Cross-talk correction in multiplexing analysis of biological sample
A method for determining fluorescence values {φ i spe } i∈{1, 2, . . . , I} of a set of I fluorescent microparticles {μP i } i∈{1, 2, . . . , I} of a multiplexed analysis, the microparticles being in a monolayer arrangement, includes acquiring a digital fluorescence image of the set of fluorescent microparticles {μP i } i∈{1, 2, . . . , I} ; and computing, for each fluorescent microparticle μP i in the set of fluorescent microparticles {μP i } i∈{1, 2, . . . , I} , a fluorescence value φ i meas based only on pixels of the acquired image corresponding to said fluorescent microparticle μP i . The method includes computing the fluorescence value φ i spe of the fluorescent microparticle μP i by correcting its first fluorescence φ i meas by a cross-talk fluorescence contribution φ i cross in the first fluorescence φ i meas from other fluorescent microparticles {μP j } j≠i in the set of fluorescent microparticles {μP i } i∈{1, 2, . . . , I} .
1. A method for determining fluorescence values {φ i spe } i∈{1, 2, . . . I} of a set of I fluorescent microparticles {μP i } i∈{1, 2, . . . I} of a multiplexed analysis configured to detect multiple fluorescently labeled biomarkers, said microparticles being in a monolayer arrangement and encoded in silicon micro-disks carrying a binary code, the method comprising:
acquiring a digital fluorescence image of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . I} ;
computing, for each fluorescent encoded microparticle μP i in the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . I} , a fluorescence value φ i meas based only on pixels of the acquired image corresponding to said fluorescent encoded microparticle μP i , and
obtaining the fluorescence value φ i spe of said fluorescent encoded microparticle μP i using each fluorescence values φ i meas ;
wherein the method comprises computing the fluorescence value φ i spe of said fluorescent encoded microparticle μP i by correcting its first fluorescence φ i meas by a cross-talk fluorescence contribution φ i cross , wherein the cross-talk fluorescence contribution φ i cross is modeled as a sum of individual contributions, each having an isotropic decay profile:
φ
i
cross
=
∑
j
≠
i
(
α
i
j
·
φ
j
spe
)
wherein:
α ij is a unitary cross-talk fluorescence contribution in the first fluorescence φ i meas of the j th fluorescent microparticle μP j depending only on the distance d i,j between microparticles μP i and μP i and predetermined parameters that are identical whatever the microparticles,
the j th set of encoded microparticles is a subset created from the set of encoded microparticles {μP i }iε{1, 2, . . . , I} other than μP i , and
φ i spe is the fluorescence of the j th fluorescent encoded microparticle μP j .
2. A method as claimed in claim 1 , wherein the computation of the fluorescence value φ i spe comprises:
computing a position X i in the digital fluorescence image for each fluorescent encoded microparticle μP i in the set of fluorescent encoded microparticles {μP i } i∈{1, 2 . . . , I} ;
modelling the first fluorescence value φ i meas as a function of the positions {X i } i∈{1, . . . , I} and fluorescence values {φ i spe } i∈{1, . . . I} of all fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I}; and
computing the inverse of said function to obtain the fluorescence value φ i spe .
3. A method as claimed in claim 1 , wherein the method comprises:
computing the distance d i,j between the i th and the j th fluorescent encoded microparticles in the digital fluorescence image;
for each couple of encoded microparticles (μP i , μP j ) in the set of I fluorescent encoded microparticles, computing the unitary cross-talk fluorescence contribution α ij of said couple (μP i , μP j ) based on the distance d i,j ;
computing the fluorescences {φ i spe } i∈{1, 2, . . . , I} of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} based on the following relationship:
(
φ
1
spe
φ
2
spe
⋮
φ
I
-
1
spe
φ
I
spe
)
=
(
1
α
12
⋯
α
1
(
I
-
1
)
α
1
I
α
21
1
⋯
α
2
(
I
-
1
)
α
2
I
⋮
⋯
⋱
⋯
⋮
α
(
I
-
1
)
1
α
(
I
-
1
)
2
⋯
1
α
(
I
-
1
)
I
α
I
1
α
I
2
⋯
α
I
(
I
-
1
)
1
)
-
1
(
φ
1
meas
φ
2
meas
⋮
φ
I
-
1
meas
φ
I
meas
)
.
4. A method as claimed in claim 1 , wherein each fluorescent encoded microparticle μP i of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} comprises an identifier Id m (i) of a set of M different unique identifiers {id m } m∈{1, 2, . . . , M} , said identifiant Id M (i) being readable through processing of a digital image of said fluorescent encoded microparticle μP i , and in that the method further comprises:
acquiring a digital image of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} ;
reading the identifier Id m (i) of each encoded microparticle μP i in the digital image; and
for each identifier Id m of the set of M different unique identifiers {id m } m∈{1, 2, . . . , M} , computing an aggregate fluorescence φ m ag based on the fluorescences φ i spe of the fluorescent encoded microparticles comprising said identifiant.
5. A method as claimed in claim 4 , wherein each fluorescent encoded microparticle μP i of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} comprises a surface coated with fluorescent complexes uniquely associated to the identifier Id m (i) of said fluorescent encoded microparticle μP i , said complexes comprising first non-fluorescent molecules fixed to the encoded microparticles and second fluorescent molecules bound to the first non-fluorescent molecules.
6. A method as claimed in claim 5 , wherein the encoded microparticles have equal dimension.
7. A method as claimed in claim 5 , wherein the method comprises:
prior to acquiring the digital fluorescence image of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} ;
disposing in a channel the microparticles without any second fluorescent molecules bound to the first non-fluorescent molecules, so as to arrange the microparticles in a monolayer; and
filling the channel with a liquid sample,
computing concentration of second fluorescent molecules in the sample based on the aggregate fluorescences φ m ag .
8. A system for determining fluorescences {φ i spe } i∈{1, 2, . . . , I} of a set of I fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} being encoded in silicon micro-disks carrying a binary code comprising:
at least one channel for receiving the set of I fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} in a monolayer arrangement;
an acquisition unit for acquiring a digital fluorescent image of the monolayer arrangement of the set fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} in the channel;
a computing unit for computing the fluorescences {φ i spe } i∈{1, 2, . . . , I} based on the acquired digital fluorescent image, the computing unit computing a first fluorescence φ i meas based only on pixels of the acquired digital fluorescent image corresponding to said fluorescent encoded microparticle μP i , said computing unit being configured to obtain the fluorescence value φ i spe of a fluorescent encoded microparticle μP i using each fluorescence values φ i meas ;
wherein the computing unit computes, for each fluorescent encoded microparticle μP i in the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} :
a cross-talk fluorescence contribution φ i cross , wherein the cross-talk fluorescence contribution φ i cross is modeled as a sum of individual contributions, each having an isotrpic decay profile, based on the following relationship:
φ
i
cross
=
∑
j
≠
i
(
α
i
j
·
φ
j
spe
)
wherein:
α ij is a unitary cross-talk fluorescence contribution in the first fluorescence φ i meas of the j th fluorescent microparticle μP j depending only on the distance d i,j between microparticles μP i and μP j and predetermined parameters that are identical whatever the microparticles,
the j th set of encoded microparticles is a subset created from the set of encoded microparticles {μP i }iε{1, 2, . . . , I} other than μP i , and φ j spe is the fluorescence of the j th fluorescent encoded microparticle μP i ; and
the fluorescence φ i spe of said fluorescent encoded microparticle μP i by correcting its first fluorescence φ i meas by the cross-talk fluorescence contribution φ i cross .
9. A system as claimed in claim 8 , wherein the computing unit computes the fluorescence value φ i spe by:
computing a position X i in the digital fluorescence image for each fluorescent encoded microparticle μP i in the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} ;
modelling the first fluorescence value φ i meas as a function of the positions {X i } i∈{1, . . . , I} and fluorescence values {φ i spe } i∈{1, . . . , I} of all fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} ; and
computing the inverse of said function to obtain the fluorescence value φ i spe .
10. A system as claimed in claim 8 , wherein the computing unit:
computes the distance d i,j between the i th and the j th fluorescent encoded microparticles in the digital fluorescence image;
for each couple of encoded microparticles (μP i , μP j ) in the set of I fluorescent encoded microparticles, computes the unitary cross-talk fluorescence contribution α ij of said couple (μP i , μP j ) based on the distance d i,j ;
computes the fluorescences {φ i spe } i∈{1, 2, . . . , I} of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} based on the following relationship:
(
φ
1
spe
φ
2
spe
⋮
φ
I
-
1
spe
φ
I
spe
)
=
(
1
α
12
⋯
α
1
(
I
-
1
)
α
1
I
α
21
1
⋯
α
2
(
I
-
1
)
α
2
I
⋮
⋯
⋱
⋯
⋮
α
(
I
-
1
)
1
α
(
I
-
1
)
2
⋯
1
α
(
I
-
1
)
I
α
I
1
α
I
2
⋯
α
I
(
I
-
1
)
1
)
-
1
(
φ
1
meas
φ
2
meas
⋮
φ
I
-
1
meas
φ
I
meas
)
.
11. A system as claimed in claim 8 , wherein each fluorescent encoded microparticle μP i of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} comprises an identifier Id m (i) of a set of M different unique identifiers {id m } m∈{1, 2, . . . , M} said identifiant Id M (i) being readable through processing of a digital image of said fluorescent encoded microparticle μP i , and in that the computing unit:
acquires a digital image of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} ;
reads the identifier Id m (i) of each encoded microparticle μP i in the digital image; and
for each identifier Id m of the set of M different unique identifiers {id m } m∈{1, 2, . . . , M} computes an aggregate fluorescence φ m ag based on the fluorescences φ i spe of the fluorescent encoded microparticles comprising said identifiant.
12. A system as claimed in claim 11 , wherein each fluorescent encoded microparticle of the set of fluorescent encoded microparticles {μP i } i∈{1, 2, . . . , I} comprises a surface coated with fluorescent complexes uniquely associated to the identifier Id m (i) of said fluorescent encoded microparticle said complexes comprising first non-fluorescent molecules fixed to the encoded microparticles and second fluorescent molecules bound to the first non-fluorescent molecules.
13. A system as claimed in claim 12 , wherein the encoded microparticles have equal dimension.