Abstract
A number of simple models of affinity chromatography are presented which can be used individually or in combination to predict such results as 1) when a column will become saturated with enzyme, 2) when a peak will emerge from a column and how sharp it will be, 3) how much purification one can expect under a given set of conditions, and 4) what concentration of a competitive inhibitor is needed to remove enzyme from a column. Kinetic problems can be important in affinity separations, and a predictive equation which is given allows one to estimate when such problems are likely to be seen.
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Abbreviations
- A:
-
A parameter defined by Eq. (4)
- As :
-
Absorbance of a protein solution in a 1 cm path length cell
- B:
-
A parameter defined by Eq. (3)
- C:
-
A parameter defined by Eq. (7)
- dp :
-
The diameter of a gel bead
- D:
-
A parameter defined by Eq. (9)
- Di :
-
The dispersion parameter in chromatography, Eq. (26)
- Ds :
-
The protein diffusivity within the gel
- E:
-
The equilibrium concentration of enzyme
- Ei :
-
The pseudo-concentration of bound plus entrapped teenzyme
- EI:
-
The equilibrium concentration of enzyme-inhibitor complex
- Eo :
-
The initial enzyme concentration before equilibration
- EL:
-
The equilibrium concentration of enzyme-ligand complex
- fBE :
-
The fraction of initial enzyme remaining bound to ligand after n washes and one elution
- fBE(j) :
-
Defined as for fBE but after j elution steps, Eq. (48)
- fB(n) :
-
The fraction of initial enzyme remaining bound to ligand after n washing steps, Eq. (43)
- fBT(n) :
-
The fraction of enzyme bond and entrapped within the gel after n washing steps, Eq. (49)
- fCR :
-
The fraction of contaminant recovered, Eqs. (38) and (44)
- fCR(j) :
-
The fraction of contaminant recovered in elution j
- fE :
-
The enzyme recovered during an elution as a fraction of the enzyme in the gel following all washing steps
- fi :
-
The fraction of enzyme lost in washing step (2.3.1)
- fo :
-
The fraction of enzyme failing to bind during the binding step
- fR :
-
The fraction of initial enzyme recovered in V′ after n washes and one elution
- fR(m) :
-
The fraction of initial enzyme recovered in V after with elution m after n washes
- H:
-
The height of a theoretical equilibrium stage
- I:
-
The soluble inhibitor concentration at equilibrium
- Io :
-
The initial concentration of soluble inhibitor
- k1 :
-
The second-order forward rate constant, Eq. (1)
- k′1 :
-
The first-order forward rate constant, Eq. (56)
- k−1 :
-
The first-order reverse rate constant, Eqs. (1) and (56)
- Kda :
-
The apparent dissociation constant, Eq. (35)
- Ke :
-
The ratio of L0 to Ki
- Ki :
-
The enzyme-ligand dissociation constant, Eq. (5)
- K′i :
-
The altered value of Ki during elution
- Ks :
-
The enzyme-inhibitor dissociation constant, Eq. (34)
- K1 :
-
A dimensionless rate constant, Eq. (69)
- K−1 :
-
A dimensionless rate constant with k−1 replacing k1, Eq. (69)
- L:
-
The equilibrium free ligand concentration
- Lc :
-
The length of the chromatography column
- Lo :
-
The initial ligand concentration
- m:
-
The amount of bound plus free enzyme in a bead, Eq. (65)
- mc :
-
The integral amount of m during crossover conditions, Eq. (71)
- md :
-
The quantity of m during a desorption process, Eq. (77)
- meq :
-
The amount of bound plus free enzyme at equilibrium, Eq. (64)
- mfl :
-
The integral amount of m during film-limiting conditions, Eq. (72)
- P:
-
The ratio of V to v
- Pf :
-
The purification factor, Eq. (55)
- r:
-
The radius of a bead
- R:
-
The fractional time a molecule remains in the mobile phase during chromatography, Eq. (15)
- Rc :
-
The roughly constant rate of enzyme gain or loss during “crossover” conditions, Eq. (68)
- Rfl :
-
The external mass transfer film-limiting rate, Eq. (70)
- t:
-
A dimensionless time, Eq. (59)
- tc :
-
The time required to elute an enzyme peak from a column or the time during column saturation when the exit concentration rises to 50% of the inlet concentration
- tcs :
-
The time at which the “crossover” period starts
- tcf :
-
The time at which the “crossover” period ends
- to :
-
The time required to elute the void volume of a column
- t1/2 :
-
The half-time for a first-order reaction, Eq. (36)
- T:
-
An arbitrary variable, Eq. (31)
- v:
-
The inter-gel volume penetrable by enzyme
- v1 :
-
The linear velocity of mobile phase
- V:
-
The void volume in a column surrounding the beads or the volume of solution in contact with the beads during a batch experiment
- V′:
-
The volume of eluting solution during a batch experiment
- Vc :
-
The volume of solution needed to elute a peak from a column
- w:
-
The volume of a washing solution during a batch experiment
- φ:
-
The fraction of enzyme molecules bound to ligand at equilibrium, Eq. (24)
- θ:
-
Real time
- τc :
-
The standard deviation of peak width, Eq. (25)
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Graves, D.J., Wu, YT. (1979). The rational design of affinity chromatography separation processes. In: Advances in Biomedical Engineering. Advances in Biochemical Engineering, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540092625_10
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DOI: https://doi.org/10.1007/3540092625_10
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