Methods and Results
If multiple species are present in solution and have an rh within a factor of ~3 of each other, then the rh measured by DLS is an average over those species, called ravg. If two proteins A and B associate to form a complex AB, then the presence of the complex increases ravg, and the increase in ravg may be used to calculate the degree of association. The method of continuous variation is a standard method whereby a parameter proportional to complex formation is measured as the molar concentration of [A] with respect to [B] is altered, e.g., from 0–100%, with the total molar concentration [A] + [B] fixed. The concentration-gradient DLS method demonstrated here is the method of continuous variation with ravg derived from DLS as the measurable parameter. It determines Kd, which gives the molar concentration of a complex given the molar concentrations of the individual species as:
[AB] = [A][B]/Kd
Concentration-gradient DLS was used to characterize the binding of the model system α-chymotrypsin and soybean trypsin inhibitor (STI), using both 10 µL/well and 1 µL/well sample volumes. Agreement of the 10 µL and 1 µL results indicated that reduction in the sample volume had minimal impact on data quality. Sample stock solutions were 500 µg/mL concentration, and the concentration gradient was produced by volumetrically combining different ratios of stock solutions.
Lower concentrations may be used, particularly for larger proteins which scatter more light such as antibodies, which may have stock concentrations of 20 µg/mL. Measurements were made with randomized placement of five replicate wells, and the error bars shown are the standard deviation of results from the five wells.
A maximum of ravg at 0.5 mole fraction is consistent with 1:1 binding. For this system, ravg reached a maximum value at ~0.75 mole fraction, indicating that STI possesses more than one binding site, as has been previously reported. The data was fit assuming STI possesses two binding sites of equal affinity along with an “incompetent fraction”, which had also been previously reported.
Measurements were made with the temperature sequence 25-20-15-10-5-25-30-35-25, and Kd determined at each temperature, with the repeat measurements at 25°C used to ensure that time and elevated temperature did not alter the system. For one series of measurements, the chymotrypsin was pretreated with the small-molecule serine protease inhibitor AEBSF. The AEBSF-treated chymotrypsin was found to no longer bind with STI, demonstrating the detection of small-molecule inhibition of binding.
The 25°C and AEBSF measurements are shown in Figure 1A, and the measurements as a function of temperature are shown in Figure 1B. Thermodynamic information was obtained using a van’t Hoff plot (Figure 1C), with results for the change in enthalpy ΔH°=12±4 kcal/mol, and the change in entropy ΔS°=70±14 cal/(mol K). The Table summerizes all measured kd values.