changes in fluorescence intensity for an actin solution can be measured in real-time with high signal to noise, and thus is well suited to kinetic assays, which are generally of the most interest for this system. We describe this assay in detail, with particular attention paid to constructing quantitative assays.

Analysis of the resulting kinetic profiles is somewhat complicated. The difficulty stems from the fact that polymerization kinetics are a combination of processes: elongation of filaments at both their fast growing ‘barbed’ end and their slow growing ‘pointed’ end, nucleation of new filaments from bulk solution, and nucleation of filaments in a filament dependent manner. These processes all have distinct kinetic effects. There is no general analytic solution for actin polymerization kinetics in the presence of nucleation factors, and thus descriptive metrics for the kinetics are typically used for quantification instead of parameters determined by fitting to the entire dataset (see Note 1). Here we describe the calculation of several simple metrics (see Note 2): the time at which half of the actin has polymerized (t_1/2), the actin polymerization rate at t_1/2, the number of barbed ends present at t_1/2 (see Note 3), and the initial nucleation rate.

2. Materials

All buffer and salt stocks are prepared using ultrapure water (>18 MOhm, using a Millipore brand Milli-Q water purification system). Except where noted, all solutions are filtered through a 0.22 μm cellulose acetate membrane. Working buffers are prepared by dilution of buffer stocks into prechilled ultrapure water. Where specific sources are recommended, the manufacturer and part numbers are indicated.

2.1. Stock Materials and Solutions

1. Rabbit muscle acetone powder (Pel-Freez #41995-2).

2. N-(1-pyrene) iodoacetamide (Invitrogen #P-29): 10 mM stock in anhydrous dimethylformamide (DMF). The solution is stored at −20°C in 1 mL aliquots.

3. Dithiothreitol (DTT): 1 mM stock in ultrapure water, filtered, and stored at − 20°C in 1 mL aliquots. When thawing, place in cool water until solution is liquid, then transfer to ice until needed. Once added to buffers, assume DTT is no longer functional after 48 hours when stored at 4°C.

4. Adenosine 5’ triphosphate disodium salt (ATP; Sigma #A7699): 100 mM stock in 100 mM Tris-HCl pH 8.0, and titrated to pH 7.4 to 7.5 with sodium hydroxide. The solution is filtered and stored at −20°C in 1 mL aliquots.

5. 0.5 M EGTA: Prepared using ethylene glycol tetraacetic acid powder and titrated to pH 8.0 with sodium hydroxide. Initially, EGTA is insoluble, but comes into solution as the pH is adjusted.

6. 1 M Tris-HCl pH 8.0: Prepared using tris base, and titrated to pH 8.0 at room temperature with concentrated hydrochloric acid.

7. 1 M Imidazole pH 7.0: Titrated with hydrochloric acid to pH 7.0 at room temperature.

8. 2 M KCl.

9. 5 M NaCl.

10. 1 M MgCl₂.

11. 1 M CaCl₂.

12. 1 M Sodium Azide.

2.2. Working Buffers

1. KMEI: 50 mM KCl, 10 mM imidazole pH 7.0, 1 mM MgCl₂, 1 mM EGTA.

2. 10x KMEI: 500 mM KCl, 100 mM imidazole pH 7.0, 10 mM MgCl₂, 10 mM EGTA.

3. Buffer G: 2 mM Tris-HCl pH 8, 200 μM ATP, 0.5 mM DTT, 0.1 mM CaCl₂, 1 mM sodium azide.

4. Buffer G-Mg: 2 mM Tris-HCl pH 8, 200 μM ATP, 0.5 mM DTT, 0.1 mM MgCl₂.

5. 10E/1M: 10 mM EGTA, pH 8, 1 mM MgCl_2.

2.3. Chromatography Columns

1. Superdex 200 pg column: This is a prepacked HiLoad 26/600 Superdex 200 pg column, with 320 mL of resin in XK26/600 column hardware (GE# 28-9893-36). The maximum flow rate is 4.25 mL/min with a maximum pressure of 0.5 MPa. We run this column run at 1–2.5 mL/min at less than 0.4 MPa back pressure.

2.4. Hardware and Equipment

1. Two centrifuges are needed: (1) An ultracentrifuge (Beckman Optima or equivalent) equipped with Type 45 Ti, Type 70 Ti and SW 41 Ti or other appropriate rotors (see Note 4). (2) A refrigerated centrifuge (Beckman Coulter Avanti Centrifuge), equipped with JA-25.50 rotors. Any refrigerated centrifuges capable of spinning 50 mL tubes at ~2,000 x g are equivalent for this purpose.

2. A liquid chromatography system capable of delivering linear gradients and operating columns at the described flow rates and pressures.

3. A 40 mL and 15 mL dounce homogenizer.

4. 14 kDa dialysis tubing and clamps.

5. A large stir plate and a magnetic stir bar.

6. Cold room or cold box with space for the stir plate.

7. Fluorometer: We recommend a system with monochrometer based excitation and emission wavelength selection, and some degree of bandpass control. Fluorescence light source must be capable of illuminating at 365 nm.

8. Fluorescence cuvettes: Many styles of cuvette may be used for this assay, but we use a 3 mm × 3 mm microvolume cuvette. This cuvette ends up being a good compromise between sample volume (200 μL), cost and ease of complete cleaning.

9. Micro-volume pipettes: P-200, P-20, P-10 or equivalent.

3. Methods

3.1. Purify and Pyrene Label Actin

1. Ensure that centrifuges and rotors are cold.

2. Weigh out 4 to 5 g rabbit muscle acetone powder.

3. Place 20 mL of cold buffer G per gram of rabbit muscle acetone powder in a beaker, add muscle acetone powder. Stir at 4°C for 30 minutes.

4. Filter solution through four layers of cheese cloth. Recover and resuspend the muscle acetone powder residue in 20 mL of cold buffer G per gram of starting weight (see step 2). Stir at 4°C for 30 minutes.

5. Filter solution through four layers of cheese cloth and combine with the filtrate from step 4.

6. Centrifuge the filtrate for 30 minutes at 16,000 rpm at 4°C in a JA25.50 rotor or equivalent.

7. Carefully decant the supernatant into a graduated cylinder (pellet is soft) and measure the volume.

8. Slowly add 2 M KCl to a final concentration of 50 mM. Slowly add 1 M MgCl₂ to a final concentration of 2 mM. Continue to stir for 2 hours at 4°C.

9. After two hours has passed, slowly add solid KCl to a final concentration of 800 mM (add 5.6 g per 100 mL of solution volume). Stir for 30 minutes at 4°C.

10. Collect actin filaments from step 9 by centrifugation. Centrifuge at > 100,000 x g for 2 hours at 4°C (35,000 rpm in a Type 70 Ti rotor) (see Note 4).

11. Discard supernatant. Rinse pellet (containing filamentous actin) with ~500 μL of buffer G.

12. Transfer the pellet into a dounce homogenizer. Place 8 mL per gram of starting rabbit muscle acetone powder weight into the body of a 40 mL dounce homogenizer. Lightly scrape the pellets from the centrifuge tube using a curved spatula and transfer to the homogenizer. The pellet will stick to the spatula, and can be transferred by scraping it onto the pestle, and then dislodging from the pestle into the buffer in the homogenizer. Gently passage the homogenizer pestle up and down about 50 times to resuspend the pellet, trying not to incorporate air. If the solution remains highly viscous as it is processed, dilute it slightly with buffer G.

13. Rinse 12 to 15 cm lengths of 14 kDa MWCO dialysis tubing in water and equilibrate a few minutes in buffer G.

14. Place resuspended actin from step 12 into 14 kDa MWCO dialysis tubing. Dialyze against 2 L buffer G overnight.

15. Change the buffer on the second and third nights, using buffer G made without DTT.

16. On the morning following the third night of dialysis, collect the solution in the dialysis bags. Retain a small amount of dialysis buffer. Remove actin filaments from the dialyzed solution by centrifugation at > 100,000 x g for 2 hours, at 4°C (using a Type 70 Ti rotor at 35,000 rpm or a SW 41 Ti rotor at 40,000 rpm) (see Note 4).

17. Equilibrate a Superdex 200pg gel filtration column with buffer G.

18. Carefully remove the centrifuge tubes from the rotor, minimizing jostling. Collect the upper 1/2 of the supernatant and inject onto the equilibrated Superdex 200pg gel filtration column, collecting in 5 mL fractions. Decant remove the remaining supernatant solution into a small glass beaker and reserve at 4°C.

19. Choose gel filtration fractions to save (see Fig. 1 and Note 5). Measure the concentration of actin in each fraction by UV absorbance (see Note 6). Transfer fractions into separate small pieces of equilibrated 14 kDa MWCO dialysis tubing (see Note 7), and store in buffer G. Store actin in a large stirred beaker at 4°C, in 2 L of buffer G; change the buffer twice per week. Seal the top of the beaker with plastic wrap and aluminum foil. Stored in this fashion, actin can typically be kept for two months.

20. Add a clean magnetic stir bar to the glass beaker with the actin supernatant in it (see step 18), and begin stirring the solution slowly at 4°C. Note the volume of supernatant. Measure the concentration of actin by UV absorbance (see Note 6), using the dialysis buffer reserved in step 16 as the absorbance blank.

21. Slowly add 2 M KCl to a final concentration of 50 mM. Slowly add 1 M MgCl₂ to a final concentration of 2 mM. Continue to stir for 2 hours.

22. From the concentration and volume measured in step 20, calculate the total actin present. Add a 5- to 10-fold molar excess of N-(1-pyrene) iodoacetamide. Close off the top of the beaker with parafilm or saran wrap. Then wrap the entire beaker with aluminum foil to protect it from light (see Note 8). Stir over night at 4°C.

23. The next morning, centrifuge the labeling reaction at 4°C, at ~2,000 x g (5,000 rpm the Beckman Avanti JA25.5 rotor) for 5 minutes to remove excess dye. Remove the supernatant with a pipet (the pellet is very soft).

24. Collect actin filaments from the supernatant from step 23 by centrifugation. Centrifuge at > 100,000 x g for 2 hours at 4°C (using a Type 70 Ti rotor at 35,000 rpm or a SW 41 Ti rotor at 40,000 rpm) (see Note 4).

25. Collect centrifuge tubes and discard supernatant. Rinse pellets (containing pyrene labeled filamentous actin) with ~500 μL of buffer G.

26. Transfer the pellet into a Dounce homogenizer. To do this, place 8–12 mL of buffer G into the homogenizer body. Lightly scrape the pellets from the centrifuge tube using a 3–7 mm wide, slightly curved spatula. The pellet will stick to the spatula, and can be transferred by scraping it onto the pestle, and then dislodging from the pestle into the buffer in the homogenizer. The pellet will typically be somewhat opaque with residual pyrene iodoacetamide. Gently passage the homogenizer pestle up and down about 50 times to resuspend the pellet, trying not to incorporate air. Once resuspended the solution will appear slightly turbid. If the solution remains highly viscous as it is processed, dilute it slightly with buffer G.

27. Rinse 12 to 15 cm lengths of 14 kDa MWCO dialysis tubing in water and equilibrate a few minutes in buffer G.

28. Place resuspended actin from step 26 into 14 kDa MWCO dialysis tubing. Dialyze against 2 L buffer G for three nights, changing the buffer on the second and third nights.

29. On the morning following the third night of dialysis, collect the solution in the dialysis bags. Remove actin filaments from the dialyzed solution by centrifugation at > 100,000 x g for 2 hours at 4°C (using a Type 70 Ti rotor at 35,000 rpm or a SW 41 Ti rotor at 40,000 rpm) (see Note 4).

30. Equilibrate a Superdex 200pg gel filtration column with buffer G.

31. Carefully remove the centrifuge tubes from the rotor, minimizing jostling. Collect the upper 2/3 of the supernatant. Inject supernatant onto equilibrated Superdex 200pg gel filtration column.

32. Choose gel filtration fractions to save (see Fig. 1 and Note 5). Measure the concentration of actin and degree of pyrene labeling in each fraction (see Note 9). Transfer fractions into separate small pieces of equilibrated 14 kDa MWCO dialysis tubing (see Note 7), and store in buffer G. Store pyrene labeled actin in a large stirred beaker at 4°C, in 2 L of buffer G; change the buffer twice per week. Seal the top of the beaker with plastic wrap and cover the whole beaker with aluminum foil to prevent light from reaching the labeled actin, which will photobleach the pyrene. Stored in this fashion, pyrene actin can typically be kept for two months.

Fig. 1.

Gel filtration chromatogram for pyrene labeled actin. An example of the UV absorbance detected chromatogram for pyrene labeled actin purification using a 320 mL Superdex 200 pg column. UV absorbance is shown with a thick black line. Fractions collected are shown with short vertical lines. Relevant fraction numbers are shown. The shape of the chromatographic peak is characteristic for actin purified using Superdex 200, and running the column in buffer G. For this purification, fractions 12, 13 and 14 were retained, and fractions 13 and 14 were used preferentially.

3.2. Pyrene Actin Polymerization Assays

Below is our protocol for preparing actin polymerization assays. The exact timing and addition order is not necessarily critical, but for best data reproducibility as specific order and timing should be planned. For clarity we also include an example of the process (see Note 10).

1. Turn on fluorometer, ignite the lamp and start the software (see Note 11).

2. Optionally re-measure the concentrations of actin and pyrene labeled actin by UV absorbance (see Notes 6 and 9).

3. Prepare actin stock. Calculate the number of reactions needed, including controls (see Note 12). Calculate the volume of actin and pyrene labeled actin needed for the entire ‘actin stock’ at the desired actin concentration and labeling (see Note 13). Check that the concentration of actin in the planned actin stock is at least 2.2 fold greater than the desired assay concentration. Following this check, mix the calculated volumes of actin and pyrene labeled actin. Store the actin stock in a lightproof tube on ice.

4. Calculate the volumes of all materials needed in the assay. The assay solution is divided into two parts. The first is an actin containing mixture (Mix A) and the second contains all additional proteins in a salt containing solution (Mix P). For our assay, Mix A and Mix P are both 100 μL in volume. The components of Mix A are typically kept constant throughout the experiment; Mix P is usually different for each reaction, as the experiment dictates. Before starting to mix the components for a reaction, calculate all the volumes needed in both Mix A and Mix P. Mix A contains the actin stock prepared above, 10E/1M buffer and buffer G-Mg (see steps 6–10 below). Mix P components include buffer KMEI, nucleation factors, additional proteins, 10X KMEI and additional KCl, if needed (see steps 11–14 and Note 14).

5. Initialize the fluorometer for data acquisition. On most fluorometer systems, positioning monochrometers, setting slit widths, and initializing the data set can be performed prior to starting data collection. This helps to minimize the delay between combining Mix A and P and beginning data collection. Pyrene-actin fluorescence is excited at 365 nm and emission is detected around 407 nm. The overall excitation and emission of pyrene is actually rather broad, but the enhancement used to detect filament formation occurs only in narrow bands. We use 1 nm bandpass for excitation, and 5 nm bandpass for emission when using a PTI QuantaMaster fluorometer with monochrometer based wavelength selection for both excitation and emission (see Note 11).

6. Begin preparing Mix A by pipetting the volume of actin stock needed to give a 4 μM final concentration in 200 μL into a 1.5 mL tube.

7. One tenth of the volume (of the actin stock) of 10E/1M is added to Mix A to exchange the Ca²⁺ for Mg²⁺.

8. Finally, add the volume of buffer G-Mg needed to give a final volume of 100 μL.

9. Mix by pipetting up and down 3 times and start a timer counting up.

10. Mix A is incubated at room temperature (~22°C) for 2 minutes. Two minutes is enough time for the exchange of calcium and magnesium bound to actin to come to complete. Any time between two minutes and one hour of exchange time will be fine, but the timing should be consistent between samples. If a different exchange time is desired, adjust the timing in steps 14 and 15 accordingly.

11. Begin preparing Mix P by pipetting the volume of KMEI needed into a new 1.5 mL tube.

12. Add the appropriate volumes of the nucleation factors and additional proteins (see step 4), beginning with the nucleation factor (if used). For improved assay reproducibility, add proteins and additives in the same order and with the same timing and pipetting operations.

13. Add 10X KMEI to Mix P. The 10x KMEI accounts for the different buffer conditions in Mix A. Add enough 10x KMEI to bring the final salt concentration (after Mix A and P are combined) to 50 mM KCl, while maintaining the final imidazole, magnesium and EGTA concentrations at those of KMEI. If different salt conditions are used, it may also be necessary to add 2 M KCl and or KMEI lacking KCl to correct the salt while keeping the other buffer components constant. In that case, correct the 10x KMEI addition to account the volume of 2M KCl, which lacks imidazole, magnesium and EGTA (see Note 14).

14. With P-200 pipet set on 200 μL pipet Mix P up and down 3 times being careful not to blow bubbles into the liquid. When the timer shows 1 minute 50 seconds, pull all of Mix P into the pipet tip.

15. At exactly 2 minutes (see Note 15) add all of Mix P (100 μL) to the tube containing Mix A. Pipet up and down one time to mix, and then transfer total volume to clean cuvette (see Note 16).

16. Place the cuvette into the fluorometer and start data collection. Record the time elapsed between addition of Mix P to Mix A and the time data collection begins (see Note 15).

17. Record the time course for pyrene intensity (see Note 11 and Fig. 2) until a maximum intensity is reached and begins to descend again. Depending on the reaction conditions, this may take less than 100 s (expected for our example) or longer than 10000 s (e.g., 1 μM actin alone). For reactions with such different time scales, it may be necessary to alter the illumination method to reduce photobleaching. While short kinetic reactions can be illuminated continuously, longer time courses may benefit from illumination in 0.1–0.5 s intervals, separated by as long 10 s (see Note 11).

18. Repeat steps 4 through 17 for each reaction desired.

Fig. 2.

Pyrene actin polymerization assay example. 4 μM actin, 5% pyrene labeled is brought from buffer G-Mg conditions to KMEI conditions to trigger polymerization of actin. Pyrene fluorescence intensity (Y-axis) as a function of time (X-axis) are shown for actin alone (thin line), actin in the presence of 10 nM bovine Arp2/3 complex (thick line) and actin in the presence of 10 nM bovine Arp2/3 complex and 250 nM N-WASP VCA (dashed line). These three curves are the controls for the basic behavior of actin and Arp2/3 complex.

3.3. Analysis of Pyrene Actin Polymerization Assays

Here we describe the calculation of several simple metrics: the time at which half of the fluorescence intensity change has occurred (t_1/2) (see steps 1–6), the actin polymerization rate at t_1/2 (see steps 1–8), the number of barbed ends present at t_1/2 (see steps 1–10), and the initial filament nucleation rate (see steps 1–5, 7, 11). The calculation of t_1/2 is the most resilient with noisy data, and does not require knowledge of actin critical concentration or growth rate constants. The other three metrics inform more directly on the underlying biochemical activities, but require additional knowledge about actin biochemistry. Typically, only one of these metrics will be presented for a dataset. To simplify automation of the analysis process, our method emphasizes a work-flow that reduces human intervention (see Note 2).

1. Import the data into a spreadsheet or other computational environment (see Note 2).

2. Correct the time values for any known delay between the mixing of Mix A and Mix P and the first time point. This is the recorded time elapsed in Section 3.2. step 16. Time corrected fluorescence intensity data will be referred to as f(t) below.

3. Plot the intensity data as a function of time, ideally comparing it to a series of control datasets to ensure that the data appears sensible, and does not show any obvious pathologies (excessive noise, spurious peaks etc.) (see Note 17).

4. Find the minimum intensity, I_min, for the data set (see Fig. 3). In cases of slow kinetics, short dead-times, and high sampling rates, choose ten points that are near the minimum and average them. For faster kinetics and hand mixed samples with dead-times of greater than 30 s, any group of points will overestimate the minimum. Instead we use the minimum intensity data point. Alternatively, we make use of the fact that the minimum intensity should agree between datasets collected in the same session (Fig. 2). This allows us to use the slowest dataset in a group (typically actin alone) to estimate the minimum intensity for all datasets collected in a given session.

5. Find the maximum intensity, I_max, for the data set (see Fig. 3). Find the ten highest intensity data points and record the associated times. Take the average of these times to estimate the time when the maximum intensity occurs (this reduces the cases where a single anomalous data point leads to incorrect identification of the maximum), retain this time at t_max. Find the ten datapoints closest to t_max, and take the average of their intensity. This average intensity is used as the maximum intensity, I_max.

6. Calculate t_1/2 for the data set (see Fig. 3). First, exclude all datapoints at times greater than t_max. Choose the fraction of the intensity change used to find t_1/2, which we term δ. δ is typically between between 0.04 and 0.2. Collect the data points with intensities between (0.5 − δ/2) * (I_max − I_min) + I_min and (0.5 + δ/2) * (I_max − I_min) + I_min. Using linear least squares, fit a line to these data points. Record the slope, m_t1/2, and intercept, b_t1/2, of the line. Visually inspect where these points fall in the dataset, and how the line fits to the considered points. t_1/2 is then found using:

   $$t_{1/2}=(0.5\ast ({\mathrm{I}}_{max}-{\mathrm{I}}_{min})+{\mathrm{I}}_{min})+b_{t1/2})/m_{t1/2}$$ (Equation 1)
7. Rescale the deadtime corrected data from fluorescence intensity values into units of filament concentration. First, find the fluorescence intensity to actin filament concentration scaling factor, SF, for the data set. For this, one needs knowledge of the initial actin concentration, [Actin](0) and the critical concentration, c₀. c₀ can be calculated from the on-rate constant, k₊, and off rate constant, k₋, for filament assembly using:

   $$c_0=k_{-}/k_{+}$$ (Equation 2)
   In KMEI at room temperature, the barbed ends of rabbit muscle actin elongate and shrink with values of 11.6 μM⁻¹ s⁻¹ and 1.4 s⁻¹ for k₊ and k₋, respectively (17). These rate constants are highly sensitive to solution conditions, particularly to the presence of salt and changes in viscosity (19). This allows calculation of the SF:

   $$\text{SF}=([\text{Actin}](0)-c_0)/({\mathrm{I}}_{max}-{\mathrm{I}}_{min})$$ (Equation 3)
8. Calculate AP_t1/2, the rate of actin polymerization at t_1/2. Use m_t1/2, the slope of the line used to find t_1/2 in step 6 (see Note 3), and SF, to calculate AP_t1/2:

   $${AP}_{t1/2}=\text{SF}\ast m_{\mathrm{t}1/2}$$ (Equation 4)
9. Find [Actin](t_1/2), the remaining free actin at t_1/2. This can be determined from values already calculated:

   $$[\text{Actin}](t_{1/2})=[\text{Actin}](0)-\text{SF}\ast ((m_{\mathrm{t}1/2}\ast t_{1/2}-b_{\mathrm{t}1/2})-{\mathrm{I}}_{min})$$ (Equation 5)
10. Find BE_t1/2, the number of filament barbed ends at t_1/2. This calculation recognizes that actin filaments grow at their ends and the rate constants for these processes are known in certain cases (e.g., rabbit skeletal muscle actin polymerizing in KMEI buffer). The calculation ignores growth at the pointed end, as the barbed end grows much faster than the pointed end, and for Arp2/3 complex nucleated reactions, many pointed ends are capped by Arp2/3 complex. Thus, barbed end growth dominates the kinetics, and the rate law for actin polymerization reduces to:

    $$\mathrm{d}[\text{Filament}](\mathrm{t})/\text{dt}=k_{+}\ast [\text{Actin}](\mathrm{t})\ast [\text{Barbed}\text{Ends}](\mathrm{t})-k_{-}\ast [\text{Barbed}\text{Ends}](\mathrm{t})$$ (Equation 6)
    Considering the rate law at t_1/2 we can solve for BE_t1/2 and substitute in the known values of actin polymerization and actin concentration, we then find BE_t1/2 using:

    $${BE}_{t1/2}={AP}_{t1/2}/(k_{+}\ast [\text{Actin}](t_{1/2})-k_{-})$$ (Equation 7)

11. Find NR₀, the initial nucleation rate. If there is a constant rate of nucleation of actin filaments through the initial portion of the reaction, then filament end concentration will grow linearly with time. This is true in some systems, and may be more directly related to the nucleation factor activity than the other metrics (see Note 18). By limiting our analysis to times where the concentration of free actin has not changed much from the initial concentration, we can directly fit the data with an approximate solution to the time dependence of the system (see Note 19).

    Choose a fraction of the intensity change to use in determining the nucleation rate, which we refer to as γ. From the time corrected dataset (see step 2), select those data points that have intensity values between I_min and γ * (I_min − I_min) + I_min, where γ is between 0.05 and 0.2 (typically 0.1 is used). Using linear least squares fitting, fit the selected data to:

    $$\mathrm{f}(\mathrm{t})=\mathrm{A}\ast {\mathrm{t}}^2+\mathrm{B}\ast \mathrm{t}+\mathrm{C}$$ (Equation 8)
    Visually inspect the quality of the fit to the data (see Fig. 3). B should be near zero and C should be near I_min (see Notes 18 and 19). Repeating the fit with slightly different values of γ (e.g., 0.06, 0.08, 0.1 and 0.12) should not result in substantially different values of A, B or C. The nucleation rate is then calculated as:

    $${NR}_0=(2\ast \mathrm{A}\ast \text{SF})/(k_{+}\ast [\text{Actin}](0)-k_{-})$$ (Equation 9)

Fig. 3.

Graphical representation of the analysis of pyrene actin polymerization data. 4 μM rabbit muscle actin (5% pyrene labeled) is induced to polymerize by shifting to KMEI conditions (see Section 3.2) and adding 10 nM bovine Arp2/3 complex and 40 nM of N-terminally modified WASP VCA. This results in nucleation of actin filaments. Raw data is shown as a thin black line. Shown are the aspects of the data used to calculate t_1/2, actin polymerization rate at t_1/2, barbed ends at t_1/2 and the initial nucleation rate. The minimum and maximum intensities are shown as horizontal lines. Enlarged purple points were averaged to determine the maximum intensity, these are also bracketed for clarity. Enlarged green points were used to find t_1/2 and to find the slope at t_1/2, these are also bracketed for clarity. Enlarged black points were used to find the initial nucleation rate, these are also bracketed for clarity. The determined value for t_1/2 is shown with a vertical line. The line fit to find t_1/2 and the slope at t_1/2 is shown as a thick, dashed, cyan line. The parabola fit to find the initial nucleation rate is shown as a thin, dashed, red line. Note that the parabola has a slight negative slope at t = 0, and undershoots the raw data at later time points, both are indications that a single nucleation rate is not a good metric for this type of data.