| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
Department of Biochemistry and Biophysical Chemistry, Groningen Biomolecular Science and Biotechnology Institute, University of Groningen, 9747 AG Groningen, The Netherlands
Correspondence: Address reprint requests to Ruud M. Scheek, Tel.: +31-50-3634328; Fax: +31-50-3634800; E-mail: scheek{at}chem.rug.nl.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONEXPERIMENTAL METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
A number of experimental approaches is available to study protein-ligand interactions. When the protein and the ligand have sufficiently different sizes, various separation techniques, e.g., size-exclusion chromatography or equilibrium dialysis, can be employed to measure separately the concentrations of bound and unbound ligand. In equilibrium dialysis, the actual concentrations of interacting species are measured after equilibrium has been established between two compartments separated by a semipermeable membrane. This is a relatively slow technique, making this approach less suitable when one of the components is labile, or for high-throughput screening programs.
The actual chemical equilibrium between ligand and protein is usually reached within minutes or seconds. This led Colowick and Womack to develop a rapid method for measuring binding of ligand molecules that are able to diffuse across a semipermeable membrane: the flow-dialysis technique (Colowick and Womack, 1969
; Womack and Colowick, 1973). The system consists of an upper chamber containing the protein-ligand system under investigation, and a lower chamber, separated from the upper chamber via a semipermeable dialysis membrane, through which a mobile phase flows. At a given flow rate, the concentration of ligand measured in the mobile phase is proportional to the concentration of free ligand in the upper chamber. This technique has found widespread use ever since (André and Linse; 2002; England and Hervé, 1992; Hellingwerf and Konings, 1980; Lolkema et al., 1990, 1992; Lolkema and Robillard, 1990; Porumb, 1994; Westerhoff et al., 1989).
Usually, a relatively small amount of radioactive ligand is added to a large pool of potential binding sites at protein concentrations that cause practically all ligand to be bound. By adding unlabeled ligand, the bound labeled ligand is replaced with the unlabeled ligand and appears in the mobile phase. At the end, an excess of unlabeled ligand is added to chase all labeled ligand from the binding sites. The radioactivity measured in the mobile phase then corresponds to all the radioactive ligand being unbound, as in an experiment without protein. Evaluation of the concentration of the labeled ligand in the mobile phase during such a titration yields the binding parameters (KD and E0).
In this article we present a different approach to obtain KD and E0 using flow dialysis. Cumulative amounts of radioactively labeled ligand are added to a fixed amount of binding sites in the regime of ligand concentrations from below the dissociation constant to near saturation. This approach enabled us to accurately determine both the KD and E0 with one sample in a single experiment within 
30 min.
Several reports in the literature have indicated that improper analysis of the obtained data (e.g., ignoring background signal, overlooking nonspecific binding, a nonlinear relationship between a measured signal and the concentration of bound or free ligand, or the presence of partially inactivated components) and the use of inappropriate mathematical procedures to evaluate the data can cause severe bias in the obtained ligand binding parameters (Fuchs and Gessner, 2001; Larsson, 1997; Rovati et al., 1988; Schumacher and Von Tscharner, 1994). Thus, although flow dialysis is experimentally a simple and fast technique, accurate determination of the protein-ligand parameters necessitates a thorough evaluation of the experimental procedure. The use of a semipermeable membrane necessarily entails a certain leak of the labeled ligand (typically 0.5–1.0%/min). Preliminary work in our group indicated that leakage of ligand at such rates during a flow dialysis experiment has a significant impact on the apparent binding parameters, so this effect has to be properly corrected for. An extensive error analysis of the flow-dialysis experiment is presented, including Monte Carlo simulations to evaluate the effects of the relevant systematic and nonsystematic errors, and to define the experimental conditions that allow accurate estimation of the important binding parameters.
|
EXPERIMENTAL METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
Cell growth and isolation of ISO membrane vesicles
Plasmids harboring the wild-type mtlA gene or the mutant mtlA-G196D gene were transformed and subsequently grown in bacterial strain Escherichia coli LGS322 as described (Boer et al., 1995). LGS322, not transformed, and thus not expressing the mtlA gene, was used in control experiments (LGSminus). ISO membrane vesicles were prepared essentially as described (Broos et al., 1999). The vesicles were washed once with 25 mM Tris-HCl, pH 7.6, 1 mM dithiotreitol, and 1 mM NaN3, and quickly frozen in small aliquots in liquid nitrogen for storage at -80°C. Vesicles used for experiments were placed at 37°C for quick thawing and directly placed on ice until further use.
The flow dialysis system
The system as described by Lolkema et al. (1990) was used and a schematic representation is shown in Fig. 1. It consists of a dialysis cell with a 1.2 mL cylindrical upper compartment containing the enzyme solution. It is separated by a dialysis membrane (ServaPor, SERVA Electrophoresis, Heidelberg, Germany), molecular mass cutoff 14,000 Da) from the lower part: a spiral groove with a volume of 20 ± 1 µL engraved in a solid support (Feldmann, 1978).
|
A typical flow dialysis experiment
A control experiment is carried out to estimate the rate of diffusion of the labeled ligand across the membrane (the leak rate) and the dead time of the system. In the control experiment, the upper compartment is filled with buffer solution and samples are collected for 20 min after the flow is started. After the first sample (six droplets) is collected, a known concentration of radioactive ligand (25–100% of the total concentration used in the experiment with protein) is introduced in the upper compartment. Sampling is continued during the next 9–10 min, after which a second addition of the same amount of radioactive ligand is made. The radioactivity of the collected samples was measured after addition of 2.0 mL of scintillation fluid. The background radioactivity (as determined from the first collected sample) was subtracted from all samples. A plot of the CPMs in the collected samples against the time yields two values for the leak rate (LR, %/min), and two values for the multiplication factor ß, relating measured radioactivity and concentration of free ligand in the upper compartment. These values are averaged and used as such.
For each flow-dialysis experiment, a new dialysis membrane was used. The titration experiment with protein consists of 9 or 10 cycles of addition of radioactive ligand, equilibration, and sampling, each cycle taking exactly 3 min. The experiment is started by mixing all components and applying the sample with protein to the upper chamber. At t = 0', a certain amount of radioactive ligand is applied to the upper chamber; 1 min after the addition of radioactive ligand, when the binding equilibrium already has been reached (Lolkema et al., 1990), the radioactivity in the mobile phase is measured by collecting, during 1.5 min, five samples of six droplets each for radioactivity counting. This cycle is repeated 9–10 times. Fig. 2 shows the precise time schedule employed during the titration cycles.
|
 | (1) |
 | (2) |
 | (3) |
) is given by
 | (4) |
Vi is the volume of added ligand at step i, V0 the initial volume in the upper compartment, and S0 the concentration of ligand in the stock solution. 
is the drop in the ligand concentration due to leak through the membrane at step i. In our system, the leak rate LR is small (usually <1%/min) and therefore the leak can be treated as a zero-order process. This makes it legitimate to average the five fractions during the same cycle. The time between halfway the sample collection of the previous titration cycle (n - 1) and halfway the sampling of cycle n is used to calculate the leak correction for cycle n. In our titration schedule (Fig. 2), these points are 1.25 min before and 1.75 min after the start point of cycle n, respectively, resulting in the following expression for the drop in the total ligand concentration due to leakage:
 | (5) |
) is only dependent on the dilution caused by the addition of S, according to:
 | (6) |
|
at each titration point. Multiplying with ß gives the signal 
(CPMs measured after n additions):
 | (7) |
Summarizing the procedure thus far, the raw data (i.e., total added volume 
from the ligand stock solution and the radioactivity counted in the mobile phase at each titration step n) are used to calculate (Eqs. 4 and 5) the total ligand concentration (corrected for the ongoing leak through the semipermeable membrane) and the concentration of free ligand (). For this we use the values for ß and the leak rate obtained from the control experiment. This leaves only the values of KD and E0 (and sometimes ß, see below) to be determined by fitting the experimental data () to Eq. 7. For this, any mathematical software package able to perform nonlinear least-squares minimization can be used. We chose the Levenberg-Marquardt algorithm.
However, since weight factors cannot be assumed to be the same for each titration point, they have to be calculated separately for each titration point, as will be shown below. Also, because the number of titration points is not enough to estimate the confidence intervals for the fitting parameters from the spread in the experimental values, we chose to implement a Monte Carlo approach to this end. All routines used were written in the software package Mathematica 4.1 (available on request).
The error function that has to be minimized is defined as:
 | (8) |
 | (9) |
The variance in the signal measured during cycle n is calculated as follows. The standard deviation in the total ligand concentration after n additions (
) is dominated by the accumulated errors in the added volumes 
:
 | (10) |
) in pipetting was determined experimentally by weighing. Equation 10 yields the standard deviation of the total ligand concentration. Variations in the ligand concentration directly influence the signal C. Therefore, the first derivative of the signal C with respect to the total ligand concentration (Eq. 7) is used to evaluate the effect of variations in the total ligand concentration on the signal :
 | (11) |
Cn/Stot.
The standard deviation in the signal due to counting uncertainties is given by:
 | (12) |
can be squared and summed to yield the total variance (
):
 | (13) |
The impact of each error source on both the KD and E0 can be investigated by a MC simulation, offering the possibility to optimize an experimental setup. The Monte Carlo computer simulations generate many virtual data sets as follows. For each addition, a value for is taken at random from a normal distribution around the actual value used in the experiment, with a standard deviation equal to 
(e.g., 0.04 µL). Equations 4–7 are then used to calculate the corresponding signal. For the parameters LR and ß, the experimental values are taken as such. For the parameters KD and E0, the values are used that yielded the best fit of Eq. 7 to the real experimental data. The counting error in the calculated signal is incorporated by replacing the calculated value for by a value taken at random from a normal distribution around with a standard deviation equal to 
. This approximates the expected Poisson distribution very well. These virtual data sets are subsequently analyzed exactly as the real experimental data sets, and the observed variation in the best-fit parameters is taken to be an accurate representation of the real variation to be expected in experimentally obtained binding parameters. Apart from the nonsystematic errors mentioned, also the effects of systematic errors (use of incorrect weights for the data points, incorrect choice of the parameters LR or ß) could be investigated with these virtual data sets, as will be shown below.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
). For both enzymes, flow dialysis experiments are presented, including the control experiments, the fitting procedure, the impact of ligand leak on the apparent binding parameters (KD and E0), and the calculation of weight factors for the individual data points. The confidence limits of the binding parameters are determined by Monte Carlo computer simulations, taking the most important random errors into account.
High-affinity mannitol binding
Fig. 3 shows the results of a binding experiment, executed as described in the Experimental Methods section, using wild-type EIImtl and [3H]mannitol. From the control experiment (Fig. 3 A), a value of 0.63%/min was calculated for the LR and a value of 16.34 CPM/nM for the factor ß, which relates the radioactivity measured in the mobile phase with the concentration of unbound mannitol in the upper compartment.
|
1 mg/mL. The buffer used included the detergent dPEG, which efficiently solubilizes the vesicles, thus preventing any buildup of mannitol inside the vesicles and making all binding sites available. The enzyme was stable under these conditions, and solubilization by dPEG only marginally affected the binding characteristics (Lolkema et al., 1993). Fitting of these data using Eq. 7, not corrected for mannitol leakage (open circles in Fig. 3 B), yielded a KD of 205 nM and an E0 of 909 nM. The correction for mannitol leakage has a significant effect on the binding parameters. Values for KD and E0 of 179 nM and 828 nM, respectively, were obtained when a leak rate of 0.63%/min was used in Eq. 5 for the leak correction (solid circles in Fig. 3 B).
The use of proper weight factors for the individual data points further improved the reliability of the obtained parameters. First the data were fitted with equal weights for each point. The best-fit values for the fitting parameters KD and E0 were then used to calculate improved weights (Eqs. 9–13) and improved values for KD and E0. This process was repeated until stable values for KD and E0 were obtained, resulting in a KD of 155 ± 23 nM and an E0 of 780 ± 46 nM, respectively (see Fig. 3 B, solid circles, connected). The weight factors employed varied from 5.4 x 10-3 for the first to 3.9 x 10-5 for the last titration point, emphasizing their importance for a correct analysis.
Low-affinity mannitol binding
Low-affinity mannitol binding was investigated with mutant EII-G196D. This mutant shows mannitol binding affinity in the micromolar regime (Boer et al., 1995). The control experiment (Fig. 4 A) was performed with a 3.39 mM [14C]mannitol stock. From both mannitol leak decays, the LR and ß-values were determined and averaged. This resulted in an LR of 1.03%/min and a ß-value of 0.140 CPM/nM.
|
20 mg/ml total membrane protein, 5 mM MgCl2, and 1.0% dPEG were added, and the mixture was incubated at 25°C for 10 min. The 20-fold higher concentration of vesicles used in this experiment had no effect on the leak rate or ß-value. This was established by using E. coli vesicles not containing EIImtl (LGSminus strain, see Experimental Methods). Fitting of the raw data resulted in a KD of 88 µM and an E0 of 95 µM (Fig. 4 B, open circles). Correction for mannitol leak as described for the high affinity experiments on wild-type EIImtl resulted in a KD of 37 µM and an E0 of 52 µM. Complete analysis, including proper weight factors for the data points, resulted in a KD of 25 ± 6 µM and an E0 of 46 ± 8 µM (Fig. 4 B, solid circles). The standard deviations reported in this and the previous section were calculated from the quality of the fit and are not very reliable due to the small number of titration points. A better procedure for estimating the reliability of the binding parameters will be given below.
Monte Carlo simulations
Accuracy of the procedure
For an accurate determination of both the dissociation constant and the number of available binding sites in a single experiment, it is important to choose the amount of protein and the ligand concentration range so that both parameters can be optimally determined. Since the flow-dialysis procedure relies on the determination of the fraction of the total added ligand that is freely diffusible across the membrane, it is crucial that during a titration a significant fraction of the total added ligand is actually bound. In addition, as in any binding experiment, a high degree of saturation of the binding sites (>80%) must be realized. This leads to the following two important requirements for a good flow-dialysis experiment:
To establish quantitatively how the choice of conditions affects the accuracy of binding experiments, we carried out a large number of Monte Carlo simulations of such experiments. For these calculations we chose KD = 1, and E0 in the range 1–300. Each simulated titration consists of eight additions of ligand from a stock solution (relative volume increments 1, 2, 2, 2, 2, 4, 4, and 8 µL, with a standard deviation of 
i = 0.08 µL) to an initial volume of 380 µL in the upper compartment. The concentration of the stock solution was chosen such that an excess of n = 3.7 of total added ligand over the binding sites was reached at the end of the titration. For each addition the total concentrations of ligand and binding sites were calculated (Eqs. 2 and 4), and from these the expected signal (Eq. 7). The ß-value was chosen inversely proportional to the concentration of ligand in the stock solution to ensure that in every titration the signal reached similar values. Fig. 5, A–F, show some typical (virtual) binding experiments and the resulting distributions of binding parameters obtained from 200 of such virtual data sets, for a range of E0 values between 1 and 300. Fig. 6 shows the obtained accuracy for both parameters under the different conditions (solid symbols: squares for the KD, circles for E0). Clearly, the optimal range for E0 is between 3 and 30, if both KD and E0 need to be determined. Since we did not specify the concentration units in these calculations we can extrapolate this to other values for the KD by multiplying all concentrations with the actual KD value of the system under study. So, for our high affinity binding experiments (KD = 150 nM), the optimal range for E0 is between 3 and 30 x 150 nM. For the low-affinity (KD = 25 µM) experiments, the concentration of binding sites should be chosen between 3 and 30 x 25 µM for optimal accuracy.
|
|
, we used values for the KD and E0 of 1 and 10, respectively, to generate 200 virtual data sets, as described in the Experimental Methods section, mimicking the conditions and procedures of real binding experiments. Four different values for the pipetting error were used. These simulated data sets were analyzed exactly as described for the real data, each data set yielding best-fit values for the model parameters KD and E0. Table 2 shows the resulting uncertainties in the values found for KD and E0.
|
was set to 0.08 µL. Calculations including only the pipetting error are shown in Fig. 7 B. Calculations including only the counting error are shown in Fig. 7 C. These figures demonstrate that the pipetting error was the most important source of error in our experimental setup.
|
Systematic errors
The effect of improper leak correction. To investigate the importance of leak correction (Eq. 5), we used the same Monte Carlo procedure to generate 200 virtual data sets under a range of conditions (E0/KD between 1 and 300), with LR equal to 0.6%/min. Analysis was done without leak correction (LR = 0%/min) or with a two-times overestimated value (LR = 1.2% min). The results are shown in Table 3, with an example of the titration curve and scatter plot obtained at E0/KD = 10 (Fig. 8). The use of incorrect leak rates results in a similar systematic trend at all E0/KD ratios. In addition, it leads to larger uncertainties in the parameters KD and E0: up to 17% for the KD, and 9% for E0 (see Table 3).
|
|
2 values were almost 50% higher (data not shown). This approach can be useful for recognizing such a systematic error. Under these conditions, one may decide to use ß as the third parameter in a three-parameter fitting procedure, as will be discussed below.
|
|
At E0/KD ratios <10, the spread in ß was more than 7%, whereas at the higher E0/KD ratios, this spread was minimal (data not shown). We concluded that accurate results could only be obtained in the regime where saturation of the binding sites at the end of the titration was virtually complete and sufficient information for a proper estimation of ß is present in the data. Interestingly, when incorrect leak rates were used for the analysis, the routine compensated for this systematic error by adjusting the value for ß, such that the relevant binding parameters KD and E0 were still estimated correctly (data not shown).
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
Commonly, the standard deviations of the best-fit binding parameters are estimated from the curvature of the 2-function near its minimum. When only a small number of data points is available, these standard deviations can fluctuate significantly from one (virtual) binding experiment to the next, and the MC simulation procedure was found to be much more reliable. In addition, the MC simulations can be used to investigate where further improvements of the system can be worthwhile.
The differences in the leak rates observed in the high-affinity and low-affinity mannitol binding experiments is caused most likely by the use of two different batches of semipermeable membranes. This further emphasizes the importance of the control experiments, since the value for LR (and hence ß) can be dependent on the membrane batch used.
The three-parameter fitting procedure was initially built to see if it was possible to obtain all parameters (KD, E0, and ß) within a single experiment. In this case, a control experiment would not be needed, provided the leak rate is known for a given experimental setup. Here we show that at low E0/KD ratios, the saturation level is too low to make a proper estimation of E0 (see Fig. 6). The regime at which three parameters can be fitted properly with eight (averaged) data points is more restricted than when only two parameters must be fitted: for two-parameter fitting, the range is optimal at E0/KD ratios between 3 and 30, whereas for three-parameter fitting this range is narrowed down to E0/KD ratios between 10 and 30. Clearly, at the lower ratios the data points do not hold enough information to accurately determine ß.
In conclusion, in this article a thorough evaluation of the accuracy of the flow-dialysis method is presented. Guidelines to optimize the experiment are given and the impact of all possible error sources that influence the KD and E0 parameters have been investigated. The use of these guidelines ensures an accurate and reliable measurement of both the KD and E0 in a single measurement.
|
ACKNOWLEDGEMENTS |
|---|
|
TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
|
FOOTNOTES |
|---|
Submitted on September 16, 2003; accepted for publication December 4, 2003.
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONEXPERIMENTAL METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
|---|
Boer, H., R. H. Ten Hoeve-Duurkens, J. S. Lolkema, and G. T. Robillard. 1995. Phosphorylation site mutants of the mannitol transport protein enzyme IImtl of Escherichia coli: studies on the interaction between the mannitol translocating C-domain and the phosphorylation site on the energy coupling B-domain. Biochemistry. 34:3239–3247.[Medline]
Broos, J., F. Ter Veld, and G. T. Robillard. 1999. Membrane protein-ligand interactions in Escherichia coli vesicles and living cells monitored via a biosynthetically incorporated tryptophan analogue. Biochemistry. 38:9798–9803.[Medline]
Colowick, S. P., and F. C. Womack. 1969. Binding of diffusible molecules by macromolecules: rapid measurement by rate of dialysis. J. Biol. Chem. 244:774–777.
England, P., and G. Hervé. 1992. Synergistic inhibition of Escherichia coli aspartate transcarbamylase by CTP and UTP: binding studies using continuous-flow dialysis. Biochemistry. 31:9725–9732.[Medline]
Feldmann, K. 1978. New devices for flow dialysis and ultrafiltration for the study of protein-ligand interactions. Anal. Biochem. 88:225–235.[Medline]
Fuchs, H., and R. Gessner. 2001. The result of equilibrium-constant calculations strongly depends on the evaluation method used and on the type of experimental errors. Biochem. J. 359:411–418.[Medline]
Hellingwerf, K. J., and W. N. Konings. 1980. Kinetic and steady-state investigations of solute accumulation in bacterial membranes by continuously monitoring the radioactivity in the effluent of flow-dialysis experiments. Eur. J. Biochem. 106:431–437.[Medline]
Larsson, Å. 1997. Regression analysis if simulated radio-ligand equilibrium experiments using seven different mathematical models. J. Immunol. Methods. 206:135–142.[Medline]
Lolkema, J. S., and G. T. Robillard. 1990. Subunit structure and activity of the mannitol-specific enzyme II of the Escherichia coli phosphoenolpyruvate-dependent phosphotransferase system solubilized in detergent. Biochemistry. 29:10120–10125.[Medline]
Lolkema, J. S., D. Swaving-Dijkstra, and G. T. Robillard. 1992. Mechanics of solute translocation catalyzed by enzyme IImtl of the phosphoenolpyruvate-dependent phosphotransferase system of Escherichia coli. Biochemistry. 31:5514–5521.[Medline]
Lolkema, J. S., D. Swaving-Dijkstra, R. H. Ten Hoeve-Duurkens, and G. T. Robillard. 1990. The membrane-bound domain of the phosphotransferase enzyme IImtl of Escherichia coli constitutes a mannitol translocation unit. Biochemistry. 29:10659–10663.[Medline]
Lolkema, J. S., E. S. Wartna, and G. T. Robillard. 1993. Binding of the substrate analogue perseitol to phosphorylated and unphosphorylated enzyme IImtl of the phosphoenolpyruvate-dependent phosphotransferase system of Escherichia coli. Biochemistry. 32:5848–5854.[Medline]
Porumb, T. 1994. Determination of calcium-binding constants by flow dialysis. Anal. Biochem. 220:227–237.[Medline]
Rovati, G. E., D. Rodbard, and P. J. Munson. 1988. DESIGN: computerized optimization of experimental design for estimating Kd and Bmax in ligand binding experiments. Anal. Biochem. 174:636–649.[Medline]
Schumacher, C., and V. von Tscharner. 1994. Practical instructions for radioactively labeled ligand receptor binding studies. Anal. Biochem. 222:262–269.[Medline]
Westerhoff, H. V., A. H. C. A. Wiechmann, K. Van Dam, and K. J. Hellingwerf. 1989. On the evaluation of data from flow-dialysis experiments. J. Biochem. Biophys. Methods. 18:53–64.[Medline]
Womack, F. C., and S. P. Colowick. 1973. Rapid measurement of binding of ligands by rate of dialysis. Methods Enzymol. 27:464–471.[Medline]
This article has been cited by other articles:
 |
|
 |
|
  R. H. Duurkens, M. B. Tol, E. R. Geertsma, H. P. Permentier, and D. J. Slotboom Flavin Binding to the High Affinity Riboflavin Transporter RibU J. Biol. Chem., April 6, 2007; 282(14): 10380 - 10386. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
G. Veldhuis, E. Gabellieri, E. P. P. Vos, B. Poolman, G. B. Strambini, and J. Broos Substrate-induced Conformational Changes in the Membrane-embedded IICmtl-domain of the Mannitol Permease from Escherichia coli, EnzymeIImtl, Probed by Tryptophan Phosphorescence Spectroscopy J. Biol. Chem., October 21, 2005; 280(42): 35148 - 35156. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 G. Veldhuis, J. Broos, B. Poolman, and R. M. Scheek Stoichiometry and Substrate Affinity of the Mannitol Transporter, EnzymeIImtl, from Escherichia coli Biophys. J., July 1, 2005; 89(1): 201 - 210. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
. The leak at each point n consists of two components. The first component (1.25', in minutes) is the leak from the previous addition (n - 1) from halfway sampling until the end of sampling (0.75') plus the remaining time until the next addition at point n (0.50'). The second component starts from the point of addition of a new amount of substrate at point n and lasts until halfway the sampling during n (1.75').
) Uncorrected data; (•) data points corrected for leakage (see text).
. For every E0/KD ratio, 200 virtual data sets were generated and fitted. Typical example titration curves of one of the virtual data sets together with the scatter plots are shown (E0/KD ratios for A, B, C, D, E, and F, are 1, 3, 10, 30, 100, and 300, respectively). The solid lines in these titration graphs represent the value of ß, relating the signal C with the concentration of free ligand. Note that all concentration units are arbitrary and can be scaled at will.
) LR = 1.2%/min; 