Size matters: Hydrodynamic Radius Vs Radius of Gyration (Rh versus Rg)

Welcome to the second installment of the blog series following on from our successful C&EN webinar on the qualitative and quantitative analyses of proteins.

In this blog series, we are addressing some of the interesting questions posed by audience members.  Today we will look at the difference between hydrodynamic radius (Rh) and radius of gyration (Rg), and what they mean for protein characterization.

Of the many parameters that describe a molecule’s size the two most commonly used are hydrodynamic radius (Rh) and radius of gyration (Rg).  Both of these parameters will tell you how large or small your molecule is, but using different means to arrive at a size value…and, perhaps more confusingly, their answers will not be the same, yet neither is wrong!

Rh, as measured by dynamic light scattering, is defined as the radius of an equivalent hard-sphere diffusing at the same rate as the molecule under observation.  In reality, solutions of proteins and their complexes do not exist as hard spheres and so, the determined hydrodynamic radius more closely reflects the apparent size adopted by the solvated, tumbling molecule.  On the other hand, Rg is defined as the mass weighted average distance from the core of a molecule to each mass element in the molecule.  For macromolecules with radii greater than 10 nm Rg is classically determined using multi-angle light scattering; a technique that relies on measuring a difference in the intensity of scattered light at different angles or otherwise known as angular dependence.  Molecules with radii less than 10 nm – accounting for the majority of known proteins – scatter light equally at all angles (Rayleigh scatterers) and therefore display no angular dependence.  In turn, Rg cannot be determined for proteins in this way.  It is possible, however, to obtain Rg for proteins and small molecules using other techniques such as small-angle neutron scattering (SANS) and small-angle x-ray scattering (SAXS) or from high-resolution x-ray structures.

For proteins and their complexes, Rg and Rh will always be in the same order of magnitude, but what do these size parameters really mean for protein characterization? 

To answer this question we need to look at three key areas of protein characterization.  First and foremost, being able to measure size offers a simple way to confirm the identity and oligomeric state of a protein in a preparation, given a priori knowledge of its monomeric size.  As such it is easy to see how size screening may be implemented in protein production laboratories to identify relevant fractions of purified protein or to check batch to batch consistency of formulations.

Second, biological processes occur in solution; therefore, the interest in studying and characterizing proteins is firmly rooted in understanding, and ultimately controlling, protein behavior.  It is believed that if one understands protein behavior in solution then the interaction with other biomolecules, drugs and with each other can be predicted.  This information can then be taken a step further and used to manipulate protein solutions in order to bring about a specific outcome e.g. formulation development.  From this, It is clear that Rh is a biologically relevant parameter since it considers the protein size in the context of its environment.

Both Rg and Rh can be used to gain insight into the third key area of protein characterization: structure. The way in which Rg is calculated means that the value itself is slightly more dependent on the structure of the molecule of interest than the value of Rh.  But it is the ratio of Rg and Rh (Rg/Rh) that really provides shape information about a protein molecule.  The characteristic Rg/Rh value for a globular protein is ~0.775, which means that Rg is smaller than Rh.  However, when molecules deviate from globular to non-spherical or elongated structures then Rg/Rh tend to values upwards of 0.775, as Rg becomes larger than Rh.

Experimentally, it is important to remember that for proteins Rg cannot be obtained through static light scattering techniques and that Rh can offer an alternative route to shape information through Perrin theory.

In summary, Rg and Rh values are not to be used in the place of one another, but each gives a different perspective of the protein in question.  In addition to the value of the information provided by molecular size, many features of the measurement itself will need to be considered, e.g. analysis time, concentration, sample volume, budget, in order to establish the real value for the user.

Coming soon…

Watch out for the next installment of this blog series in which we will shed light on the aggregation point and how it relates to the stability of proteins and biotherapeutic formulations.