Radiant energy – Luminophor irradiation
Reexamination Certificate
1999-06-23
2002-04-23
Hannaher, Constantine (Department: 2878)
Radiant energy
Luminophor irradiation
C250S459100
Reexamination Certificate
active
06376843
ABSTRACT:
This invention relates to the field of fluorescence spectroscopy, and more particularly to a method for determining characteristic physical quantities of fluorescent molecules or other particles present in a sample.
The primary data of an experiment in fluorescence correlation spectroscopy (FCS) is a sequence of photon counts detected from a microscopic measurement volume. An essential attribute of the fluorescence correlation analysis is the calculation of the second order autocorrelation function of photon detection. This is a way how a stochastic function (of photon counts) is transformed into a statistical function having an expected shape, serving as a means to estimate some parameters of the sample. However, the calculation of the autocorrelation function is not the only way for extracting information about the sample from the sequence of photon counts. Further approaches are based on moment analysis and analysis of the distribution of the number of photon counts per given time interval (Qian and Elson, Proc. Natl. Acad. Sci. USA, 87:5479-483, 1990; Qian and Elson, Biophys. J. 57:375-380, 1990).
The intensity of fluorescence detected from a particle within a sample is not uniform but depends on the coordinates of the particle with respect to the focus of the optical system. Therefore, a reliable interpretation of measurements should account for the geometry of the illuminated measurement volume. Even though the calculation of a theoretical distribution of the number of photo counts is more complex for a bell-shaped profile than for a rectangular one, the distribution of the number of photon counts sensitively depends on values of the concentration and the specific brightness of fluorescent species, and therefore, the measured distributions of the number of photon counts can be used for sample analysis. The term
“
specific brightness” denotes the mean count rate of the detector from light emitted by a particle of given species situated in a certain point in the sample, conventionally in the point where the value of the spatial brightness profile function is unity.
The first realization of this kind of analysis was demonstrated on the basis of moments of the photon count number distribution (Qian and Elson, Proc. Natl. Acad. Sci. USA, 87: 5479-483, 1990). The k-th factorial moment of the photon count number distribution P(n) is defined as
F
k
=
∑
n
n
!
(
n
-
k
)
!
P
(
n
)
.
(
1
)
In turn, factorial moments are closely related to factorial cumulants,
F
k
=
∑
l
=
0
k
-
l
C
l
k
-
1
K
k
-
l
F
i
,
or
(
2
)
K
l
=
F
k
-
∑
i
=
1
k
-
1
C
l
k
-
1
K
k
-
l
F
i
.
(
3
)
(C
1
k
s are binomial coefficients, and K
k
s are cumulants). The basic expression used in moment analysis, derived for ideal solutions, relate k-th order cumulant to concentrations (c
1
) and specific brightness values (q
1
).
K
k
=
χ
k
∑
i
c
i
(
q
i
T
)
k
.
(
4
)
Here, X
k
is the k-th moment of the relative spatial brightness profile B(r):
χ
k
=
∫
(
V
)
B
k
(
r
)
ⅆ
V
.
(
5
)
Usually in FCS, the unit of volume and the unit of B are selected which yield X
1
=X
2
=1. After selecting this convention, concentrations in the equations are dimensionless, expressing the mean number of particles per measurement volume, and the specific brightness of any species equals the mean count rate from a particle if situated in the focus divided by the numeric value of B(0). The value of this constant is characteristic of optical equipment. It can be calculated from estimated parameters of the spatial intensity profile (see below). Qian and Elson used experimental values of the first three cumulants to determine unknown parameters of the sample. The number of cumulants which can be reliably determined from experiments is usually three to four. This sets a limit to the applicability of the moment analysis.
The idea behind the so-called fluorescence intensity distribution analysis (FIDA), which has in detail been described in the international patent application PCT/EP 97/05619 (international publication number WO 98/16814), can be well understood by imagining an ideal case when a measurement volume is uniformly illuminated and when there is almost never more than a single particle illuminated at a time, similar to the ideal situation in cell sorters. Under these circumstances, each time when a particle enters the measurement volume, fluorescence intensity jumps to a value corresponding to the brightness of a given type of particles. Naturally, the probability that this intensity occurs at an arbitrary time moment equals the product of the concentration of a given species and the size of the measurement volume. Another fluorescent species which may be present in the sample solution produces intensity jumps to another value characteristic of this other species. In summary, the distribution of light intensity is in a straightforward way determined by the values of concentration and specific brightness of each fluorescent species in the sample solution.
It is assumed that the light intensity reaching the detector from a particle as a function of coordinates of the particle is constant over the whole measurement volume, and zero outside it. Also, it is assumed that the diffusion of a fluorescent particle is negligible during the counting interval T. In this case, the distribution of the number of photon counts emitted by a single fluorescent species can be analytically expressed as double Poissonian: the distribution of the number of particles of given species within this volume is Poissonian, and the conditional probability of the number of detected photons corresponding to a given number of particles is also Poissonian. The double Poissonian distribution has two parameters: the mean number of particles in the measurement volume, c and the mean number of photons emitted by a single particle per dwell time, qT. The distribution of the number of photon counts n corresponding to a single species is expressed as
P
(
n
;
c
,
q
)
=
∑
n
=
0
∞
c
m
m
!
ⅇ
-
c
(
mqT
)
n
n
!
ⅇ
-
mqT
,
(
6
)
where m runs over the number of molecules in the measurement volume. If P
i
(n) denotes the distribution of the number of photon counts from species i, then the resultant distribution P(n) is expressed as
P
(
n
)
=
∑
(
n
1
)
∏
l
P
l
(
n
l
)
δ
(
n
,
∑
i
n
i
)
(
7
)
This means that P(n) can be calculated as a convolution of the series of distribution P
i
(n).
Like in FCS, the rectangular sample profile is a theoretical model which can hardly be applied in experiments. One may divide the measurement volume into a great number of volume elements and assume that within each of them, the intensity of a molecule is constant. Contribution to photon count number distribution from a volume element is therefore double Poissonian with parameters cdV and qTB(r). (Here q denotes count rate from a molecule in a selected standard position where B=1, and B(r) is the spatial brightness profile function of coordinates). The overall distribution of the number of photon counts can be expressed as a convolution integral over double Poissonian distributions. Integration is a one-dimensional rather than a three-dimensional problem here, because the result of integration does not depend on actual positions of volume elements in response to each other. Figuratively, one may rearrange the three-dimensional array of volume elements into a one-dimensional array, for example in the decreasing order of the value of B.
In a number of first experiments described in the international patent application PCT/EP 97/05619, the photon count number distribution was indeed fitted, using the convolution technique. The sample model consisted of twenty spatial sections, each characterized by its volume V
j
and brightness B
j
. However, the technique described in this patent application is slow and inconvenient in cases involving a high number of samples to
Evotec OAI AG
Hannaher Constantine
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