50
34
36
38
40
42
44
46
2 4 6 8 1
Concentration (mg/ml)
kD = 17.9 ml/g
kD = -5.1 ml/g
Diusion
Coecient
(µm/s)
When k
D
is positive, it indicates there are repulsive forces between
molecules; when negative, it indicates attractive forces. Attractive
or associative forces may indicate concentration-dependent
aggregation propensity, and indicate that a biologic sample may
not hold up for shipping and long-term storage as it is currently
formulated. For formulation work, it is crucial to understand
how a protein or antibody will behave at high concentrations for
ultimate scale-up and clinical development.
If your biologic gives you an undesirable k
D
, it is
possible to change the environment by altering
the buffer or additives in order to discourage
association. See Section 6 for more information.
An alternative to the k
D
is B
22
. This is known as the
second virial coefficient, and is directly related to
the k
D
. The equation relating B
22
to the k
D
requires
very accurate knowledge of the molecular weight
of a particle, and can be difficult to derive if the k
D
approaches 0— i.e., when no significant interaction
is occurring. B
22
is determined using static light
scattering (SLS), which is not covered in this book
but is another useful characterization tool.
