The self- and interface-acting mechanisms for how nucleotide dictates the strength of tubulin:tubulin interactions are illustrated in Figure 1A: the self-acting mechanism posits that the nucleotide bound to β-tubulin (GTP or GDP) controls how tightly that tubulin interacts with the lattice, whereas the interface-acting mechanism posits that the nucleotide at the interface between tubulin dimers controls how tightly they interact. At the plus-end, the two mechanisms can lead to different outcomes because there are two nucleotides involved – one bound to the terminal tubulin and one at the interface below (Figure 1A, top panels). At the minus-end, however, the two mechanisms are indistinguishable because there is only one nucleotide involved: the nucleotide bound to the terminal subunit is also the nucleotide at the interface with the lattice (Figure 1A, bottom panels). Using kinetic simulations of microtubule elongation, we sought to identify a testable difference between the self- and interface-acting mechanisms. We first expanded our model (Ayaz et al., 2014; Cleary et al., 2022b; Kim and Rice, 2019; Piedra et al., 2016) to simulate both plus- and minus-end elongation and to include multiple nucleotide states for unpolymerized tubulin (summarized in Figure 1—figure supplement 1). We then used the model to predict how GDP-tubulin might affect plus- and minus-end elongation with either the self- or interface-acting mechanisms of nucleotide action.

We performed ‘mixed nucleotide’ simulations of plus- and minus-end growth at 1 µM total tubulin with varying fractions of GDP-tubulin (0–20%). For simplicity, simulations used arbitrarily chosen parameters that supported elongation in the chosen concentration regime (Table 1). To provide the simplest possible biochemical setting and to set the stage for experiments described below, simulations did not attempt to explicitly model different conformations of αβ-tubulin (see Discussion), and also ignored GTP hydrolysis. For both self-acting and interface-acting nucleotide, simulated minus-end growth rates decreased identically and in linear proportion to the amount of GDP-tubulin in the simulation (Figure 1B). However, simulated plus-end growth rates decreased much more for interface-acting nucleotide than for self-acting nucleotide (Figure 1C). Similar results were obtained for alternative parameter choices (Figure 1—figure supplements 2 and 3). Based on these robust end-specific differences from simulations, comparative measurements of how GDP-tubulin affects plus- and minus-end elongation should provide a new way to test the self- or interface-acting mechanisms of nucleotide action.

To establish a baseline for measurements with mixed nucleotides, we first used interference reflection microscopy (IRM) to measure plus-and minus-end growth rates in 1 mM GMPCPP (a slowly hydrolyzable GTP analog) at multiple concentrations of bovine brain tubulin. Growth rates displayed the expected linear dependence on tubulin concentration (Figure 2A). Both ends showed the same apparent critical concentration (C_c^app) of 50 nM, but plus-end growth showed a roughly two-fold higher apparent on-rate constant (k_on^app) than minus-end growth, 3 µM^–1 s^–1 MT^–1 and 1.5 µM^–1 s^–1 MT^–1, respectively (Figure 2B).

As a way to test the predictions from our simulations (Figure 1BC), we next measured the growth rates of microtubule plus- and minus-ends at a constant concentration of tubulin (1.25 µM) but using different ratios of GDP and GMPCPP (1 mM total nucleotide concentration). Growth rates at both ends decreased substantially in mixtures containing as little as 2.5% GDP (25 µM GDP and 975 µM GMPCPP) (Figure 2C), but plus-end growth rates decreased to a greater degree than minus-end growth rates. For instance, at 25 µM GDP, plus-end growth rates fell ~50% (from 2.2 nm/s to 1.1 nm/s) relative to ‘all GMPCPP’ growth rates, whereas minus-end growth rates only fell ~30% (from 1 nm/s to 0.7 nm/s). This ~1.5-fold stronger inhibition by GDP of plus-end growth rates held across multiple nucleotide mixing ratios (Figure 2C). Importantly, the larger decrease in the growth rate at the plus-end agrees with the predictions made by the interface-acting mechanism (Figure 1A) compared to the self-acting mechanism.

Tubulin binds different nucleotides with different affinities (Aldaz et al., 2005; Chakrabarti et al., 2000; Correia et al., 1987; Fishback and Yarbrough, 1984; Hyman et al., 1992; Mejillano and Himes, 1991; Monasterio and Timasheff, 1987; Zeeberg and Caplow, 1979), so the ratio of GDP and GMPCPP in a reaction does not directly translate to the fractions of GDP- and GMPCPP-tubulin. To estimate the concentrations of GDP- and GMPCPP-tubulin for each nucleotide mixture, we assumed that only GMPCPP-tubulin contributes to minus-ended growth, consistent with our simulations (Figure 1 BC). This assumption allowed us to estimate the concentration of GMPCPP-tubulin in each nucleotide mixture by matching the observed growth rates to the control ‘all GMPCPP’ growth curve (Figure 2B). A potential problem with this approach is that the estimated GMPCPP-tubulin concentration in each mixture will be affected by error in the growth rate measurements. To minimize the impact of error, we performed a global fit to all measurements using a simple competitive inhibition model that enforced consistent nucleotide binding affinity (Figure 3A). The GMPCPP-tubulin concentrations that best recapitulate minus-end growth rates are consistent with tubulin binding 12.5-fold less tightly to GMPCPP (K_D^GMPCPP) than to GDP (K_D^GDP) (Figure 3B). This inferred difference of affinities was supported by direct measurements of nucleotide binding (Figure 3—figure supplement 1), and agrees with prior reports (Correia et al., 1987; Hyman et al., 1992).

To determine whether the observed decrease in growth rate was stoichiometric with the amount of GMPCPP-tubulin in the assay, we used the binding affinities and the known nucleotide concentrations in each mixture (Figure 3B) to extrapolate equivalent ‘GMPCPP-only’ growth rates (Figure 3 CD solid lines) from the control ‘all GMPCPP’ curves (Figure 2A). Minus-end growth rates decreased stoichiometrically as the concentration of GDP-tubulin increased, matching or even slightly exceeding the ‘all GMPCPP’ extrapolation. The only exception was at the highest concentration of GDP-tubulin (Figure 3C inset), where growth rates were slow and most challenging to quantify. In contrast, plus-end growth rates decreased super-stoichiometrically (were slower than expected based on the ‘all GMPCPP’ extrapolation) for a given concentration of GDP-tubulin (Figure 3D). This super-stoichiometric effect at the plus-end was observed over a range of GDP-tubulin concentrations, and was most apparent when 25–55% of unpolymerized tubulin was bound to GDP (Figure 3D inset). The super-stoichiometric effect of GDP-tubulin on plus-end growth over a wide range of GDP-tubulin concentrations provides strong support for the interface-acting nucleotide mechanism.

To establish a biochemical baseline for simulating mixed nucleotide states, we first fit the interface-acting nucleotide model to the ‘all GMPCPP’ data (Figure 2). The plus-end growth rates were recapitulated well using the same parameters obtained in a prior study (Cleary et al., 2022b; k_on^plus of 0.74 µM^–1 s^–1, K_D^longitudinal of 86 µM, K_D^corner of 25 nM; Figure 4A). To extend the model to fit the minus-end growth rates, we retained the same interaction affinities as for the plus-end (consistent with the equal apparent critical concentration at both ends, Figure 2B) and optimized a minus-end-specific on-rate constant. This procedure yielded a k_on^minus of 0.31 µM^–1 s^–1 (Figure 4A), roughly 2-fold slower than the plus-end, which is in line with the ~twofold lower concentration-dependence of growth rates observed at the minus-end (Figure 2A). We next performed mixed nucleotide (GMPCPP and GDP) simulations at a constant tubulin concentration of 1.25 µM. Simulated minus-end growth rates decreased linearly as the concentration of GDP-tubulin increased, recapitulating the experimental measurements (Figure 4B) and in agreement with our initial prediction using arbitrary parameters (Figure 1). In contrast, simulated plus-end growth rates decreased super-stoichiometrically as the concentration of GDP-tubulin increased (Figure 4C). An outsized effect of GDP-tubulin at the plus-end is expected from the interface-acting mechanism, but the model overpredicted the magnitude of the effect.

In the interface-acting nucleotide mechanism, the outsized effect of GDP at the plus-end occurs because GDP-tubulin can bind tightly to (and reside longer at) the plus-end if the interfacial nucleotide is GMPCPP (Figure 4D). This ‘extended stay’ of GDP-tubulin on the plus-end poisons the protofilament end against further growth and is the origin of the super-stoichiometric effect of GDP-tubulin at the plus-end (Figure 4D). We reasoned that our model might be overpredicting the magnitude of the GDP-poisoning effect (Figure 4C) because it was neglecting some other mechanism that normally limits the lifetime of GDP-tubulin at the plus-end.

Recent work (Luo et al., 2023; Piedra et al., 2016) has reinforced early results (Chen and Hill, 1983; Chen and Hill, 1985; Mitchison, 1993) that pointed to the potential role of nucleotide exchange in microtubule dynamics at the plus-end. We implemented a finite rate of nucleotide exchange in the model (see Methods) to determine whether exchange might allow the simulations to better recapitulate the magnitude by which GDP-tubulin super-stoichiometrically decreased plus-end growth (Figure 5A). We performed interface-acting plus-end simulations using a range of nucleotide exchange rates (Figure 5—figure supplement 1). Faster rates of nucleotide exchange yielded smaller decreases in plus-end growth rates for a given concentration of GDP-tubulin (Figure 5B). The rate of nucleotide exchange that best recapitulated the observed effects was 0.3–0.5 s^–1, which compares favorably to other estimates (Amayed et al., 2000; Melki et al., 1989; Yarbrough and Fishback, 1985; Figure 5—figure supplement 1). In summary, using simulations and measurements of plus- and minus-end growth, we showed that microtubule plus- and minus-ends exhibit different sensitivities to GDP-tubulin, lending strong support for the interface-acting mechanism of nucleotide action.

PC-grade bovine brain tubulin was purified as previously described (Cleary et al., 2022b; Uppalapati et al., 2009), double cycled, quantified by absorbance at 280 nm (ε_tubulin of 115,000 M^–1 cm^–1), diluted to 100 µM in BRB80 (80 mM K-Pipes, 2 mM EGTA, 2 mM MgCl₂, pH 6.9), aliquoted, flash frozen in liquid nitrogen, and stored at –80 °C. Prior to experiments, tubulin aliquots were thawed on ice, diluted to 20 µM in BRB80, and concentrations reconfirmed by A₂₈₀.

Tubulin was biotinylated as previously described (Cleary et al., 2022b). Briefly, microtubules were polymerized by combining 40 µM tubulin, 1 mM GTP, 1 mM MgCl₂ and 5% DMSO in BRB80, incubating at 37 °C for 30 min. An equimolar amount of EZ-Link NHS-Biotin in DMSO (ThermoFisher 20217) was added and allowed to react for 30 min at 37 °C. Microtubules were then pelleted, the pellet resuspended in cold BRB80 and incubated on ice for 30 min to depolymerize the microtubules, the solution centrifuged at 30 psi for 10 min in a Beckman Airfuge using a pre-chilled rotor, and supernatant collected. This biotinylated tubulin was then cycled, the tubulin concentration checked by A₂₈₀, and the degree of biotinylation quantified using the Biocytin Biotin Quantification Kit (Thermo Fisher Scientific #44610). Final stocks of biotinylated tubulin were mixed with unlabeled tubulin to 40 µM total tubulin to obtain a 33% biotin-labeled fraction, aliquoted, frozen in liquid nitrogen, and stored at –80 °C.

Biotinylated microtubule seeds were polymerized by combining 20 µM biotinylated tubulin (33% biotin-labeled), 1 mM GMPCPP (Jena Biosciences) and 4 mM MgCl₂, and incubating at 37 °C for 1 hr. The seeds were then elongated by diluting the total tubulin concentration to 2 µM in BRB80 with 0.5 mM GMPCPP and 2 mM MgCl₂ and incubating for 5 hr at 37 °C. The seeds were pelleted, resuspended in BRB80 with 20% glycerol, flash frozen in liquid nitrogen, and stored at –80 °C. On the day of experiments, the aliquot was rapidly thawed at 37 °C, the seeds pelleted to remove glycerol, and resuspended in a solution containing 0.5 mM Mg-GMPCPP.

Coverslips (18×18 mm Corning) were cleaned in 7X Cleaning Detergent (MP Biomedicals 097667093) diluted to 1X in ddH₂O. The solution was heated at 45 °C until clear, the coverslips were then immersed for 2 hours, removed and rinsed with ddH₂O, and plasma cleaned (Harrick Plasma) for 12 min. Following cleaning, coverslips were silanized by incubating in a vacuum-sealed desiccator with 1 H,1H,2H,2H-perfluorodecyltrichlorosilane (Alfa Aesar L165804-03) overnight. Before use, the degree of silanization was checked using a droplet test to confirm hydrophobicity.

To construct flow cells, a second ethanol-washed and ddH₂O-rinsed coverslip (60x24 mm Corning) was scored, split to a width smaller than 18 mm, and attached to the silanized coverslip with two strips of double-sided tape spaced roughly 10 mm apart. For the experiment, 600 nM neutravidin (Thermo Fisher) was flowed into the chamber, followed by 5% F127 (Sigma P2443-250G), 2 mg/mL casein (Sigma C-7078), and biotinylated microtubule seeds at a concentration that resulted in approximately 10 seeds per 90x90 µm² field of view. Biotinylated BSA (1 mg/mL) was then added to the flow chamber to block any free neutravidin on the cover slip.

Due to the slow growth conditions in these experiments, it was necessary to pre-establish the plus- and minus-ends of the seeds in every field of view. Polarity was determined by injecting into the flow cell a solution containing 12.5 µM tubulin, 1 mM Mg-GTP and an oxygen scavenging system consisting of 80 μg/mL Catalase (Sigma C1345-1G), 100 mM DTT, 200 mM D-Glucose (EMD Millipore Corp DX0145-1), and 200 μg/mL Glucose Oxidase (EMD Millipore Corp 345386–10 gm) in BRB80. The flow cell was allowed to warm for 5 min in contact with the objective of the Nikon TE-2000 TIRF with an objective heater set to 30 °C. Microtubules were visualized using IRM with a blue (440 nm) LED at 0.5% power (pE-300white, CoolLED, UK). Microtubule growth in GTP was monitored for 5 min, and the faster growing end of each microtubule in the field was defined as the plus-end. The tubulin solution was then replaced with tubulin-free cold BRB80, the flow cell was incubated for 5 min to depolymerize the microtubules with depolymerization confirmed by visualization, and finally any residual tubulin was removed by flowing through five flow cell volumes of cold BRB80.

While monitoring the same field of view, a solution was introduced containing tubulin, 1 mM nucleotide (either Mg-GMPCPP or a mixture of Mg-GDP/GMPCPP, with concentrations quantified by absorbance at 252 nm, using ε=13,700 M^–1 cm^–1), and an oxygen scavenging system. Once the final polymerization mixture was introduced, the chamber was sealed with nail polish and allowed to equilibrate to 30 °C while in contact with the objective. Images were subsequently taken at 1 frame per second for up to 2.5 hr. All measurements were performed at least two separate times, except for the 25% GDP condition.

Each video was flat-fielded to correct for uneven illumination, as follows using ImageJ (Schindelin et al., 2015). First, an out-of-focus movie was acquired and a median image generated. The median image was then converted to 32-bits, and normalized to 1 by dividing every pixel value by the mean pixel intensity in the image. Finally, every experimental video was flat-fielded by dividing the intensity values in every frame by this normalized median image. Stage drift was corrected as previously described (Cleary et al., 2022b): fiduciary markers were tracked using FIESTA (Ruhnow et al., 2011) and used as input for an in-house drift correction program written in Matlab. To quantify microtubule growth, kymographs were generated from pixel-corrected movies using the line-scan tool in ImageJ. Plus- and minus-end growth rates were determined by fitting a line to smooth and continuous growth events and calculating the slope.

The relative binding affinities of tubulin for GDP and GMPCPP were estimated by fitting the minus-end growth rates at varying nucleotide ratios to a model in which only GMPCPP-tubulin contributes to minus-end growth, as follows. From Figure 2B, the minus-end growth rate (GR_minus in nm/s) as a function of [tubulin_GMPCPP] (in µM) was:(1)GRminus=0.9∗[tubulinGMPCPP]−0.05

In a mixture of GMPCPP and GDP, the concentration of GMPCPP-tubulin can be determined by a competitive binding model (analogous to competitive inhibition of an enzyme Cheng and Prusoff, 1973) in which the two nucleotides compete for binding to tubulin:(2)[tubulinGMPCPP]=[tubulintotal]([GMPCPP][GMPCPP]+KDGMPCPP(1+[GDP]KDGDP))

Because [GMPCPP] was relatively high in all cases, we made the assumption that GMPCPP≫KDGMPCPP, which simplifies Equation 2 to:(3)[tubulinGMPCPP]=[tubulintotal]([GMPCPP][GMPCPP]+[GDP]KDGMPCPPKDGDP)

Plugging (3) into (1) gives:(4)GRminus=0.9∗[tubulintotal]([GMPCPP][GMPCPP]+[GDP]KDGMPCPPKDGDP)−0.05

Finally, because the total nucleotide concentration was kept constant at 1000 µM, we could replace [GMPCPP] by 1000 – [GDP], yielding:(5)GRminus=0.9∗[tubulintotal](1000−[GDP]1000−[GDP]+[GDP]KDGMPCPPKDGDP)−0.05

The minus-end growth rates as a function of [GDP] in Figure 2B (where tubulintotal was 1.25 µM) were fit to Equation 5. Here, the only free parameter is the relative affinity of tubulin for GMPCPP and GDP (KDGMPCPP / KDGDP). The fit was weighted by the inverse of the standard error of the mean (SEM).

The affinity of tubulin for GMPCPP and GDP was determined using a competition assay that relies on the quenching of tryptophan fluorescence by 6-Thio GTP (Amayed et al., 2000; Fishback and Yarbrough, 1984; Piedra et al., 2016). Aliquots of tubulin (~80 μM) and Bovine Serum Albumin (BSA – 50 mg/mL) were rapidly thawed, filtered through a 0.1 µm spin filter (Millipore-Sigma, UFC30VV25) at 11,000 rpm and 4 °C to remove aggregates, and concentrations quantified by absorbance at A₂₈₀ with ε_tubulin=115,000 M^–1 cm^–1 and ε_BSA=43,824 M^–1 cm^–1. The affinity of 6-Thio GTP for tubulin was measured by preparing 220 μL samples of either 0.2 μM tubulin or 0.56 μM BSA with varying concentrations of 6-Thio GTP. The BSA concentration was chosen to match the tryptophan fluorescence of tubulin, which allowed for the correction of the inner filter effect due to absorbance of 6-Thio GTP at the tryptophan emission peak. A buffer-only well was included in every plate as a zero fluorescence control, and the value of the blank was subtracted from each BSA and tubulin measurement. Tryptophan fluorescence readings (297 nm excitation and 332 nm emission) were performed in 96-well, flat bottom, UV-star plates (Greiner bio-one, 655809) on a Molecular Devices FlexStation 3 Multimode Microplate Reader. Each recorded fluorescence value was an average of 250 signal determinations. The fluorescence readings were corrected for the inner filter effect by dividing the tubulin fluorescence signal by the BSA fluorescence signal at each nucleotide concentration (Fishback and Yarbrough, 1984). The standard error of the mean (SEM) was calculated using propagated errors of the relative SEM for each variable:SEM=((SEMBSA)BSA¯2+(SEMTubulin)Tubulin¯2+(SEMBlank)Blank¯2)∗(Tubulin¯BSA¯)

The affinity of tubulin for 6-Thio GTP (K_D^{6-Thio GTP}) was determined by adding increasing concentrations of 6-Thio GTP, measuring the fall in fluorescence due to fluorescence quenching by the nucleotide, and fitting the data to a binding isotherm weighted by the inverse of the SEM:y=B-A*6-ThioGTP6-ThioGTP+KD6-ThioGTP

where A corresponds to the amplitude of the fall in fluorescence and (B - A) is the remaining fluorescence under full quenching conditions. Competition assays were then performed by adding increasing concentrations of GMPCPP or GDP to a solution containing 3 μM 6-Thio GTP. Competition between the unlabeled nucleotides and the 6-Thio GTP caused unquenching of fluorescence, allowing for determination of the affinity of tubulin for GMPCPP (K_D^GMPCPP) and GDP (K_D^GDP). Data for each nucleotide were fit to a competition model:y=C+A*NucleotideNucleotide+KDNucleotide1+6-ThioGTPKD6-ThioGTP

Here, A is the amplitude fluorescence quenching, which was constrained by the measured value at 3 μM 6-Thio GTP, and C is a free parameter corresponding to the quenched fluorescence value at zero unlabeled nucleotide. For this fit, the means were weighted by the inverse of the SEM.

Simulations of plus- and minus-end elongation were performed using extended versions of previously-described code and analysis algorithms (Cleary et al., 2022a; Cleary et al., 2022b; Kim and Rice, 2019; Mickolajczyk et al., 2019; Piedra et al., 2016). The main features of the model are outlined in Figure 1—figure supplement 1 and described in detail in our previous publication (Cleary et al., 2022b). Briefly, the code performs kinetic Monte Carlo simulations of microtubule elongation at the level of individual association and dissociation events, creating a ‘biochemical movie’ of polymerization with one reaction (association, dissociation, or nucleotide exchange) per frame. First-order subunit association rate constants are calculated by multiplying the bimolecular on-rate constant (k_on) by the tubulin concentration (on-rate=k_on*[tubulin]). Subunit dissociation rates (k_off = k_on*K_D) are dependent on the interaction affinity (K_D) at a specific site, which is determined by the number and type of tubulin-tubulin interactions at the respective site.

The simulation code from the present work is available as a GitLab repository (Rice et al., 2023). To compare the effects of interface-acting and self-acting mechanisms, plus-end simulation code was modified to implement self-acting (cis) nucleotide instead of interface-acting nucleotide (Figure 1—figure supplement 1B). To simulate the minus-end, simulation rules were updated to reflect the lack of an exposed nucleotide on the minus-end, and the orientation of interactions across the seam (Figure 1—figure supplement 1C). Simulating GDP- and GMPCPP-tubulin mixtures required two new parameters: (1) the concentration of GDP-tubulin and (2) a factor to weaken GDP-mediated contacts, represented as a multiplicative factor on the GMPCPP interaction affinity. We assumed that there were no inherent differences between the association rates of GMPCPP- and GDP-tubulin, and used the same on-rate constant (k_on^plus or k_on^minus, respectively) for GDP- and GMPCPP-tubulin.

We generalized our prior implementation of nucleotide exchange (Piedra et al., 2016) to allow all terminal nucleotides (whether GMPCPP or GDP) to exchange. The probability of replacement by GDP or GMPCPP was set to be proportional to the fractional concentration of either nucleotide. Our implementation assumes that the rate-limiting step in nucleotide exchange is dissociation of the (previously) bound nucleotide. To reflect the 12.5-fold difference between the affinity of tubulin for GDP and GMPCPP, the rate of GMPCPP exchange (the off-rate) was set to be 12.5-fold faster than the rate of GDP exchange (as measured in Figure 3).

Experimental plus-end growth rates were recapitulated using biochemical parameters obtained in a prior study (k_on^plus = 0.74 µM^-1 s^–1, K_D^longitudinal = 86 µM, K_D^corner = 25 nM; Cleary et al., 2022b ). Simulations of the minus-end used the same K_D^longitudinal and K_D^corner as for the plus-end. Iterative fitting in MATLAB was used to optimize an on-rate constant (k_on^minus) that could best recapitulate experimentally observed minus-end growth rates. Each fitting attempt used 50 independent simulations, 300 s in length, of minus-end growth at the same concentrations used for measurements of GMPCPP microtubules.

For all other simulations, 50 independent simulations of 600 s were run for each condition tested. Mixed nucleotide simulations in Figure 1 were performed at 1 µM total [αβ-tubulin], with varying percentages of GDP-tubulin (up to 20%, in 5% increments). Mixed nucleotide simulations in Figures 4 and 5 were performed at 1.25 µM total [αβ-tubulin] to mimic experimental conditions, with varied percentages of GDP-tubulin (up to 50%, in 5% increments). Simulations with GDP-tubulin used a ‘GDP weakening factor’ comparable to one used previously (Cleary et al., 2022b), such that the GDP longitudinal interface was 3000- (in Figure 1, where we used arbitrary affinities) or 3500-fold weaker (in Figures 4 and 5, where we fit affinities to recapitulate growth rates) than the GMPCPP-longitudinal interface; this magnitude weakening is consistent with the large difference between depolymerization rates of GMPCPP and GDP microtubules. Additional simulations in Figure 1—figure supplements 2 and 3 used a GDP weakening factor such that the GDP longitudinal interface was 300-fold or 30,000-fold weaker than the GTP longitudinal interface.

Simulation parameters and calculated rates for Figures 1—5 are summarized in Tables 1 and 2. Parameters and calculated rates for Supplemental Figures are summarized in Tables 3 and 4.