Thermodynamic modeling of protein separation
Ju Ho Lee Ph. D. Course
Scope
Roles of thermodynamics in biochemical engineering
Factors in protein purification
Purification of protein
Thermodynamic modeling of protein separation and precipitation.
Roles
For rational, efficient and rapid
process development and equipment design in bioprocesses.
L(light)=10L/min
H(Heavy)=100L/min
Xo=20g/L X4=0.1g/L
[ Multistage countercurrent liquid extraction of Penicillian-G ]
Organic solvent KD=YL/XH=50
1 stage 2 stage 3 stage 4 stage
Potential role of thermodynamics
Predictions of product behavior
(aggregation, degradation) given T,pH,I
Predictions of chromatographic behavior based on product properties
Prediction of solvent-product interactions
Prediction of two-phase aqueous extraction via equilibrium
Factors affecting protein properties
Ionic Strength
pH
Temperature
Solubility
Organic Solvents
Primary, Secondary, tertiary, quarternary structure
Purification process of protein
Precipitation
Solid-Liquid Equilibria Liquid-Liquid Equilibria
Aqueous two phase system
Polymer-Polymer-protein-Water
Polymer-Salts-protein-Water
Precipitations.
By adding Salts ((NH4)2SO4, Na2SO4)
log S/So = -Ks(I)
(So : solubility of protein at I=0)
By adding Polymers(PEG, DEX) - reducing the amount of water
acting on protein molecules
Aqueous two phase systems(I)
Polymer-Polymer-water-protein system
Phase : PEG(Dextran)
Dilute solution of protein i,j,k…, and salt
Phase : Dextran(PEG)
Dilute solution of protein i,j,k…, and salt
Aqueous two phase systems
Polymer-Salt-water-protein system
Phase : PEG
Dilute solution of protein i,j,k…, and salt
Phase : Phosphate salts
Dilute solution of protein i,j,k…, and salt
Modeling(I) : Salt-Induced Protein Precipitation
Potentials of mean force for aqueous protein-protein interactions
(C.J.Coen et al, 1995)
W(r) = Wdisp(r) + Wq-q(r) (DLVO)
+ Wq-(r) + W-(r)
+ WOA(r)
∞+ − −−
= 2 d 3A 10 2
0 1
2 2
dr 1}4π}
T)/kT]
, a W(r, {exp[
) 2 ,
(
hs NA
B T
a B
) (
1 2
2 2 2
,
2 B c By LALLS R M
Kc
w
+
=
θ
Modeling(I) : Salt-Induced Protein Precipitation
Approach using EOS ( Prausnitz et al, 1996)
Saturated liquid phase
Pure protein phase ( Precipitate)
Saturated liquid phase
Precipitate +
electrolyte + water Assume
LLE
RPA(Random-Phase Approximation) equation of state
=
−
+ +
= +
+
=
=
dr r
r W
U pp 2
3
3 2
ref
ref
) ( 4
η) (1
η η
η ) 1
ρkT ( P
2kT ) ρU
ρkT ( P
ρkT Z P
π
Equation of States approach
Protein-Protein Potential
Wij(r)=Welec(r)+Wdisp(r)+Wosmotic(r)+Wspecific(r)
δ) (σ
0(r
)) (σ
r (σ
ε (r)
W
16σ ] r 4σ
kT)[1 3r (ρ
3 πσ (r) 4
W
r )}
2ln(1 σ r
σ σ
- r { σ 12 (r) H
W
/2) κσ (1
ε 4ππ
)]
σ κ(r (1/r)exp[
e z (r) z
W
ij
ij ij
sp speific
3 s ij, 3 s
ij, s
2 s ij, osmotic
2 2 ij 2
2 ij 2
ij 2
2 ij ij
disp
2 ij r
o
ij 2
j i elec
+
>
=
+
<
<
−
=
+
−
−
=
− +
+
−
=
+
−
= −
δ
Correlation of experimental supernatant phase protein
a)Hen-egg-white lysozyme in ammonium sulfate
b)a-chymotrypsin in ammonium sulfate
Modeling(II) :
Protein-Electrolytes
Adsoprtion lattice model(Baskir, 1987)
+ Pitzer long-range electrostatic term
( Qunhua Peng et al,1995 )
1/2 3/2 x LR x
4
2 σ
2 1
σ 1
*
* 4
ρIx 1
I lnγ 2A
kT
) Δμ n
Δμ (n
kT ) ΔU
Ω ln( Ω kT
g lnγ g
= +
− + +
−
− =
=
Characteristics of Model
Assumptions
► Protein : neutral molecule
► No electrolyte in the
adsorption layers of protein
► No interaction between
proteins
Modeling(III) :
Protein-Polymer/electrolyte
Integral-Equation Theory
(C.A. Haynes et al, 1993)
ij ij
ij ij
ij
d r
r h
d r
kT r
u r
C
<
−
=
>
−
=
+
− +
=
1 )
(
/ ) ( )
(
)dr (r'
|)h r' r
(|
C ρ
(r) C
h
k
r
0
ik kj
k ij
ij
Characteristics of Model
A`Ex = A`Ex,hs+ A`Ex,na+ A`Ex,ic+ A`Ex,cc+ A`Ex,ve
) B , B , m(B m
b, )
c R m(c
) c (c
K'
c M 2B
1 R
Kc
T) , (μ V β
n n RTN
A'
jj ij
ii j
i q
j i
i ii θ w
i
0
i j 0
o
* ij j i Av
EX
i
= +
+ + =
+
=
=
≠ ≠
(for Polymer and protein)
(Cross osmotic second virial coefficients for macromolecules)
Comparison between exp and calc
a) PEG3350-Dextran T70-potassium phosphate
b) PEG3350-Dextran T70-potassium chloride
Conclusion.
현재까지 실제 공정에 적용할 수 있는 정량적인 예측능력을 가진 모델은 없다.
단백질의 상평형을 모사하기 위해서는
계에 존재하는 힘들을 적절하게 묘사하는
항들이 포함되어야 한다.
Lattice fluid를 Bio-separation에 적용하기 위해서는 segment들의 크기를 고려한
항들이 추가되어야 한다.