click to enlarge click to enlarge Figure 1. Characterization of α-chymotrypsin dimerization as a function of acidic buffer salinity. (a) Average hydrodynamic radius as a function of α-chymotrypsin concentration. Symbols represent measured data; fits are shown as solid lines; error bars show s.d. Profile expected for no association is shown by dotted line. (b) Equilibrium dissociation constants as a function of salinity. Kd values obtained from the DLS fits in Figure 2a are shown in black, and values determined from alternate techniques are shown in grey. Error bars represent change in Kd value required to increase reduced χ2 by 1. (All figures reprinted with permission from Biophysical Journal)

Dynamic light scattering (DLS) uses time-dependent fluctuations in the intensity of scattered light to measure the hydrodynamic radius (r_h), ie, the size, of the particles in solution. Recent technological developments have led to the introduction of a new DLS technique called concentration-gradient DLS, a method designed to facilitate precise quantitative characterization of protein-protein interactions, which are pivotal to the study of cellular function and pharmaceutical development.

Purification and characterization of protein complexes can be challenging. Protein complexes are often transient, existing in equilibrium with partially formed complexes and monomers, making it impossible to have a pure solution of only the complex. For this reason, techniques capable of characterizing equilibrium solutions, containing both complex and monomers, are essential. Ideally, these techniques should not require tagging or immobilization of the binding partners. Modifications can influence the interactions or provide false negative results. Commonly used free solution, label-free methods avoid modifications of the proteins, but require large quantities of sample and are not suitable for high-throughput analyses.

click to enlarge Figure 2. Characterization of a 1:1 a-chymotrypsin : bovine pancreatic trypsin inhibitor interaction at neutral pH at two temperatures. Profile expected for no association is shown by dotted line. Fits are shown as solid lines. Inset shows negative control of a-chymotrypsin and lysozyme, for which no association was expected or detected. Error bars show s.d.

Concentration-gradient DLS addresses these challenges, enabling detection and characterization of protein-protein interactions, and small-molecule inhibition of these interactions, without tags or immobilization, in equilibrium solutions. Whereas sedimentation equilibrium analyses may require up to 72 hours to be completed, a concentration-gradient DLS study can be completed in under an hour.

Methods
A variant of the method of continuous variation (Job plot) was used to characterize the interactions. The total molar concentration of the two proteins was held constant, while their relative molar ratio was varied in a series of solutions. The average hydrodynamic radius, r_avg, (Eqn. 1) was measured for each solution in this “concentration gradient”.

The r_avg given in Equation 1 is the cumulant “r_h” value reported by most DLS analysis software. If proteins A and B associate, there will be an increase in the measured r_avg beyond monomer baseline level. For a self-associating system, r_avg is expected to increase with total concentration.

While it is not possible to fully characterize an unknown mixture of species present in solution with only a single measurement, multiple measurements over a series of concentrations can yield an accurate characterization.

Concentration gradient solution series were pipetted into a microtiter plate in randomized quintuplicate, and placed in a Wyatt Technology DynaPro temperature-controlled plate reader. Wyatt Technology Dynamics software was used to schedule the measurements and collect the data. A plot of the measured r_avg vs. molar ratio was then fit to determine the reaction stoichiometry and dissociation constant.¹

Results
Four protein systems were characterized using concentration gradient dynamic light scattering. Three of these demonstrated specific interactions, each with a distinct stoichiometry. The first system, α-chymotrypsin at acidic pH, was found to form a dimer (Figure 1a). K_d values varied inversely with buffer salinity, as chymotrypsin is more prone to dimerize at higher salinities.

The second system, α-chymotrypsin (25.5 kDa r_h = 2.27 nm) and bovine pancreatic trypsin inhibitor (6.5 kDa, r_h = 1.38 nm), had the maximum increase in the measured r_avg value at a mole fraction of 0.5, which indicated an n:n complex (Figure 2). Fitting gave 1:1 stoichiometry, and a dimer radius of 2.45 nm. As a negative control, chymotrypsin and lysozyme were also tested, and showed no interaction (Figure 2, inset).

α-chymotrypsin and soybean trypsin inhibitor (21.5 kDa), both had measured r_h values of 2.27 nm.

The proteins interacted with maximum increase at ~0.75 mole fraction (Figure 3a). The skew to higher chymotrypsin content indicated multiple chymotrypsins were incorporated in the complex. Fit of the data gave a trimer composed of two chymotrypsin monomers and a single soybean trypsin inhibitor monomer. At 25˚C, the average K_d was 0.53 (+0.11, -0.13) µM, in agreement with the literature value of 0.32±0.16 µM. Dimer and trimer radii were found to be 3.22 nm and 3.95 nm, respectively. The sample plate was measured with the following temperature sequence: 25-20-15-10-5-25-30-35-25 (˚C). Association increased with temperature (Figure 3b). The multiple runs at 25˚C (Figure 3a) confirmed that cycling the temperature did not impact binding ability. Also, absence of a gradual reduction of r_avg with time indicated that proteolytic activity of chymotrypsin did not appreciably affect either protein.

click to enlarge Figure 3. Characterization of a 2:1 a-chymotrypsin:soybean trypsin inhibitor interaction at neutral pH as a function of temperature. Data are presented as ravg vs. mole fraction of 0 to 1, with the mole fraction being the total molar concentration of chymotrypsin divided by the molar concentrations of both chymotrypsin and soybean trypsin inhibitor, yielding a range of entirely soybean trypsin inhibitor (0), to entirely chymotrypsin (1). Symbols represent measured data; fits are shown as solid lines. (A) Control measurements and small molecule inhibition study (AEBSF). (B) Association as a function of temperature. Profile expected for no association is shown by dotted line. In A & B error bars show s.d. (C) Determination of a parameter and incompetent fraction by simultaneous collection of both static and dynamic light scattering data. Static light scattering data is shown in blue, DLS data is shown in black. (D) van’t Hoff plot. Ka values from fits in B shown in black. Slope of -DH°/R and an intercept of ∆DS°/R.

Thermodynamic information was obtained using a van ’t Hoff plot (Figure 3d). To validate low volume capability, two sets of experiments were performed with different sample volumes, 1 µL and 10 µL. ∆H° values were 12±4 and 12 (+4,-5) kcal mol-1; ∆S° values were 70±14 and 70 (+16,-14) cal mol^-1 K^-1. Agreement of the 1 µL and 10 µL results indicated that reduction in sample volume had minimal impact on data quality.

In contrast to untreated chymotrypsin, the AEBSF-treated chymotrypsin did not associate with the soybean trypsin inhibitor (Figure 3a). As the molar mass of AEBSF, (240 g mol^-1, r_h ~0.2 nm), differed by more than a factor of five from that of chymotrypsin, (25,500 g mol^-1, r_h =2.27 nm), their binding did not result in a measureable change in rh. The chymotrypsin-AEBSF complex retained the rh of the uninhibited protein, 2.27 nm (Figure 1a). As only chymotrypsin-AEBSF and soybean trypsin inhibitor (2.27 nm) were present in solution, the measured rh was 2.27 nm over the entire mole fraction range.

Table 1 summarizes all measured K_d values, which spanned more than 3 orders of magnitude. It was possible to measure the response to environmental conditions such as buffer salinity and temperature, as well as the thermodynamics of the association. Measured values were shown to be constant down to the smallest solution volume of 1 µL. Although not optimized for reduced sample use, these nondestructive experiments used only 426 picomoles of protein (Twenty 1 µL solutions at 500 ug/mL, minimum molar mass of 6.5 kDa). As the intensity of scattered light is proportional to the product of molar mass squared and molar concentration, similar studies with antibodies (150 kDa) should require only 2.9 femtomoles (Twenty 1 µL solutions at 22 µg/mL).

A significant limitation of concentration gradient DLS is that the molar mass of the interacting protein must be no more than five times larger or smaller than its binding partner. The silver lining here is that the protein hydrodynamic radius is not altered by the binding of a small molecule. This means the impact of small molecules binding to, or associating with, one of the proteins, may be studied without the complication of an altered protein radius.

Conclusion
An efficient, dependable method for rapid and precise characterization of protein-protein interactions, concentration-gradient DLS has emerged as a label-free alternative to other techniques. The method has a broad range of applications beyond protein-protein interactions, for example, the association characterization of non-protein biomolecules such as tRNA. In addition, when combined with other techniques, such as small molecule screening or site directed mutagenesis, concentration-gradient DLS can be used to identify residues involved in protein molecular recognition. As a result, the method may not only characterize biomolecular interactions, but also explain them.

References
1. Hanlon AD, Larkin MI, Reddick RM. Free solution, label free protein protein interactions characterized by dynamic light scattering. Biophysic J. 2010;98(2):297.

This article was published in Drug Discovery & Development magazine: Vol. 13, No. 6, July/August, 2010, p. 18-20.