at which flux drops to zero (historically
called cg) and then dividing this
concentration by the constant e (e =
2.718). However, this approach only
gives an approximation of the optimum
point for processes where the flux
decay follows a well-defined standard
curve. For standard pressure-controlled
UF/DF processes, a more accurate
and generally applicable approach
for determining the optimum point at
which to diafilter is to first plot flux
versus the log of protein concentration.
It is important to plot this data with the
protein in both the initial and final
buffers, since flux can often change
significantly with different buffers. A
typical trend is shown in figure 12.
Next, choose several protein
concentrations along each curve that
span the range from initial to final
concentrations expected in the process
and calculate the value of the DF
Optimization Parameter at each point
using the following equation:
DF Optimization Parameter = C * Jf
where:
C = product concentration in
feedstock at data point [g L-1]
Jf = filtrate flux at data point
[L m-2 h-1]
DF Optimization ParameterStarting Buffer
Diafiltration Buffer
Smaller Retentate Volume
Lower Buffer Usage
Higher Membrane Area
Larger Retentate Volume
Higher Buffer Usage
Higher Membrane Area
Optimum Cb
for Diafiltration
0 20 40 60 80 100 120
Product Concentration (g L-1)
Figure 13. Determination of the optimum protein concentration for diafiltration for a
standard TFF process
required, it may not always be
practical. Product volume at this
concentration may be below the
minimum recirculation volume of the
unit operation or the product may not
be stable at this concentration. In
these cases, choose a lower
concentration at the expense of using
more diafiltration buffer and more
membrane area or longer processing
time. Alternately, choose a
concentration higher than the optimum
if the goal is to minimize the volume of
diafiltration buffer required at the
expense of adding more membrane
area or processing time.
Finally, the goal of a diafiltration
step is to reduce buffer or contaminant
species from a product in the retentate.
Since the number of diavolumes that
are performed directly impacts both
yield and extent of purification, it must
be determined with the goal in mind.
Figure 6 illustrates the relationship
between product retention and
product yield as a function of volume
0.001
R = 0.4
R = 0
R = 0.2
05 10 15 20
Remaining Contaminant (%) = 100* e(R-1)*N
100
Finally, plot the optimization
parameter versus protein concentration
for each buffer, as shown in figure 13,
to find the product concentration
where the value of the optimization
parameter is maximized. This is the
optimum concentration at which to
diafilter to minimize membrane area
requirements. If the optimum is very
different for the two buffers, it is most
Contaminant Remaining in Retentate(% of Original)
10
1
0.1
conservative to choose the optimum
based on the buffer curve that results
in the lower value. The actual value
will be between the two curves, since
throughout the diafiltration the product
0.01
Diavolumes (-)
will be gradually exchanged from the
starting to the final buffer.
Although operating at this concen-Figure 14. Removal of a contaminant during a constant-volume diafiltration process
tration minimizes the membrane area where the product is in the retentate and the contaminant is in the filtrate
12
concentration factor and diavolumes.
Buffer exchange and contaminant
removal are easier to view in terms of
percent removal versus diavolumes, as
shown in figure 14.
There are several common reasons
why actual contaminant removal can
be lower than the theoretical removal
shown in figure 14. For example,
retention of the contaminant can
change throughout a diafiltration as its
concentration and the buffer
composition change. The contaminant
can bind to the product of interest. The
formation of surfactant micelles can
change retention or cause partitioning
of the contaminant into the micelle.
The Donnan effect can increase
retention when low ionic strength
solutions are used. Finally, deadlegs
in the system piping can result in small
volumes of solution that are not fully
washed throughout the diafiltration.
Since contaminants or residuals often
must be removed from the product to
