Analysis method for interpreting Taylor dispersion data
View Patent ↗Disclosed is a method for preparing dispersion gradients and an SPR injection method for determining full kinetics and affinity analysis in the presence of a competitor molecule. The SPR injection provides a dispersion gradient of two or more samples to a SPR flow cell and detector.
1. A method for determining the presence of an aggregate form of an analyte in a heterogeneous solution comprising:
identifying at least one monomer of the analyte within said solution and determining a diffusion coefficient (D m ) for said monomer;
determining a total analyte concentration (C tot ) within said solution, said total analyte concentration including both the monomer concentration (C m ) and any aggregate concentration (C a ) present in said solution;
performing SPR analysis on a sample of said solution containing said monomer and aggregate by injecting said sample under Taylor Dispersion conditions using a pulse injection technique;
determining the SPR bulk refractive index response curve under Taylor Dispersion conditions;
using a least squares fitting technique, fit Equation #1a to the SPR bulk refractive index response curve for said sample:
Y
=
2
*
C
m
*
dndc
*
Vi
π
3
/
2
*
d
2
*
k
m
*
t
*
e
-
0.25
*
L
2
*
(
1
-
t
τ
)
2
k
m
*
t
+
2
*
C
a
*
dndc
*
Vi
π
3
/
2
*
d
2
*
k
a
*
t
*
e
-
0.25
*
L
2
*
(
1
-
t
τ
)
2
k
a
*
t
(
Equation
#1
a
)
where
dndc=Refractive Index Increment estimate (RII) of the analyte (typically mL/mg*RU)
V j =sample injection volume (m 3 )
d=tubing diameter (m)
τ=mean analyte residence time=L/u (s)
L=length of tube (m)
u=average velocity of fluid (m/s)
k m =Taylor-Aris dispersion coefficient of the monomer species (m 2 /s)
k a =Taylor-Aris dispersion coefficient of the aggregate species (m 2 /s)
D a =analyte diffusion coefficient of aggregate species (m2/s)
after fitting Equation #1a to the bulk refractive index response curve, thereby providing an approximate C a , solving for D a , wherein when D a does not equal D m provides a positive determination of the presence of an aggregate form of the analyte in said heterogeneous solution.
2. The method of claim 1 , further comprising the step of using a ratio of D m to D a to estimate the number of monomers within said aggregate wherein D m divided by D a equals the average number of monomers in the aggregate form found in said sample.
3. A method for determining the concentration of an aggregate form of an analyte in a heterogeneous solution comprising:
identifying at least one monomer of the analyte within said solution and determining a diffusion coefficient (D m ) for said monomer;
determining a total analyte concentration (C tot ) within said solution, said total analyte concentration including both the monomer concentration (C m ) and any aggregate concentration (C a ) present in said solution;
performing SPR analysis on a sample of said solution containing said monomer and aggregate by injecting said sample under Taylor Dispersion conditions using a pulse injection technique;
determining the SPR bulk refractive index response curve under Taylor Dispersion conditions;
using a least squares fitting technique, fit Equation #1a to the SPR bulk refractive index response curve for said sample:
Y
=
2
*
C
m
*
dndc
*
Vi
π
3
/
2
*
d
2
*
k
m
*
t
*
e
-
0.25
*
L
2
*
(
1
-
t
τ
)
2
k
m
*
t
+
2
*
C
a
*
dndc
*
Vi
π
3
/
2
*
d
2
*
k
a
*
t
*
e
-
0.25
*
L
2
*
(
1
-
t
τ
)
2
k
a
*
t
(
Equation
#1
a
)
where
dndc=Refractive Index Increment estimate (RII) of the analyte (typically mL/mg*RU)
V j =sample injection volume (m 3 )
d=tubing diameter (m)
τ=mean analyte residence time=L/u (s)
L=length of tube (m)
u=average velocity of fluid (m/s)
k m =Taylor-Aris dispersion coefficient of the monomer species (m 2 /s)
k a =Taylor-Aris dispersion coefficient of the aggregate species (m 2 /s)
D a =analyte diffusion coefficient of aggregate species (m2/s)
after fitting Equation #1a to the bulk refractive index response curve, calculating the D a and C a for said aggregate within said sample.
4. The method of claim 3 , further comprising the step of using a ratio of D m to D a to estimate the number of monomers within said aggregate wherein D m divided by D a equals the average number of monomers in the aggregate form found in said sample.
5. A method for determining the presence of an aggregate form of an analyte in a heterogeneous solution comprising:
identifying at least one monomer of the analyte within said solution and determining a diffusion coefficient (D m ) for said monomer;
determining a total analyte concentration (C tot ) within said solution, said total analyte concentration including both the monomer concentration (C m ) and any aggregate concentration (C a ) present in said solution;
performing SPR analysis on a sample of said solution, said sample having a combined concentration of said monomer and aggregate of at least 0.05 mg/ml, by injecting said sample under Taylor Dispersion conditions using a pulse injection technique;
determining the SPR bulk refractive index response curve under Taylor Dispersion conditions;
using a least squares fitting technique, fit Equation #1a to the SPR bulk refractive index response curve for said sample:
Y
=
2
*
C
m
*
dndc
*
Vi
π
3
/
2
*
d
2
*
k
m
*
t
*
e
-
0.25
*
L
2
*
(
1
-
t
τ
)
2
k
m
*
t
+
2
*
C
a
*
dndc
*
Vi
π
3
/
2
*
d
2
*
k
a
*
t
*
e
-
0.25
*
L
2
*
(
1
-
t
τ
)
2
k
a
*
t
(
Equation
#1
a
)
where
dndc=Refractive Index Increment estimate (RII) of the analyte (typically mL/mg*RU)
V j =sample injection volume (m 3 )
d=tubing diameter (m)
τ=mean analyte residence time=L/u (s)
L=length of tube (m)
u=average velocity of fluid (m/s)
k m =Taylor-Aris dispersion coefficient of the monomer species (m 2 /s)
k a =Taylor-Aris dispersion coefficient of the aggregate species (m2/s)
D a =analyte diffusion coefficient of aggregate species (m2/s)
after fitting Equation #1a to the bulk refractive index response curve, thereby providing an approximate C a , solving for D a , wherein when D a does not equal D m provides a positive determination of the presence of an aggregate form of the analyte in said heterogeneous solution.
6. The method of claim 5 , further comprising the step of using a ratio of D m to D a to estimate the number of monomers within said aggregate wherein D m divided by D a equals the average number of monomers in the aggregate form found in said sample.
7. A method for determining the concentration of an aggregate form of an analyte in a heterogeneous solution comprising:
identifying at least one monomer of the analyte within said solution and determining a diffusion coefficient (D m ) for said monomer;
determining a total analyte concentration (C tot ) within said solution, said total analyte concentration including both the monomer concentration (C m ) and any aggregate concentration (C a ) present in said solution;
performing SPR analysis on a sample of said solution, said sample having a combined concentration of said monomer and aggregate of at least 0.05 mg/ml, by injecting said sample under Taylor Dispersion conditions using a pulse injection technique;
determining the SPR bulk refractive index response curve under Taylor Dispersion conditions;
using a least squares fitting technique, fit Equation #1a to the SPR bulk refractive index response curve for said sample:
Y
=
2
*
C
m
*
dndc
*
Vi
π
3
/
2
*
d
2
*
k
m
*
t
*
e
-
0.25
*
L
2
*
(
1
-
t
τ
)
2
k
m
*
t
+
2
*
C
a
*
dndc
*
Vi
π
3
/
2
*
d
2
*
k
a
*
t
*
e
-
0.25
*
L
2
*
(
1
-
t
τ
)
2
k
a
*
t
(
Equation
#1
a
)
where
dndc=Refractive Index Increment estimate (RII) of the analyte (typically mL/mg*RU)
V j =sample injection volume (m 3 )
d=tubing diameter (m)
τ=mean analyte residence time=L/u (s)
L=length of tube (m)
u=average velocity of fluid (m/s)
k m =Taylor-Aris dispersion coefficient of the monomer species (m 2 /s)
k a =Taylor-Aris dispersion coefficient of the aggregate species (m 2 /s)
D a =analyte diffusion coefficient of aggregate species (m2/s)
after fitting Equation #1a to the bulk refractive index response curve, calculating the D a and C a for said aggregate within said sample.
8. The method of claim 7 , further comprising the step of using a ratio of D m to D a to estimate the number of monomers within said aggregate wherein D m divided by D a equals the average number of monomers in the aggregate form found in said sample.
9. A method for determining the presence of an aggregate form of an analyte in a heterogeneous solution comprising:
identifying at least one monomer of the analyte within said solution and determining a diffusion coefficient (D m ) for said monomer;
determining a total analyte concentration (C tot ) within said solution, said total analyte concentration including both the monomer concentration (C m ) and any aggregate concentration (C a ) present in said solution;
performing SPR analysis on a sample of said solution containing said monomer and aggregate by injecting said sample under Taylor Dispersion conditions using a sigmoid injection technique;
determining the SPR bulk refractive index response curve under Taylor Dispersion conditions;
using a least squares fitting technique, fit Equation #2a to the SPR bulk refractive index response curve for said sample:
Y
=
C
m
*
dndc
2
*
[
1
-
erf
1
-
t
τ
2
k
m
uL
*
t
τ
]
+
C
a
*
dndc
2
*
[
1
-
erf
1
-
t
τ
2
k
a
uL
*
t
τ
]
(
Equation
#2
a
)
where
dndc=RII Refractive Index Increment estimate (RII) of the analyte (typically mL/mg*RU)
erf=Gauss error function
d=tubing diameter (m)
τ=mean analyte residence time=L/u (s)
L=length of tube (m)
u=average velocity of fluid (m/s)
k m =Taylor-Aris dispersion coefficient of the monomer species (m 2 /s)
k a =Taylor-Aris dispersion coefficient of the aggregate species (m 2 /s)
D a =analyte diffusion coefficient of aggregate species (m2/s)
after fitting Equation #1a to the bulk refractive index response curve, thereby providing an approximate C a , solving for D a , wherein when D a does not equal D m provides a positive determination of the presence of an aggregate form of the analyte in said heterogeneous solution.
10. The method of claim 9 , further comprising the step of using a ratio of D m to D a to estimate the number of monomers within said aggregate wherein D m divided by D a equals the average number of monomers in the aggregate form found in said sample.
11. A method for determining the presence of an aggregate form of an analyte in a heterogeneous solution comprising:
identifying at least one monomer of the analyte within said solution and determining a diffusion coefficient (D m ) for said monomer;
determining a total analyte concentration (C tot ) within said solution, said total analyte concentration including both the monomer concentration (C m ) and any aggregate concentration (C a ) present in said solution;
performing SPR analysis on a sample of said solution containing said monomer and aggregate by injecting said sample under Taylor Dispersion conditions using a sigmoid injection technique;
determining the SPR bulk refractive index response curve under Taylor Dispersion conditions;
using a least squares fitting technique, fit Equation #1a to the SPR bulk refractive index response curve for said sample:
Y
=
C
m
*
dndc
2
*
[
1
-
erf
1
-
t
τ
2
k
m
uL
*
t
τ
]
+
C
a
*
dndc
2
*
[
1
-
erf
1
-
t
τ
2
k
a
uL
*
t
τ
]
(
Equation
#1
a
)
where
dndc=Refractive Index Increment estimate (RII) of the analyte (typically mL/mg*RU)
erf=Gauss error function
d=tubing diameter (m)
τ=mean analyte residence time=L/u (s)
L=length of tube (m)
u=average velocity of fluid (m/s)
k m =Taylor-Aris dispersion coefficient of the monomer species (m 2 /s)
k a =Taylor-Aris dispersion coefficient of the aggregate species (m 2 /s)
D a =analyte diffusion coefficient of aggregate species (m2/s)
after fitting Equation #1a to the bulk refractive index response curve, calculating the D a and C a for said aggregate within said sample.
12. The method of claim 11 , further comprising the step of using a ratio of D m to D a to estimate the number of monomers within said aggregate wherein D m divided by D a equals the average number of monomers in the aggregate form found in said sample.
13. A method for determining the presence of an aggregate form of an analyte in a heterogeneous solution comprising:
identifying at least one monomer of the analyte within said solution and determining a diffusion coefficient (D m ) for said monomer;
determining a total analyte concentration (C tot ) within said solution, said total analyte concentration including both the monomer concentration (C m ) and any aggregate concentration (C a ) present in said solution;
performing SPR analysis on a sample of said solution, said sample having a combined concentration of said monomer and aggregate of at least 0.05 mg/ml, by injecting said sample under Taylor Dispersion conditions using a sigmoid injection technique;
determining the SPR bulk refractive index response curve under Taylor Dispersion conditions;
using a least squares fitting technique, fit Equation #1a to the SPR bulk refractive index response curve for said sample:
Y
=
C
m
*
dndc
2
*
[
1
-
erf
1
-
t
τ
2
k
m
uL
*
t
τ
]
+
C
a
*
dndc
2
*
[
1
-
erf
1
-
t
τ
2
k
a
uL
*
t
τ
]
(
Equation
#1
a
)
where
dndc=Refractive Index Increment estimate (RII) of the analyte (typically mL/mg*RU)
erf=Gauss error function
d=tubing diameter (m)
τ=mean analyte residence time=L/u (s)
L=length of tube (m)
u=average velocity of fluid (m/s)
k m =Taylor-Aris dispersion coefficient of the monomer species (m 2 /s)
k a =Taylor-Aris dispersion coefficient of the aggregate species (m 2 /s)
D a =analyte diffusion coefficient of aggregate species (m2/s)
after fitting Equation #1a to the bulk refractive index response curve, thereby providing an approximate C a , solving for D a , wherein when D a does not equal D m provides a positive determination of the presence of an aggregate form of the analyte in said heterogeneous solution.
14. The method of claim 13 , further comprising the step of using a ratio of D m to D a to estimate the number of monomers within said aggregate wherein D m divided by D a equals the average number of monomers in the aggregate form found in said sample.
15. A method for determining the presence of an aggregate form of an analyte in a heterogeneous solution comprising:
identifying at least one monomer of the analyte within said solution and determining a diffusion coefficient (D m ) for said monomer;
determining a total analyte concentration (C tot ) within said solution, said total analyte concentration including both the monomer concentration (C m ) and any aggregate concentration (C a ) present in said solution;
performing SPR analysis on a sample of said solution, said sample having a combined concentration of said monomer and aggregate of at least 0.05 mg/ml, by injecting said sample under Taylor Dispersion conditions using a sigmoid injection technique;
determining the SPR bulk refractive index response curve under Taylor Dispersion conditions;
using a least squares fitting technique, fit Equation #1a to the SPR bulk refractive index response curve for said sample:
Y
=
C
m
*
dndc
2
*
[
1
-
erf
1
-
t
τ
2
k
m
uL
*
t
τ
]
+
C
a
*
dndc
2
*
[
1
-
erf
1
-
t
τ
2
k
a
uL
*
t
τ
]
(
Equation
#1
a
)
where
dndc=Refractive Index Increment estimate (RII) of the analyte (typically mL/mg*RU)
erf=Gauss error function
d=tubing diameter (m)
τ=mean analyte residence time=L/u (s)
L=length of tube (m)
u=average velocity of fluid (m/s)
k m =Taylor-Aris dispersion coefficient of the monomer species (m 2 /s)
k a =Taylor-Aris dispersion coefficient of the aggregate species (m 2 /s)
D a =analyte diffusion coefficient of aggregate species (m2/s)
after fitting Equation #1a to the bulk refractive index response curve, calculating the D a and C a for said aggregate within said sample.
16. The method of claim 15 , further comprising the step of using a ratio of D m to D a to estimate the number of monomers within said aggregate wherein D m divided by D a equals the average number of monomers in the aggregate form found in said sample.