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The rational design of affinity chromatography separation processes

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Advances in Biomedical Engineering

Part of the book series: Advances in Biochemical Engineering ((ABE,volume 12))

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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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Authors and Affiliations

  1. Department of Chemical and Biochemical Engineering, The University of Pennsylvania, 19104, Philadelphia, PA, USA

    David J. Graves

  2. Chemicals and Plastics Division, Union Carbide Corporation, 08805, Bound Brook, NJ, USA

    Yun-Tai Wu

Authors
  1. David J. Graves
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© 1979 Springer-Verlag

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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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  • Print ISBN: 978-3-540-09262-9

  • Online ISBN: 978-3-540-35266-2

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