Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Mechanical measurement system
Reexamination Certificate
2002-11-04
2004-11-02
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Mechanical measurement system
C709S241000, C709S241000, C600S453000
Reexamination Certificate
active
06813569
ABSTRACT:
The present invention relates to an assembly and a method for a correlator structure. More precisely it concerns an assembly and a method for a correlator structure giving direct access to measurement errors such as the variance and the standard deviation.
Correlation and autocorrelation analyses are methods to test for the dependence of signals on each other or on themselves in space or time. Two signals A and B are said to be correlated in space or time if signal A at a certain position or time depends on the value of signal B at a certain distance in space or time from A. That is, if one knows the value of one of the signals A or B one can infer characteristics of the other signal B or A. This analysis is possible not only for different signals and their mutual correlation (cross correlation) but as well for one signal and its correlation with itself (autocorrelation). For instance, if one observes a signal in time, this signal will undergo characteristic fluctuations. These fluctuations will depend on the underlying process or processes that cause these fluctuations. Thus one can gain insight into these processes if one studies the fluctuations. This is typically done by an autocorrelation analysis which will determine the length and number of the fluctuations. A typical example of this is Fluorescence Correlation Spectroscopy (FCS). FCS is an easy to apply optical method which was introduced more than two decades ago (Ehrenberg, M., and Rigler, R. (1974)
Chem. Phys.
4, 390-401; Elson, E. L., and Madge, D. (1974)
Biopolym.
13, 1-27; Madge, D., Elson, E. L., and Webb, W. W. (1974)
Biopolym.
13, 1-27; Ehrenberg, M., and Rigler, R. (1976)
Quart. Rev. Biophys.
9, 69-81) and has been reviewed by several authors (Thompson, N. L. (1991) in
Topics in fluorescence spectroscopy, Volume
1:
Techniques
(Lakowicz, J. R., Ed.) pp 337-378, Plenum Press, New York: Rigler, R., Widengren, J., and Mets, Ü. (1992) in
Fluorescence Spectroscopy
(Wolfbeis, O. S., Ed.) pp 13-24, Springer-Verlag, Berlin/Heidelberg/New York; Widengren, J. (1996) in
Department of Medical Biophysics
, Karolinska Institute, Stockholm, Sweden; Widengren, J., and Rigler, R. (1998)
Cell. Mol. Biol.
44, 857-879).
FCS uses statistical fluctuations in the fluorescence intensity of a small illuminated sample volume, usually a confocal volume element, to obtain information about the processes that provoke these fluctuations. Processes that can be characterized by this method are in general equilibrium fluctuations (e.g. translational and rotational diffusion, reversible chemical reactions, lifetimes of excited states) but can include as well non-equilibrium processes as, for instance; enzymatic reactions (Edman, L., Foldes Papp, Z., Wennmalm, S., and Rigler, R. (1999)
Chem. Phys.
247, 11-22). From these measured parameters information can be obtained about processes that influence these parameters, e.g. oligomerization and aggregation influence the diffusion coefficients of the fluorescent particles and can thus be monitored by this method (e.g. (Rauer, B., Neumann, E., Widengren, J., and Rigler, R. (1996)
Biophys. Chem.
58, 3-12; Schuler, J., Frank, J., Trier, U., Schafer Korting, M., and Saenger, W. A. (1999)
Biochemistry
38, 8402-8408; Wohland, T., Friedrich, K., Hovius, R., and Vogel, H. (1999)
Biochem.
38, 8671-8681). Especially in the last years it has been shown that FCS is a very useful tool in biological research (e.g. (Brock, R., Hink, M., and Jovin, T. (1998)
Biophys. J.
75, 2547-2557; Brock, R., and Jovin, T. M. (1998)
Cell. and Mol. Biol.
44, 847-856; Rigler, R., Pramanik, A., Jonasson, P., Kratz, G., Jansson, O. T., Nygren, P., Stahl, S., Ekberg, K., Johansson, B., Uhlen, S., Uhlen, M., Jornvall, H., and Wahren, J. (1999)
Proc. Natl. Acad. Sci. USA
96, 13318-13323; Schwille, P., Haupts, U., Maiti, S., and Webb, W. W. (1999)
Biophys. J.
77, 2251-2265; Schwille, P., Korlach, J., and Webb, W. W. (1999)
Cytometry
36, 176-182), and that FCS has great potential in industrial applications, especially in high-throughput screening (Rogers, M. V. (1997)
Drug Discovery Today
2, 156-160; Sterrer, S., and Henco, K. (1997)
J Recept Signal Transduct Res
17, 511-520; Auer, M., Moore, K. J., MeyerAlmes, F. J., Guenther, R., Pope, A. J., and Stoeckli, K. A. (1998)
Drug Discovery Today
3, 457-465; Winkler, T., Kettling, U., Koltermann, A., and Eigen, M. (1999)
Proc. Natl. Acad. Sci. USA
96, 1375-1378).
One of the remaining problems is the evaluation of the autocorrelation functions (ACF) measured by FCS. To obtain correct parameter estimations the ACFs have to be fitted with a valid mathematical model. But the decision on the validity of this model and on the quality of the fit depends on detailed knowledge of the accuracy of the particular values in the autocorrelation function (Meseth, U., Wohland, T., Rigler, R., and Vogel, H. (1999)
Biophys. J.
76, 1619-1631). This information is contained in the variance of the measured ACF. Although the statistical accuracy of FCS measurements was treated theoretically and experimentally by several authors (Meseth, U., Wohland, T., Rigler, R., and Vogel, H. (1999)
Biophys. J.
76, 1619-1631; Koppel, D. E. (1974)
Phys. Rev,. A
10, 1938-1945; Qian, H. (1990)
Biophys. Chem.
38, 49-57; Kask, P., Gunther, R., and Axhausen, P. (1997)
Eur. Biophys. J.
25, 163-169)), the variance and standard deviation of the autocorrelation function was neither directly calculated nor measured. Analytical calculations of the variance were done for exponential functions (Koppel, D. E. (1974)
Phys. Rev. A
10, 1938-1945) but are of limited value because most measured autocorrelation functions show non-exponential characteristics (non-exponential dependence is a direct result of the excitation intensity profile which is usually not uniform as assumed for instance in the calculations by Koppel mentioned above (Elson, E. L., and Madge, D. (1974)
Biopolym
13, 1-27). Analytical calculations for a non-exponential dependence is in general not possible because the calculations involve often non-converging integrals and thus numerical solutions have to be found.
The application of fluctuation measurements for the calculation of correlation functions is known from EP 175545. The manipulation of time series is disclosed in U.S. Pat. No. 4,954,981. Nevertheless, none of those document takes into account the necessity of measuring the variance of an ACF online. EP 175545 describes the general method of measuring correlations in a liquid medium but it takes not account of the necessity to calculate the variance of the measurement for an efficient data evaluation. On the other side, U.S. Pat. No. 4,954,981 describes the manipulation of time series but needs these time series completely present in memory and gives no solution for the online calculation of the variance.
Therefore it is of utmost importance to develop a method that can calculate the variance of an autocorrelation function directly from the measurements without any assumptions or conditions on the experiment. To ensure that the method does not compromise the feasibility of the measurement two additional constraints have to be considered:
1) The measurement time and evaluation time should be kept as short as possible to allow the measurement of large sample numbers. 2) The amount of stored data should be as small as possible, so that it can still be easily and quickly managed.
For instance, it is possible to estimate the variance by repeating a measurement several times (for adequate statistics typically at least 10 times), but this automatically increases the measurement times several fold and thus decreases the number of possible measurements by the same factor thus violating the first constraint. The second constraint is important because the variance could be calculated by storing the complete set of intensity data and then evaluating these intensity traces. But this will lead to very large amounts of data that will be difficult to treat, and whose evaluation will take additional time.
As it will be explained fu
Rigler Rudolf H. A.
Vogel Horst
Wohland Thorsten
Barlow John
Cherry Stephen J.
Ecole Polytechnique Federale de Lausanne (EPFL)
Nixon & Vanderhye P.C.
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