Methods for normalization of experimental data

Methods for normalization of experimental data with experiment-to-experiment variability. The experimental data may include biotechnology data or other data where experiment-to-experiment variability is introduced by an environment used to conduct multiple iterations of the same experiment. Deviations in the experimental data are measured between a central character and data values from multiple indexed data sets. The central character is a value of an ordered comparison determined from the multiple indexed data sets. The central character includes zero-order and low order central characters. Deviations between the central character and the multiple indexed data sets are removed by comparing the central character to the measured deviations from the multiple indexed data sets, thereby reducing deviations between the multiple indexed data sets and thus reducing experiment-to-experiment variability. Preferred embodiments of the present invention may be used to reduce intra-experiment and inter-experiment variability. When experiment-to-experiment variability is reduced or eliminated, comparison of experimental results can be used with a higher degree of confidence. Experiment-to-experiment variability is reduced for biotechnology data with new methods that can be used for bioinformatics or for other types of experimental data that are visual displayed (e.g., telecommunications data, electrical data for electrical devices, optical data, physical data, or other data). Experimental data can be consistently collected, processed and visually displayed with results that are accurate and not subject to experiment-to-experiment variability. Thus, intended experimental goals or results (e.g., determining polynucleotide sequences such as DNA, cDNA, or mRNA sequences) may be achieved in a more efficient and effective manner.

FIELD OF THE INVENTION
 This invention relates to normalizing experimental data. More specifically,
 it relates to methods for normalizing experimental data, such as
 biotechnology data, to reduce experiment-to-experiment variability.
 BACKGROUND OF THE INVENTION
 Biotechnology data is collected and analyzed for many diverse purposes. As
 is known in the art, biotechnology data typically includes data obtained
 from biological systems, biological processes, biochemical processes,
 biophysical processes, or chemical processes. For example, sequences of
 deoxyribonucleic acid ("DNA") from many different types of living
 organisms are often determined and mapped. DNA is double-stranded
 polynucleotide including a continuous string of four nucleotide base
 elements. The four nucleotide base elements include deoxyadenosine,
 deoxycytidine, deoxyguanosine, and deoxythymidine. The four nucleotide
 bases are usually abbreviated as "A," "C," "G" and "T" respectively. DNA
 is used to make ribonucleic acid ("RNA"), which in turn is used to make
 proteins. "Genes" include regions of DNA that are transcribed into RNA,
 which encodes a translated protein.
 One fundamental goal of biochemical research is to map and characterize all
 of the protein molecules from genes in a living organism. The existence
 and concentration of protein molecules typically help determine if a gene
 is "expressed" or "repressed" in a given situation. Protein
 characterization includes, identification, sequence determination,
 expression, characteristics, concentrations and biochemical activity.
 Responses of proteins to natural and artificial compounds are used to
 develop new treatments for diseases, improve existing drugs, develop new
 drugs and for other medical and scientific applications.
 Biotechnology data is inherently complex. For example, DNA sequences
 include large numbers of A's, C's, G's and T's, that need to be stored and
 retrieved in a manner that is appropriate for analysis. There are a number
 of problems associated with collecting, processing, storing and retrieving
 biotechnology data using "bioinformatics" techniques known in the art. As
 is known in the art, bioinformatics is the systematic development and
 application of information technologies and data mining techniques for
 processing, analyzing and displaying data obtained by experiments,
 modeling, database searching and instrumentation to make observations
 about biological processes. Biotechnology data is commonly presented as
 graphical plots of two or more variables. A "peak," i.e., a local maximum
 in a plot of two or more variables, is often a feature of interest in
 biotechnology data.
 When biotechnology data is collected, the collection process often
 introduces variability based on an environment used to conduct the
 experiment. For example, DNA sequences may be determined by processing
 samples using gel-electrophoresis. A label (e.g., a dye) is incorporated
 into the samples placed on gel-plates for detection by laser-induced
 fluorescence.
 Gel-electrophoresis resolves molecules from the samples into distinct bands
 of measurable lengths on a gel plate. Gel-plates created with different
 batches of the same gel may be used to complete the same experiment, with
 the same target (e.g., the same polynucleotide sample), multiple times.
 All of the experiments should ideally yield the same results, since the
 same target is used in the same experiment. However, the
 gel-electrophoresis process typically introduces small errors in the
 biotechnology data due to variability in the gel-electrophoresis process.
 For example, a gel may have been prepared by two different lab technicians,
 may have come from two packages of the same product, may have been
 purchased at different times, or may be applied to gel-plates at slightly
 different consistency or thickness, either by a lab technician or by with
 an automated process (e.g., a robot), etc. These factors and other factors
 typically introduce "experiment-to-experiment variability" into an
 experiment completed multiple times that ideally should yield exactly the
 same results.
 Another problem is that biotechnology data is also collected with
 micro-arrays. Micro-arrays can also be used to provide sequence
 information instead of gel-electrophoresis. Micro-arrays may also
 introduce variability into the same experiment due to variations in sample
 preparation for the micro-arrays. Yet another problem is that
 biotechnology data that is data collected with experiment-to-experiment
 variability typically only grossly appropriate for visual display using
 bioinformatics techniques known in the art.
 As is known in the art, one of the most commonly used methodologies in
 biotechnology is "comparison." Many biological objects are associated with
 families that share the same structural or functional features. For
 example, many proteins with a similar sequence may have common
 functionality. If a protein with a sequence similar to a known protein is
 located, the located protein may have a common functionality, and thus may
 have a common response to an environmental condition (e.g., a new drug).
 Visual display of biotechnology data is typically recognized as typically
 being "necessary" for biotechnology research. Visual display tools allow
 creation of complex views of large amounts of inter-related data.
 Experimental data is typically displayed using a Graphical User Interface
 ("GUI") that may include a multiple windowed-display on a computer
 display.
 Visual display and comparative analysis is typically hampered by
 variability introduced into experimental data. For example, if five
 iterations of the same experiment with the same target are visually
 displayed, the output values should ideally be superimposed on one
 another. However, due to experiment-to-experiment variability, the output
 values for the five iterations of the experiment typically will differ
 slightly and a visual display will tend to "magnify"
 experiment-to-experiment variability. This may lead to confusion during
 analysis and cause a user to lose confidence in a process used to collect
 and display experimental data.
 In addition, in many instances, experiment-to-experiment variability is of
 a same order of magnitude as desired experimental results. Using visual
 display of experimental results with experiment-to-experiment variability,
 a user may not be able to determine if differences in results are due to a
 new target (e.g., a new polynucleotide sequence) or
 experiment-to-experiment variability.
 Thus, it is desirable to reduce experiment-to-experiment variability in
 data obtained from experiments. The reduction of experiment-to-experiment
 variability should allow visual display and comparative analysis to be
 completed without confusion or loss of confidence in processes used to
 collect, process and display experimental data.
 SUMMARY OF THE INVENTION
 In accordance with preferred embodiments of the present invention, some of
 the problems associated with experiment-to-experiment variability in
 experimental data are overcome. Methods for normalization of experimental
 data are provided. One aspect of the invention includes a method for data
 normalization of multiple data sets of experimental data. Multiple sets of
 experimental data are indexed with one or more indices to create multiple
 indexed data sets. However, other data organization schemes could also be
 used and the present invention is not limited to indexing multiple data
 sets. Deviations are measured between a determined central character and
 data values from the multiple indexed data sets. In one exemplary
 preferred embodiment of the present invention, the determined central
 character is a value for an ordered comparison determined from the
 multiple indexed data sets. Deviations between the determined central
 character and the multiple indexed data sets are removed by comparing the
 determined central character to the measured deviations from the multiple
 indexed data sets, thereby reducing deviations between the multiple
 indexed data sets and thus reducing experiment-to-experiment variability.
 Another aspect of the invention includes applying a central character
 normalization transform to data values from the multiple indexed data sets
 to utilize data information across indices from multiple indexed data
 sets. The normalization transform is applied before the determined central
 character is used to remove deviations from the multiple indexed data
 sets. The normalization transform includes, but is not limited to, for
 example, zero-order normalization transformations and low-order
 normalization transformations. Yet another aspect of the present invention
 includes a method for creating a zero-order central character from
 multiple indexed data sets. The zero-order central character is typically
 a data-value-independent constant. Yet another aspect of the present
 invention includes creating a low-order central character from multiple
 indexed data sets. The low-order central character is typically a
 data-value-dependent smoothly ranging scaling function.
 Preferred embodiments of the present invention may be used to reduce
 experiment-to-experiment variability. Experimental data may then be
 consistently collected, processed and visually displayed with a higher
 degree of confidence that obtained results are accurate and include
 reduced experiment-to-experiment variability. Thus, intended experimental
 goals or results (e.g., determining a new polynucleotide sequence) may be
 achieved in a quicker, and a cost effective manner with reduced
 experiment-to-experiment variability.
 In one exemplary preferred embodiment of the present invention, new methods
 that can be used for bioinformatics, are used to reduce
 experiment-to-experiment variability of biotechnology data. However,
 preferred embodiments of the present invention are not limited to reducing
 experiment-to-experiment variability for biotechnology data. The present
 invention may also be used to reduce experiment-to-experiment variably in
 other types of experimental data, including but not limited to,
 telecommunications data, electrical data, optical data, physical data, or
 other experimental data with experiment-to-experiment variability due to
 an environment used to conduct experiments.
 The foregoing and other features and advantages of preferred embodiments of
 the present invention will be more readily apparent from a detailed
 description that follows. The detailed description proceeds with
 references to the accompanying drawings.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
 In one exemplary preferred embodiment of the present invention,
 biotechnology data for simultaneous sequence-specific identification of
 expressed genes is processed with the methods and system described
 herewith. However, the present invention is not limited to processing
 biotechnology data, and methods and system described herein can be used to
 process other data (e.g., telecommunications data, electrical data,
 optical data, physical data, other data, etc.).
 Gene Mapping
 As was discussed above, deoxyribonucleic acid ("DNA") is a double-stranded
 heteropolymer that can be thought of symbolically as a continuous string
 of four nucleotide base elements, deoxyadenosine, deoxycytidine,
 deoxyguanosine, and deoxythymidine. The four bases are usually abbreviated
 as "A," "C," "G" and "T" respectively, and base elements on one strand of
 DNA interact with a counterpart on the other strand. For example, an "A"
 can only interact with a "T," and a "G" can only interact with a "C." This
 relationship is called "base pairing."
 "Genes" are regions of DNA, and "proteins" are the products of genes.
 Proteins are built from a fundamental set of amino acids, and DNA carries
 amino-acid coding information. When DNA is replicated or copied, a new DNA
 strand is synthesized using each of the original strands as templates.
 DNA itself does not act as a template for protein decoding or synthesizing.
 A complementary copy of one of the two strands of DNA is synthesized out
 of ribose nucleotides to generate a ribonucleic acid ("RNA") copy of a
 gene with a method called "transcription." The RNA copy of a gene is then
 decoded by protein synthesis with a method called "translation." Since the
 RNA carries protein codes, it is called messenger RNA ("mRNA"). The
 transcription of mRNA is very precise and always starts at one precise
 nucleotide and ends exactly at another. Complementary DNA ("cDNA") is an
 exact, double-stranded DNA copy of mRNA. One of the cDNA strands is
 complementary to the mRNA, and other is identical.
 There are many techniques known in the biotechnology arts to identify RNA
 species including those described in "Differential display of eukaryotic
 messenger RNA by means of polymerase chain reaction," by P. Liang and A.
 B. Pardee, Science, Vol. 257, pages 967-971, 1992; "Arbitrarily primed PCR
 fingerprinting of RNA," by J. Welsh, K. Chada, S. S. Dalal, R. Cheng, D.
 Ralph and M. McCelland, Nucleic Acids Research, Vol. 20, pages 4965-4970,
 1992; "A simple and very efficient method for generating cDNA libraries,"
 Gene, Vol. 25, pages 263-269, 1983; "Tissue-specific expression of mouse
 .alpha.-amylase genes," by K. Schibler, M. Tosi, A. C. Pittet, L. Fabiani
 and P. K. Wellauer, Journal of Molecular Biology, Vol. 142, pages 93-116,
 1990; "Discovering the secrets of DNA," by P. Friedland and L. H. Kedes,
 Communications of the Association for Computing Machinery ("CACM"), Vol.
 28, No. 11, pages 1164-1186, November 1985; and others.
 RNA isolated from a target organism (e.g., a cell to which a new drug has
 been applied) is analyzed using a method of simultaneous sequence-specific
 identification of mRNAs. In one preferred embodiment of the present
 invention, simultaneous sequence-specific identification of mRNAs is
 provided with a TOtal Gene expression Analysis method ("TOGA"), described
 in U.S. Pat. No. 5,459,037 and U.S. Pat. No. 5,807,680, incorporated
 herein by reference. However, other methods can also be used to provide
 sequence-specific identification of mRNAs, and the present invention is
 not limited to TOGA sequence-specific identification of mRNAs.
 In one preferred embodiment of the present invention, preferably, prior to
 the application of the TOGA method or other methods, the isolated RNA is
 enriched to form a starting polyA-containing mRNA population by methods
 known in the art. In such a preferred embodiment, the TOGA method further
 comprises an additional Polymerase Chain Reaction ("PCR") step performed
 using one of four 5' PCR primers and cDNA templates prepared from a
 population of antisense complementary RNA ("cRNA"). A final PCR step using
 one of a possible 256 5' PCR primers and a universal 3' PCR primer
 produces as PCR products, cDNA fragments that corresponded to a 3'-region
 of the starting mRNA population.
 A label (e.g., a dye) is incorporated in the PCR products to permit
 detection of the PCR products by laser-induced fluorescence.
 Gel-electrophoresis or equivalent techniques are used to resolve molecules
 from the PCR products into distinct bands of measurable lengths (See,
 e.g., FIG. 6). The produced PCR products can be identified by a) an
 initial 5' sequence comprising a nucleotide base sequence of a remainder
 of a recognition site or a restriction endonuclease that was used to cut
 and isolate a 3' region of cDNA reverse transcripts made from a mRNA
 population, plus the nucleotide base sequence of preferably four parsing
 bases immediately 3' to the remainder of the restriction enconuclease
 recognition site, or more preferably the sequence of the entire fragment;
 and b) the length of the fragment.
 Processing PCR product data, including determining a nucleotide base
 sequence is a very complex task. Whether the TOGA method is used or not,
 the nucleotide sequences near the end of mRNA molecules give each mRNA an
 almost unique identity. In addition, data concerning a position and an
 amplitude of laser-induced fluorescence signals for PCR products are
 digitized and used to determine the presence and relative concentration of
 corresponding starting mRNA species. For example, PCR product data is
 digitized by creating a data file with digital information. The data file
 may include digital values, for example, of optical brightness of
 electrophoresis patterns or other data used to identify the mRNA (e.g.,
 data from a micro-array on a chip used to isolate the mRNA). To aid in the
 detection and analysis of mRNA sequences, a data file including
 experimental data is processed. In one exemplary preferred embodiment of
 the present invention, an experimental data processing system is used to
 process experimental data.
 In one preferred embodiment of the present invention, the experimental data
 includes polynucleotide data for DNA, cDNA, cRNA, mRNA, or other
 polynucleotides. The polynucleotide data can include, but is not limited
 to, a length of a nucleotide fragment, a base composition of a nucleotide
 fragment, a base sequence of a nucleotide fragment, an intensity of a dye
 label signal used to tag a nucleotide fragment, or other nucleotide data.
 However, tie present invention is not limited to polynucleotide data and
 other experimental data can also be used.
 Exemplary Experimental Data Processing System
 FIG. 1 is a block diagram illustrating an exemplary experimental data
 processing system 10 for one exemplary preferred embodiment of the present
 invention. The experimental data processing system 10 includes a computer
 12 with a computer display 14. The computer display 14 presents a windowed
 graphical user interface ("GUI") 16 to a user. A database 18 includes
 biotechnology experimental information or other experimental information.
 The database 18 may be integral to a memory system on the computer 12 or
 in secondary storage such as a hard disk, floppy disk, optical disk, or
 other non-volatile mass storage devices.
 An operating environment for the data processing system 10 for preferred
 embodiments of the present invention include a processing system with one
 or more speed Central Processing Unit(s) ("CPU") and a memory. The CPU may
 be electrical or biological. In accordance with the practices of persons
 skilled in the art of computer programming, the present invention is
 described below with reference to acts and symbolic representations of
 operations or instructions that are performed by the processing system,
 unless indicated otherwise. Such acts and operations or instructions are
 referred to as being "computer-executed" or "CPU executed."
 It will be appreciated that acts and symbolically represented operations or
 instructions include the manipulation of electrical signals or biological
 signals by the CPU. An electrical system or biological system represents
 data bits which cause a resulting transformation or reduction of the
 electrical signals or biological signals, and the maintenance of data bits
 at memory locations in a memory system to thereby reconfigure or otherwise
 alter the CPU's operation, as well as other processing of signals. The
 memory locations where data bits are maintained are physical locations
 that have particular electrical, magnetic, optical, or organic properties
 corresponding to the data bits.
 The data bits may also be maintained on a computer readable medium
 including magnetic disks, optical disks, organic memory, and any other
 volatile (e.g., Random Access Memory ("RAM")) or nonvolatile (e.g.,
 Read-Only Memory ("ROM")) mass storage system readable by the CPU. The
 computer readable medium includes cooperating or interconnected computer
 readable medium, which exist exclusively on the processing system or be
 distributed among multiple interconnected processing systems that may be
 local or remote to the processing system.
 Analyzing Biotechnology Data
 In one exemplary preferred embodiment of the present invention, a label is
 incorporated in target biotechnology products (e.g., polynucleotide PCR
 products) for detection by laser-induced fluorescence and electrophoresis
 is used to obtain biotechnology data. However, other techniques may also
 be used to collect experimental biotechnology data (e.g., micro-arrays).
 A complex, multi-component information signal based on an indicated
 fluorescence intensities of the biotechnology products is included in a
 resulting experimental data file as digital data. The multi-component
 information signal includes raw multi-component label fluorescence
 intensities. Label responses are relatively broadband spectrally and
 typically include spectral overlap. Energy measured as a second
 fluorescence response typically includes energy in the tail of a first
 fluorescence response, which might also be present, and vice-versa.
 This spectral overlap needs to be removed because the relative quantities
 of commingled energy may be of a same order of magnitude as relative
 fluorescence responses of the data representing target data (e.g.,
 polynucleotide data). For example, a small fluorescence response for a
 given polynucleotide data fragment in a biotechnology product may be
 "overwhelmed" if it occurs in a spectral overlap region between two
 fluorescence responses. In an exemplary preferred embodiment of the
 present invention, spectral overlap is removed and a normalized baseline
 is created with a combination of filtering techniques.
 Removing Spectral Overlap and Normalizing Data
 FIG. 2 is a flow diagram illustrating a Method 20 for data normalization of
 a multi-component data signal. At Step 22, a multi-component data signal
 is read. The multi-component data signal includes multiple individual data
 signal components of varying spectral characteristics with varying
 amplitudes. The multiple individual data signal components overlap within
 portions of the multi-component data signal. At Step 24, a spectral filter
 is applied to the multi-component data signal to create multiple
 non-overlapping individual data signal components. At Step 26, a spatial
 filter is applied to multiple signal artifacts in the multi-component data
 signal that introduce ambiguity to base values in the multiple
 non-overlapping individual data signal components to spatially detrend and
 normalize the multiple non-overlapping individual data signal components
 to a uniform base value.
 In one preferred embodiment of the present invention, the spectral
 characteristics of the multi-component data signal comprise physical
 attributes and conditions including but not limited to, an absorption
 spectrum of a dye label, an emission spectrum of a dye label, an emission
 wavelength power and pulse duration of an exciting laser, or other
 spectral characteristics. The spectral filtering at Step 24 of Method 20
 includes "demultiplexing" or separating individual components of raw
 fluorescence intensities that are combined by overlap of spectral
 characteristics of different dyes used to tag polynucleotide data (e.g.,
 mRNA, cDNA, or DNA). Polynucleotide data or other data tagged with a dye
 is called "dye taggant." However, Method 20 is not limited to processing
 fluorescence intensities from polynucleotide data and can be used to
 process other types of data that generate a multi-component data signal.
 In one exemplary preferred embodiment of the present invention, spectral
 filtering makes use of a set of coefficients that represent a relative
 degree to which energy in fluorescence responses of various dye taggants
 overlap. Denoting this set of coefficients by {m(p,q)}, m(p,q) is a
 measurement of an amount of energy measured at a wavelength that
 corresponds to a center of a fluorescence response of a p-th dye taggant,
 which is actually due to fluorescence response of a q-th dye taggant at
 that wavelength. The total unfiltered fluorescence response measured at
 any such central wavelength is then taken to be a weighted sum of the
 actual dye-specific fluorescence response. An unfiltered, measured
 fluorescence intensity at the central wavelength of the p-th dye taggant
 is denoted as A'(p) and an actual dye-specific fluorescence intensity is
 denoted as A(q). In terms of these conventions, Equation 1 illustrates a
 relationship between measured and actual fluorescence intensities.
EQU A'(p)=.SIGMA..sub.q m(p,q)A(q) (1)
 The spectral filter comprises extracting the actual fluorescence intensity
 A(q), by inverting a linear system of equations in Equation 1 using a
 singular value decomposition of a coefficient matrix m(p,q). The spectral
 overlap coefficients m(p,q) and unfiltered fluorescence intensity A'(p)
 are typically obtained from measurements as part of the calibration of
 instrumentation used to produce and record the fluorescence intensities.
 However, these values can also be obtained from other sources. This
 extraction is an exemplary spectral filter used at Step 24 of Method 20.
 However, other spectral filters could also be used and the present
 invention is not limited to the spectral filters illustrated by the
 inversion of Equation 1.
 The spectral filter is followed by a spatial filter at Step 26 of Method
 20. In one exemplary preferred embodiment of the present invention, the
 spatial filter is a nonlinear morphological gray-scale "rolling ball"
 transformation, which spatially detrends and normalizes the intensities to
 a set of uniform base line values. However, other types of spatial filters
 could also be used and the present invention is not limited to the spatial
 filters described herein.
 In one exemplary preferred embodiment of the present invention, the
 nonlinear morphological gray-scale rolling ball transformation that
 spatially "detrends" and "normalizes" the fluorescence intensity traces to
 a set of uniform base line values has two stages. The first stage creates
 a version of a trace that excludes local variations whose spatial extent
 is below a certain scale. This scale is chosen to be slightly greater than
 a measured extent along a trace of typical standard data peaks, so a
 resulting trace very closely resembles an original trace with peaked
 regions on a spatial scale of standard peaks and smaller peaks smoothed
 away. In preferred embodiments of the present invention, data peaks
 include entities having at least two dimensions characterized by a maximum
 amplitude and a width. The data peaks may also be described by a width at
 a half-maximum amplitude or a position of a maximum amplitude.
 This inherently nonlinear process is followed in a second stage by forming
 a difference between an original and a smoothed version of the trace,
 leaving a uniformly base-lined residual including peaked regions on a
 spatial scale of standard peaks and smaller. The term "rolling ball"
 refers to how the smoothed version of a trace is formed in a first stage
 of this filtering. In effect, a "ball" of a radius set by a exclusion
 scale of interest is first "rolled" along an under side of a trace, while
 maintaining at least one point of contact with the trace. A new trace is
 formed by taking, at each sample index (e.g., a scan line), a highest
 point of the ball when its center is on a sample index. This is followed
 by a pass of the same ball along the top side of this new trace, with a
 final new trace formed by taking, at each sample index, the lowest point
 of the ball when its center is on the sample index.
 If f(n) is a fluorescence intensity of a trace measured at sample index n,
 f.sub.min is set equal to a minimum fluorescence intensity across an
 entire trace. A spatial scale of standard peak features is taken to be
 slightly less than N-sample indices (e.g., N-scan lines). The trace is
 first "eroded" by forming a new trace f_(n) as illustrated in Equation 2.
EQU f_(n).ident.min{f(n+m)-f.sub.min :-N/2.ltoreq.m.ltoreq.N/2} (2)
 The eroded trace f_(n) from Equation 2 is "dilated" as illustrated in
 Equation 3.
EQU f.sub..+-. (n).ident.max{f_(n+m)+f.sub.min :-N/2.ltoreq.m.ltoreq.N/2} (3)
 A fluorescence intensity of the rolling ball filtered version of an
 original trace at sample index n is f.sub.0 (n) as is illustrated in
 Equation 4.
EQU f.sub.0 (n).ident.f_(n)-f.sub..+-. (n) (4)
 It is a sequence of finding minima and maxima (e.g., Equations 3 and 4)
 that accounts for the nonlinearility of the filter. Data values are
 normalized to a set of uniform base values.
 The present invention with Method 20 is not limited to processing and
 normalizing biotechnology data multi-component signal or processing data
 with Equations 1-4 and can be used for other data from a multi-component
 signal (e.g., telecommunications signals, electrical signals data for
 electrical devices, optical signals, physical signals, or other data
 signals).
 In one exemplary preferred embodiment of the present invention, "control"
 or "standard" polynucleotide data fragments (i.e., known polynucleotide
 data fragments) are tagged with a dye, which under laser illumination
 responds with a "red" fluorescence, while "target" polynucleotide data
 fragments (i.e., polynucleotide data to be identified) are tagged with a
 dye which has a "blue" response. However, the dyes used for the control
 and target could also be interchanged. Both the red and blue dye responses
 are relatively broadband spectrally, to the extent that energy measured as
 red fluorescence response includes energy in a tail of any blue
 fluorescence response which might also be present and vice-versa. This
 spectral overlap is taken into account because the relative quantities of
 commingled energy are of the order of the relative fluorescence
 intensities of the target polynucleotide data and standard polynucleotide
 data fragments.
 FIG. 3A is a block diagram 28 of an unfiltered multi-component data signal
 30. FIGS. 3A-3D are used to illustrate use of Method 20 of FIG. 2. In one
 exemplary preferred embodiment of the present invention, the
 multi-component data signal 30 is a measurement of signal intensity of
 fluorescence on a vertical axis 32 at a fixed point in an
 electrophoresis-gel at successive points in time. The signal intensity of
 fluorescence is directly proportional to a parameter on a horizontal axis
 34 representing a sample index (e.g., a scan line). However, other
 multi-component signal data could also be used and the present invention
 is not limited to polynucleotide fluorescence intensity data. A magnitude
 of the fluorescence intensity at a given scan line has been demonstrated
 to represent an amount of tagged polynucleotide fragments at a fixed point
 in time of a scan (e.g., tagged with red or blue dyes). The scale of
 standard polynucleotide fragment fluorescence intensity is illustrated by
 the narrow peak 36, of about two-hundred fluorescence units, which is
 illustrated in the region near sample index 2500 (e.g., 2500 scan lines)
 on the horizontal axis 34. In one preferred embodiment of the present
 invention, FIG. 3A illustrates a multi-component data signal 30 for a
 standard set of polynucleotide fragments.
 FIG. 3B is a block diagram 38 illustrating the unfiltered multi-component
 data signal 30 for a standard set of polynucleotides fragments of FIG. 3A
 as an unfiltered multi-component data signal 40 displayed with a larger
 scale. FIG. 3C is a block diagram 42 illustrating a filtered version of a
 multi-component data signal 44 for a target set of polynucleotides. The
 filtered version of the multi-component data signal 44 for the target set
 of polynucleotides (FIG. 3C) is at least an order of magnitude greater
 than that of the unfiltered multi-component data signal 40 for a standard
 set of polynucleotides (FIG. 3B).
 A degree of spectral overlap is illustrated by the presence, in the
 unfiltered multi-component data signal 40 for a standard set of
 polynucleotides of FIG. 3B, of such artifacts as the broad peaks 46 in the
 region of sample index 2500 (e.g., 2500 scan lines) on the horizontal axis
 32. The broad peaks 46 of FIG. 3B, when compared with the narrower peaks
 48 of FIG. 3C, are due to spectral overlap of blue fluorescence
 intensities from blue-tagged target polynucleotide fragments since there
 are no red-tagged standard polynucleotide fragments that could produce
 such levels of fluorescence intensities. An ambiguous baseline in this
 region (i.e., 2500 scan lines) illustrates "spectral bleed through" of
 blue-tagged target polynucleotide fragments that dramatically dwarf
 red-tagged standard polynucleotide fragments of interest.
 FIG. 3D is a block diagram 52 illustrating application of Method 20 of FIG.
 2 to the unfiltered multi-component data signal 30 for the standard set of
 polynucleotide fragments of FIG. 3A. FIGS. 3A and 3D use the same signal
 intensity scale to allow direct comparison. Note the clean data peaks 54,
 56, 58, 60, 62, 64, 66, 68, 70 and 72 in FIG. 3D normalized to a uniform
 base value by applying the spectral and spatial filters of Method 20 to
 the unfiltered multi-component data signal 30 for the standard set
 polynucleotide fragments of FIG. 3A. Method 20 of FIG. 2 is also applied
 to the multi-component data signal for the target set of polynucleotides
 of FIG. 3B to produce set of clean peaks similar to those in FIG. 3D (this
 is not illustrated in FIG. 3).
 Standards Size Data Detection, Error Removal and Clutter Rejection
 The multi-component data signals filtered and normalized to a baseline
 value with Method 20 of FIG. 2 may still contain false or erroneous data
 peaks due to false peak clutter. Such erroneous or false data peaks, if
 not removed, may skew experimental results. In one exemplary preferred
 embodiment of the present invention, size standards detection with removal
 of false peak clutter rejection is used to identify a set of valid
 biotechnology fragment data from a filtered set of biotechnology fragment
 data (e.g., polynucleotide data). However, size standards detection with
 removal of false peak clutter can also be used on data other than
 biotechnology fragment data.
 FIG. 4 is a flow diagram illustrating a Method 74 of clutter rejection. At
 Step 76, a first set of data points is selected from a filtered set of
 data points (e.g., filtered using Method 20, FIG. 2) using initial
 threshold criterion. At Step 78, multiple overlapping subsets of data
 points are selected from the first set of data points. At Step 80,
 multiple linear mappings are applied to the multiple overlapping subsets
 of data points. At Step 82, multiple error values are determined from the
 application of the multiple linear mappings to the multiple overlapping
 sub-set of data points. At Step 84, a first final subset of overlapping
 data points with a smallest error value is selected from the first set
 data points. Data points in the first final subset of overlapping data
 points include data points that fall within a standardized range where
 false data points have been removed.
 In one exemplary preferred embodiment of the present invention, peaks in
 candidate biotechnology fragment data are located at Step 76 (FIG. 4) in
 filtered biotechnology fluorescence intensity data (e.g., with Method 20)
 using thresholds on simple ratios of differences between "microscale" and
 "mesoscale" average fluorescence intensity levels relative to mesoscale
 variances. However, other thresholds could also be used.
 There are typically a very large number of sets of filtered data points
 that can be selected for use with Method 74. Thus, selecting an
 appropriate filtered set of data points is a "combinatorics" problem. As
 was discussed above, combinatorics relates to the arrangement of,
 operation on, and selection of discrete elements belonging to finite sets
 of data points. However, Method 74 reduces the combinatorics of data
 selection to a "best" possible solution using multiple linear mappings,
 and allows a best set of data points (e.g. for a data peak mapping) to be
 created from a very large set of filtered data points. Method 74 provides
 an accurate selection of data points on data sub-scale, instead of a
 electrophoresis-gel scale, thus reducing the combinatorics of data
 selection to a level usable on the current generation of computing
 systems.
 In one exemplary preferred embodiment of the present invention, a
 "signal-to-noise" ratio combined with a "height-and-width" ratio is used
 at Step 76. However, other initial thresholds can also be used, and the
 present invention is not limited to the initial threshold wherein
 described. The initial threshold is used in one exemplary preferred
 embodiment of the present invention as an initial threshold overview to
 identify a likely set of false standard biotechnology fragment peak
 features (e.g., in polynucleotide fragments). Data outside the initial
 threshold is rejected as is illustrated in FIG. 5 below. An actual sample
 index location of a given candidate is taken to be that of a local maximum
 of a peak feature, if this is unique, or alternatively to a spatial center
 of a feature interval.
 FIG. 5 is a block diagram 86 illustrating a filtered and normalized
 multi-component data signal using Method 20 from FIG. 2. To illustrate the
 difficulty in size standard detection for polynucleotide data fragments,
 FIG. 5 illustrates a relatively clean set of superficially acceptable data
 peaks. However, there are features 88 and 90 near sample indices 1400 and
 3250, which may satisfy a signal-to-noise criterion but fail a
 height-and-width criterion used to determine a data peak (Items 88 and 90
 of FIG. 5 correspond to items 98 and 100 of FIG. 6). The features 88 and
 90 are rejected with the initial criterion at Step 76. However, there are
 also features 92 and 94 near sample index 2700 that meet the initial
 criterion, but which are not valid standard peaks for this exemplary
 biotechnology data trace (items 92 and 94 of FIG. 5 correspond to item 102
 of FIG. 6). These features 92, 94 are removed with the remainder of Method
 74 at Steps 78-84. It is desirable to consistently remove such invalid
 peaks to create a valid set of standard peaks (e.g., for polynucleotide
 data fragments), to allow reproducible results every time an experiment is
 conducted.
 In one exemplary preferred embodiment of the present invention, modeling
 physics of gel electrophoresis used to record polynucleotide data
 fragments is done using Fickian diffusion with drift. However, other
 modeling techniques could also be used and the present invention is not
 limited to Fickian diffusion with drift. As is known in the art, Fickian
 diffusion is molecular diffusion, governed by Fick's laws, which describe
 a rate of flow of diffusants across a unit area of a certain plane as
 directly proportional to a concentration gradient. For more information on
 Fickian diffusion see "Diffusion Processes and Their Sample Paths" by
 Henry P. McKean and Kiyoshi Ito, Springer Verlag, 1996, ISBN-3540606297,
 or "Mathematics of Diffusion" by John Crank, Oxford University Press,
 1975, ISBN-0198534116, both of which incorporated herein by reference.
 Using Fickian diffusion on a gel, the drift properties of diffusants are
 associated with the times of arrival of their maximum concentrations at a
 fixed point in a gel. For linear molecules of interest, this arrangement
 leads to at least three significant model predictions for polynucleotide
 data fragments. First, the polynucleotide data fragments drift with
 velocity inversely proportional to their size. Second, for sparse
 mixtures, fluorescence peak heights are proportional to polynucleotide
 data fragment counts. Finally, both of these proportionalities are
 independent of polynucleotide data fragment size. The value of gel
 electrophoresis in biomolecular size assays is due to the fact that it is
 possible to engineer instruments and protocols for which these predictions
 are valid for a significant variety of conditions and molecules.
 In one exemplary preferred embodiment of the present invention, comigrating
 standard polynucleotide fragment sets of known size provide a means of
 rejecting the false peak clutter. Since an inverse proportionality between
 fragment size and drift velocity is independent of fragment size, and a
 standard fragment set is both known and ordered, a straight line drawn
 through a plot of standard fragment sizes as a function of their scan line
 locations should reveal those data peaks that are clutter. The clutter
 peaks will either not fall on, or sufficiently near a line, or they will
 cause a line to miss a significant fraction of the other data.
 Given this approach to clutter rejection, there are at least two remaining
 problems in applying it to biotechnology data. First, potential
 combinatorics of quickly choosing an appropriate subset of valid peaks
 from candidate peaks can be computationally impossible or forbidding for
 currently available computing systems. Secondly, a degree to which an
 inverse proportionality of fragment and drift velocity size is genuinely
 independent of fragment size depends upon a degree to which gel properties
 are consistent and uniform over a period of observation.
 FIG. 6 is a block diagram 96 illustrating filtered standard polynucleotide
 fluorescence responses for a sequence of scans for a set of lanes in a gel
 which were loaded with standard polynucleotide fragments at a same time.
 The physical edges of the gel correspond to the edges of this image, and
 the bright bands in any one lane represent the scan line locations of
 candidate standard fragments in that lane. For example, the three scan
 lines near sample index 2000 (FIG. 6) represent the three data peaks near
 sample index 2000 (FIG. 5). Note the smaller bright features 98, 100 and
 102, roughly in the center of lanes 10, 19, and 25, that do not belong to
 bands that extend across the image. These are examples of the "false peak
 clutter" at issue. For example, item 98 (FIG. 6) may correspond to false
 peak 88 (FIG. 5), item 100 may correspond to false peak 90 (FIG. 6) and
 item 102 (FIG. 6) may correspond to false peaks 92, 94 (FIG. 5).
 If the properties of the gel were uniform throughout the gel over a period
 of successive scans, the bright bands would be strictly horizontal (e.g.,
 exemplary horizontal dashed line 104). Not only are the bands not
 horizontal, the degree to which they curve increases as a function of
 time, with larger scan lines indices corresponding to scans occurring
 later in time. The drifting fragments in the gel are charged particles
 moving through a resistive medium under the influence of an applied
 electric field. The resulting characteristic "smile" (e.g., scan line 106
 versus horizontal line 104) in such electrophoretic gel imagery is due to
 the differential heating of the gel by this current over time, the edges
 of the gel more effectively dissipating heat than the more central
 regions.
 The smaller a linearly ordered set of standard fragment sizes (e.g., a
 mask) is, the more the resulting combinatorics of selecting a valid subset
 (e.g., flickering a mask) become tractable. For overlapping regions of the
 gel to which each mask is applied, the more uniform and consistent the
 relevant gel properties become localized.
 In one exemplary preferred embodiment of the present invention, a given a
 set of candidate standard peak scan line locations are obtained at Step 76
 by the initial threshold criterion outlined above. In such an embodiment,
 clutter and false peak rejection proceeds by choosing proper, overlapping
 subsets of a complete standard size set at Step 78.
 At Step 78, linear mappings are applied to the multiple overlapping subsets
 of data points. For an ordered, sequential three element set of standard
 sizes {M.sub.a, M.sub.b, M.sub.c } whose peaks occur at scan lines
 {n.sub.a, H.sub.b, n.sub.c }, respectively, linear regression techniques
 give a predictive linear mapping of scan line n.sub.x to fragment size as
 is illustrated in Equation 5. However, other set sizes and linear mappings
 could also be used and the present invention is not limited to the linear
 mappings in Equation 5.
EQU .mu..sup.(0).sub.abc +.mu..sup.(1).sub.abc *n.sub.x, (5)
 The coefficients {.mu..sup.(j).sub.abc } are functions of a particular set
 of (size, scan line) pairs. With any scan line n lying between two
 consecutive standard peak scan line locations, {n.sub.b, n.sub.c }, a
 local Southern linear mapping method associates a fragment size as is
 illustrated in Equation 6. However, other linear mapping methods can also
 be used, and the present invention is not limited to the local Southern
 method linear mappings illustrated in Equation 6.
EQU M'.sub.n.ident.(.mu..sup.(0).sub.abc +.mu..sup.(1).sub.abc
 *n+.mu..sup.(0).sub.bcd +.mu..sup.(1).sub.bcd *n)/2 (6)
 The set {M.sub.b, M.sub.c, M.sub.d } is a rightmost overlapping "bcd" and
 sequential set of standard sizes for a leftmost overlapping "abc" and
 sequential set {M.sub.a, M.sub.b, M.sub.c }, the former for standard size
 peaks occurring at scan lines {n.sub.b, n.sub.c, n.sub.d }. An individual
 error in this association of standard peak size (i.e., data point value)
 and scan line location (i.e., data point) is calculated as a difference
 illustrated by Equation 7.
EQU .epsilon..sub.n.ident.M.sub.n -M'.sub.n (7)
 At Step 82, multiple error values (e.g., Equation 7) are determined from
 the application of multiple linear mappings (e.g., Equation 6) to the
 multiple overlapping subset of data points. In one preferred embodiment of
 the present invention, a Root Mean Square ("RMS") error evaluation of the
 "goodness" of each of the local fits allows them to be ranked. However,
 other error evaluation methods can also be used and the present invention
 is not limited to RMS.
 Given a set of peak scan line locations for a set of standard biotechnology
 fragments sizes, straight lines are fit to possible sets of three adjacent
 fragment sizes as a function of the three associated adjacent scan line
 locations, using linear regression. A local linear mapping of any given
 scan line to its associated fragment size is then formed by averaging the
 two most relevant of these three-point linear fits.
 A first relevant fit includes two closest standard scan lines, which are
 smaller than a given scan line, and one closest standard scan line, which
 is greater. A second relevant fit includes two closest standard scan
 lines, which are greater than a given scan line, and one closest standard
 scan line which is smaller. A total RMS error over the K (size, scan line)
 pairs {(M.sub.n(k), n(k))} is illustrated in Equation 8.
EQU error=[.SIGMA..sub.k=1, . . . ,K.epsilon..sup.2.sub.n(k) /K].sup.1/2
 =[.SIGMA..sub.k=1, . . . ,K (M.sub.n(k) -M'.sub.n(k)).sup.2 /K].sup.1/2
 (8)
 A set of subsets of scan line locations which yields a smallest total RMS
 error is chosen at Step 84, provided that both a total error and an error
 for any one standard size are below certain error thresholds. If these
 error thresholds cannot be satisfied by any subset of scan line locations
 for a complete set of standard sizes, a size of a standard size set is
 reduced by one and the error calculation is repeated. This method of
 evaluating local linear fits to possible subsets of standard scan line
 locations is repeated, over possible standard size sets of the reduced
 size. The RMS process (e.g., Equation 8) is repeated until either error
 threshold criterion are satisfied, or until a reduced size of the standard
 size set becomes too small. There is also a selection criterion on the
 subsets of the complete standard size set that prevents more than a given
 number of adjacent lacunae in final size set.
 FIG. 7 is a block diagram 108 illustrating exemplary biotechnology peaks
 (e.g., polynucleotide peaks) using size standard detection with false peak
 clutter rejection from Method 74 of FIG. 4. Target biotechnology fragment
 peaks 110, 112, 114, 116, 118, 120, 122, 124, 126 and 128 identified by
 Method 80 (FIG. 4) while standard biotechnology peaks (e.g., sample
 indices for known polynucleotide data sequences) are indicated by with
 dashed vertical lines. For example, the dashed line through the data peak
 110 indicates a known polynucleotide intensity. The false peaks 88, 90
 (FIG. 5) near scan lines 1400 and 3250 that may satisfy a signal-to-noise
 criterion but fail a height-and-width criterion are properly identified
 and removed with initial criterion at Step 76 of Method 80. The false
 peaks 92, 94 (FIG. 5) have been properly identified and rejected as
 clutter by the remaining steps of Method 80. Note that several of the data
 peaks (e.g., 114, 118, 122) for target data do no line up exactly on a
 dashed line for known data. Such data peaks are adjusted as is described
 below.
 Method 74 (FIG. 4) may also allow for the application of a number of very
 powerful and convenient quality control measures. First, Method 74 may
 implicitly bootstrap a sizing calibration. This allows a quality of
 fluorescence intensity data to be immediately assessed from their
 susceptibility to accurate calibration. This may be an effective measure
 of the degree of conformance between experimental data and a good physical
 model of the processes implicated in their creation. Secondly, limits are
 placed on both the total number and distribution of size standards
 fragments that can be deleted from the initial set in producing a set of
 local linear mappings with acceptable error. Finally, it is assumed that
 false peak clutter usually has its source in either residual spectral
 bleed-through, or more problematically for any given lane, standard
 fragment sets which actually belong to adjacent lanes. This latter
 phenomenon is known as "crosstalk." By keeping track of both how many
 candidate standard peak scan line locations co-occur in adjacent lanes as
 well as how many detected standard peaks are co-located in adjacent lanes
 even after application Method 74, it is possible to form yet another
 useful data quality measure. This measure may be particularly relevant to
 clutter rejection because it essentially qualifies its self-consistency.
 Data Size Calibration and Adjustment
 The actual size and location of the filtered and false peak clutter
 rejected data (e.g., polynucleotide fragment output) is typically adjusted
 to allow experimental data to be more accurately visually displayed. This
 adjustment provides more accurate data values for visual display. For
 example, target data peaks illustrated in FIG. 7 that do not line up
 exactly on a known data peak values are adjusted.
 FIG. 8 is a block diagram illustrating a Method 130 for data size
 calibration and adjustment. At Step 132, a first final subset of
 overlapping data points with a smallest error value is selected as a
 standard set of data points from a first set of data points. Data points
 in the first final subset of overlapping data points include data points
 with values that fall within a standardized range and where false data
 points have been removed. At Step 134, higher order mappings are applied
 to the first final subset of data points to further reduce the smallest
 error value for the final subset of overlapping data points and create a
 second final subset of data points.
 In one preferred embodiment of the present invention, a first subset of
 overlapping data points is selected at Step 132 from application of Method
 74 (FIG. 4). However, other methods can also be used to select the final
 subset of overlapping data points, and the present invention is not
 limited to the application of Method 74.
 At Step 132, the first final subset of overlapping data points selected
 from application of Method 74 including a local Southern method (e.g.,
 Equations 5 and 6), size-calibrates data with a pre-determined precision
 (e.g. typically no better than one to two base pairs for polynucleotide
 fragment data). If the data points can be calibrated in Step 132 to within
 a pre-determined quality control limit, the local Southern calibration is
 followed by a higher order mapping at Step 134 that further reduces a
 calibration error. In one exemplary preferred embodiment of the present
 invention, the calibration error is reduced to zero. In another exemplary
 preferred embodiment of the present invention, the calibration error is
 reduced to a very small value approaching zero, but not to zero (i.e.,
 slightly greater than zero).
 Method 130 combines the local statistical robustness of regression
 techniques (i.e., with their natural rejection of outliers) and a
 precision possible with higher order methods (e.g., higher order splines).
 In one exemplary preferred embodiment of the present invention, absolute
 precision in the calibration biotechnology data is desired to provide
 accurate and reproducible results. However, the present invention can also
 be used if only relative precision is desired.
 At Step 134, higher order mappings are used with the residual error from
 the local Southern Method, and a second-order generalization of that
 linear, or first-order local Southern Method. In one exemplary preferred
 embodiment of the present invention, local quadratic or second-order maps
 are constructed using residual errors for the same three element sets of
 (fragment size, scan line location) pairs used for the Local Southern
 Method. However, the present invention is not limited to second order maps
 and higher order maps can also be used (e.g., third order, fourth order,
 etc.).
 Since a second-order mapping has three coefficients, or three "degrees of
 freedom," the three residual errors for each set of three pairs can in
 principal, be accounted for in a very exact manner. Computational
 degeneracy in a numerical order of an error is accomplished by using a
 singular value decomposition to solve a linear system of equations that a
 conventional least squares method produces when fitting a quadratic to
 three data points.
 Given the local Southern approximation of a size associated with any
 specific scan line location, an additive correction higher order mapping
 is formed by averaging two most relevant of these second three-point
 quadratic fits. A first approximation, for two closest standard scan lines
 which are smaller than a given scan line and one closest standard scan
 line which is greater. A second approximation for two closest standard
 scan lines which are greater than a given scan line and one closest
 standard scan line which is smaller. Since each quadratic fit is locally
 exact at the scan line locations of relevant three standard fragment
 peaks, averaging any two fits on these peak locations is also exact, which
 results in an absolutely precise interpolation on the detected standard
 fragment set.
 For a scan line n, the local Southern method (e.g., Equations 5 and 6)
 associates a fragment size M'.sub.n, with error .epsilon..sub.n at the
 standard peak locations. With the same notation and conventions used for
 the discussion of the local Southern method above, a least squares method
 gives exact second order mappings of an error at any one standard peak
 location for leftmost sequential set of standard sizes as illustrated in
 Equation 9. However, other methods can also be used and the present
 invention is not limited to a least squares methods.
EQU .gamma..sup.(0).sub.abc +.gamma..sup.(1).sub.abc *n+.gamma..sup.(2).sub.abc
 *n.sup.2 (9)
 Exact second order mappings of an error at any one standard peak location
 for rightmost sequential set of standard sizes is illustrated in Equation
 10.
EQU .gamma..sup.(0).sub.bcd +.gamma..sup.(1).sub.bcd *n+.gamma..sup.(2).sub.bcd
 *n.sup.2 (10)
 Both sets of coefficients {.gamma..sup.(j).sub.abc } and
 {.gamma..sup.(j).sub.bcd } are functions of their respective particular
 set of (size, scan lines) pairs and the error .epsilon..sub.n. For any
 scan line n lying between two consecutive standard peak scan line
 locations, {n.sub.b, n.sub.c}, a higher-order residual mapping adds a
 correction factor .delta..sub.n to a local Southern method size
 association as illustrated in Equation 11.
EQU .delta..sub.n.ident.(.gamma..sup.(0).sub.abc +.gamma..sup.(1).sub.abc
 *n+.gamma..sup.(2).sub.abc *n.sup.2 +.gamma..sup.(0).sub.bcd
 +.gamma..sup.(1).sub.bcd *n+.gamma..sup.(2).sub.bcd *n.sup.2)/2 (11)
 In one preferred embodiment of the present invention, this correction
 .delta..sub.n, or higher order mapping, gives a net association that is
 exact at scan line locations of the standard peak features. However, the
 present invention is not limited to such a correction .delta..sub.n and
 other correction features could also be used.
 FIGS. 9A and 9B are block diagrams 136, 138 illustrating data size
 calibration using Method 130 from FIG. 8. FIG. 9A illustrates an exemplary
 data peak 140 (e.g., for an unknown polynucleotide sequence) before
 application of Method 130 (FIG. 8). The data peak 140 is slightly offset
 from a relevant desired data peak location 142 (e.g., for a known
 polynucleotide sequence) whose desired location is illustrated by a dashed
 line, that would be achieved if there were no errors for a data set
 acquired from a desired experiment. FIG. 9B illustrates an exemplary data
 peak 144 after application of Method 130 (FIG. 8). The data peak 146 is
 more accurately aligned over the desired data peak location 142 after
 application of Method 130.
 FIGS. 9A and 9B illustrates only one exemplary data peak. However, Method
 130 is applied to all data peaks (e.g., 54, 56, 58, 60, 62, 64, 66, 68, 70
 and 72 of FIG. 3D) in a final subset of overlapping data points (e.g.,
 produced by Method 74 of FIG. 4) to further reduce error for a set of data
 points that will be visually displayed. Method 130 may improve a set of
 data points that will be displayed and analyzed by further reducing data
 errors that may be introduced as a result of running a desired experiment.
 Data peaks that have been sized and adjusted may still include data
 "stutter." (See e.g., FIG. 11A). For example, the data peaks illustrated
 in the figures are illustrated as a "smooth" data peaks. However, actual
 experimental data peaks typically include multiple sub-peaks, that are a
 function of the actual data. It is desirable to remove the multiple
 sub-peaks, or data stutter before visual display.
 Reduction of Data Magnitude and Data Smoothing
 In the current generation of biotechnology equipment known in the art, scan
 lines from gel-electrophoresis are formed at a rate which, after size
 calibration, results in an over-resolution of the sized traces by about an
 order of magnitude. That is, there are about ten scan lines between each
 successive integer base-pair value. In addition, biotechnology fragments
 (e.g., polynucleotide fragments) typically occur in cluster around the
 most significant fragment sizes, rather than as cleanly isolated peaks of
 integer base-pair width. This can be seen by comparing the broader and
 more complex peak features (e.g., feature 44) in the biotechnology
 fragment trace in FIG. 3C, with the narrow and more simple standard
 fragment peaks in FIG. 3D (e.g., data point 68).
 Representing these complex biotechnology fragment traces at their full
 resolution on the windowed display 16 is further complicated by the
 inevitable limits imposed by the current generation computer monitor and
 graphics display systems. Consequently, before creating graphical images
 to display, the biotechnology data points are further decimated and
 smoothed using an "envelope detector" that enhances a visibility of data
 points for display on the windowed display 16 by moderating resulting
 fragment "stutter."
 FIG. 10 is a flow diagram illustrating a Method 146 for envelope detection.
 At Step 148, an envelope criterion is established for sub-sampling of a
 second final subset of overlapping data created from a first final subset
 of overlapping data. The second final subset of overlapping data points
 have been adjusted to fall within a standard size. Significant features of
 the second final subset of overlapping data are preserved within the
 envelope criterion. At Step 150, the envelope criterion is applied to
 compress the number of data values in the second final subset of
 overlapping data by at least one order of magnitude, reduce data stutter,
 and to create a third final subset of overlapping data.
 In one exemplary preferred embodiment of the present invention, the second
 final subset of overlapping data is produced by applying Method 20 (FIG.
 2), Method 74 (FIG. 4) and Method 130 (FIG. 8) discussed above. However,
 the present invention is not limited to overlapping data sets produced
 with these method and other data sets produced with other methods known in
 the art, that will be displayed on the windowed display 16 can also be
 used with Method 146 (FIG. 9).
 In one exemplary preferred embodiment of the present invention, the
 envelope criterion established at Step 148 is based on a "nonlinear
 box-car-extremum" filter that compresses data size resolution by about an
 order of magnitude and removes data stutter. However, other envelope
 criterion could also be used and the present invention is not limited to a
 nonlinear box-car-extremum filter.
 In one preferred embodiment of the present invention, graphical images for
 the windowed display 16 illustrate a size resolution of about one
 polynucleotide base pair, with each point on a trace sampled at integer
 base-pair sizes. At Step 150, the box-car envelope detector first segments
 a size axis of a size-calibrated full resolution trace data into
 contiguous regions centered on these integer sizes. The term "box-car"
 reflects the view of these contiguous, disjoint regions as box-cars
 aligned end-to-end along a size axis.
 A trace envelope is formed by replacing signal intensities associated with
 sizes in a given box-car by their maximum. This is a many-to-one
 replacement, or "decimation", on the order of the average number of scan
 lines associated with an integer base pair in the full resolution data.
 Preferably, this decimation factor is about ten-to-one. However, other
 decimation factors can also used.
 In one exemplary preferred embodiment of the present invention, at Step
 150, an envelope criterion f*.sub.k, is applied in Equation 12.
EQU f*.sub.k.ident.max{f.sub.0 (n):(M*.sub.k +M*.sub.k-1)/2.ltoreq.(M'.sub.n
 +.delta..sub.n)&lt;(M*.sub.k+1 +M*.sub.k)/2} (12)
 The notation and conventions in Equation 12 reflect notation from Equations
 1-11 discussed above. For example, f.sub.0 is determined with Equation 4,
 M'.sub.n with Equation 6, and .delta..sub.n with Equation 11, etc.
 FIGS. 11A and 11B are block diagrams 152,154 illustrating envelope
 detection using Method 146 of FIG. 10. FIG. 11A illustrates an envelope
 156 created around a target data peak 158. Data "stutter" is illustrated
 by two small peaks on the left side (i.e., towards 2000 sample index), and
 one small peak on the right side (i.e., towards 2500 sample index) of
 target data peak 158. FIG. 11B illustrates a new data peak 160 after
 application of Method 146. The number of data points in the new data peak
 160 is reduced by an order of magnitude and the "stutter" of the data peak
 158 has been removed. FIGS. 11A and 11B illustrates only one exemplary
 data peak. However, Method 150 is applied to data peaks in the second
 final subset of overlapping data. Data peaks described herein, also
 typically include data "stutter." However, data peaks in other than FIG.
 11A are illustrated as smooth and do not illustrate data stutter that does
 exist before application of Method 146 simplify the drawing of such data
 peaks.
 Method 146 may further enhance a visibility of data points for display on
 the windowed display 16 by moderating resulting fragment "stutter." The
 number of data points may also be reduced by an appropriate amount (e.g.,
 one order of magnitude) for easier display.
 Processing of General Multi-component Signal Data
 In one exemplary preferred embodiment of the present invention, a general
 multi-component data signal can be processed to yield a set of data peaks
 for a target experiment suitable for display on the windowed display 16 of
 the display device 14. In such an embodiment, the general multi-component
 data signals may include general biotechnology multi-component data
 signals. However, the present invention is not limited to processing
 general biotechnology multi-component signal data, and other signal data
 could also be processed (telecommunications signals, electrical signals
 data for electrical devices, optical signals, physical signals, or other
 data signals).
 FIGS. 12A and 12B is a flow diagram illustrating a Method 162 for
 processing experimental data. At Step 164, of FIG. 12A, a multi-component
 data signal is read. The multi-component data signal includes multiple
 individual data signal components of varying spectral characteristics and
 varying amplitudes. The multiple individual data signal components overlap
 within portions of the multi-component data signal. At Step 166, filters
 are applied to the multi-component data signal to create multiple
 non-overlapping individual data signal components. The filter also filters
 multiple signal artifacts in the multi-component data signal that
 introduce ambiguity to base values in the multiple non-overlapping
 individual data signal components to spatially detrend and normalize the
 multiple non-overlapping individual data signal components to a uniform
 set of base values. At Step 168, multiple linear mappings are applied to
 multiple overlapping subsets of data points from the multiple
 non-overlapping individual data signal components to select a first final
 subset of overlapping data points with a smallest error value. The data
 points in the first final subset of overlapping data points include data
 points that fall within a standardized range and wherein false data points
 have been removed.
 At Step 170 of FIG. 12B, multiple higher order mappings are applied to the
 first final subset of overlapping data points to further reduce the
 smallest error value for the final subset of overlapping data points and
 create a second final subset of data points. At Step 172, an envelope
 criterion is applied to compress the number of data values in the second
 final subset of overlapping data by at least an order of magnitude, reduce
 data stutter, and create a third final subset of overlapping data.
 Significant features of the second final subset of overlapping data are
 preserved within the envelope criterion. The third final subset of
 overlapping data is suitable for the windowed display 16 on the display
 device 14.
 Method 162 allows the processing of multi-component data signals from
 biotechnology experiments or experiments from other arts to be automated.
 When a multi-component data signal is input, a third final subset of
 overlapping data with multiple data peaks suitable for display on a
 windowed device is automatically produced. This may help reduce or
 eliminate inconsistencies in experimental data processing that typically
 lead to unreliable or erroneous results.
 In one exemplary preferred embodiment of the present invention, the
 multi-component data signal includes multi-component fluorescence
 intensities for polynucleotide data including DNA, cDNA or mRNA. However,
 the present invention is not limited to multiple-component data signals
 for polynucleotide data, or other biotechnology data, and multi-component
 data signals from other arts can also be used (e.g., telecommunications
 signals, electrical signals data for electrical devices, optical signals,
 physical signals, or other data signals).
 In yet another exemplary preferred embodiment of the present invention,
 Method 162 is accomplished by applying Method 20 (FIG. 2) at Steps 164,
 166 (FIG. 12A), Method 74 (FIG. 4) at Step 168 (FIG. 12A), Method 130
 (FIG. 8) at Step 170 (FIG. 12B), and Method 146 (FIG. 10) at step 172
 (FIG. 12B). However, the present invention is not limited to applying all
 the steps of these methods to accomplished Method 162 (FIGS. 12A and 12B).
 Method 162 can be accomplished by applying selected steps from these
 methods.
 FIGS. 13A and 13B are block diagrams 174, 176 illustrating Method 162 of
 FIGS. 12A and 12B. FIG. 13A illustrates a multi-component data signal 178
 of interest. FIG. 13B illustrates set of processed desired data peaks 180,
 182, 184, 186, 188, 190, 192, 194, 196, 198, 200 from the multi-component
 data signal 178 after processing with Method 162. The multi-component data
 signal has been filtered, normalized to a predetermined size, had false
 peaks, errors and data stutter removed, has been smoothed, and had the
 number of data values reduced by at least one order of magnitude. The
 processed desired data peaks are suitable for display on the windowed
 display 16 of the display device 14.
 In one exemplary preferred embodiment of the present invention, the desired
 data peaks 180, 182, 184, 186, 188, 190, 192, 194, 196, 198 and 200 (FIG.
 13B) are polynucleotide fragment peaks (e.g., DNA, cDNA or mRNA). However,
 the present invention in not limited to multi-component data signals
 including polynucleotide fragment data and other multi-component data
 signals including other experimental information could also be used (e.g.,
 telecommunications signals, electrical signals data for electrical
 devices, optical signals, physical signals, or other data signals).
 Exemplary Multi-component Data Processing System
 FIG. 14 is a block diagram illustrating an exemplary multi-component data
 processing system 202. The multi-component data processing system includes
 a data sample and reference calibration module 204, an optional broadband
 signal collection module 206, a storage module 208, a filtering and
 baseline module 210, a reference and sample calibration module 212 and a
 display module 214.
 The data sample and reference calibration module 204 is used for processing
 known and target biotechnology samples. The optional broadband signal
 collection module 206 is used for collecting experimental data from
 multi-component data signals when laser-induced fluorescence of
 biotechnology products is used. In another embodiment of the present
 invention, the optional broadband signal collection module 206 can be
 eliminated if other technologies are used instead of laser-induced
 fluorescence (e.g., micro-arrays). The storage module 208 is used to store
 experimental data. The filtering and baseline module 210 is used to remove
 spectral overlap and normalize experimental data if laser-induced
 fluorescence is used, or can be used to perform other filtering and
 baselines if other technologies are used (e.g., micro-arrays).
 The reference and calibration module 212 is used for standard size
 detection with false peak and clutter removal, data size calibration,
 envelope detection and data stutter removal of experimental data. The
 display module 214 visual displays processed experimental data. However,
 the present invention is not limited to these modules and more or fewer
 modules could also be used. In additional, the functionality of the
 modules described could be combined or split into additional modules.
 In one exemplary preferred embodiment of the present invention,
 experimental data processing system 10 (FIG. 1) includes the storage
 module 208, the filtering and baseline module 210, the reference and
 sample calibration module 212 and the display module 214 (FIG. 14) as an
 integral combination of hardware and software (i.e., indicated by the
 dashed line in FIG. 14). This allows virtually any experimental technique
 (e.g., gel-electrophoresis, miro-arrays, etc.) to be used to generate data
 files that are stored in the storage module 208 and processed with the
 methods described herein with software resident on the computer 12. Such
 an embodiment provides flexibility to process experimental data from a
 wide variety of applications on a conventional personal computer system,
 or other larger computer system.
 The methods and system described herein are used to process data for
 display on the windowed display 16 of display device 14, as is illustrated
 by FIG. 13B. However, a final processed set of data (e.g., the third final
 subset of data) may still require additional processing for visual display
 and comparative analysis.
 Display of Processed Experimental Data
 As was discussed above, "raw" experimental data starting with
 multi-component data signals can be processed with one or more methods to
 produce a "processed" set of data suitable for visual display. Some of the
 problems associated with processing such raw experimental data are
 overcome in co-pending application Ser. No. 09,318,699, filed May 25,
 1999, assigned to the same Assignee as the present application.
 In one exemplary preferred embodiment of the present invention, the methods
 illustrated in FIG. 2, FIG. 4, FIG. 8, and FIG. 10, or FIGS. 12A and 12B
 are used to produce multiple final sets of processed experimental data
 from raw experimental data. The multiple final sets of processed
 experimental data are typically grossly suitable for visual display,
 comparative analysis or other analysis. However, the present invention is
 not limited to using the methods illustrated in FIG. 2, FIG. 4, FIG. 8,
 and FIG. 10, or FIGS. 12A and 12B, and other methods could be used to
 produce a final set of processed experimental data from raw experimental
 data.
 In exemplary preferred embodiments of the present invention, the multiple
 final sets of processed experimental data are indexed with one or more
 sample indices to create multiple indexed data sets that are suitable for
 visual display and comparative analysis. Preferred embodiments of the
 present invention are used to further process the multiple indexed data
 sets grossly suitable for visual display or comparative analysis to help
 overcome "experiment-to-experiment variability."
 As was discussed above, one of the most commonly used methodologies in
 biotechnology is "comparison." Visual display of biotechnology data is
 typically recognized as typically being "necessary" for biotechnology
 research. If experimental data can be consistently collected, processed
 and displayed with a high degree of confidence that the results are
 accurate and not subject to experiment-to-experiment variability an
 intended result may be achieved in a quicker and more appropriate manner.
 For example, a sequence for a polynucleotide may be established with fewer
 experiments with a higher level of confidence in results.
 Normalizing Processed Experimental Data
 Processed experimental data typically comes from different experimental
 environments (e.g., different electrophoresis-gels or micro-arrays). The
 specific processes used to produce processed experimental data represented
 in any given experimental data set will typically differ from
 experiment-to-experiment. This variability can be of a same order of
 magnitude as data of interest. Thus, when processed experimental data is
 displayed from a same experiment completed multiple times with the same
 target, experiment-to-experiment variability may overwhelm data of
 interest.
 When differential display techniques are used for analysis of experimental
 data, it is implicit in a differential display technique that a first set
 of processed experimental data displayed should have similar
 characteristics to a second set of experimental data (e.g., a similar
 scale or baseline) for a same experiment with a same target. Otherwise any
 significance of any variability revealed by the differential comparison
 would be inherently ambiguous.
 In one exemplary preferred embodiment of the present invention, gross
 measurements of an essential centrality of significant features in indexed
 data sets are created. For example, a "mode" value from a centrality of
 significant features in an indexed data set is created. As is known in the
 art, a mode is a most frequent value in a set of data or a value for which
 a function used to define a set of data points achieves a maximum value.
 This mode value is called a "central character." A carefully constrained
 demodulation of a coarse-grained departure of any given indexed data set
 from this central character has been determined experimentally to remove
 experiment-to-experiment variability.
 Part of the effectiveness of such normalization is dependent upon a utility
 and an accuracy with which the central character is identified as well as
 an extent to which fine-grained departures of each indexed set of data
 points are preserved. For example, if biotechnology data from
 polynucleotides is being used, it is desirable to compare fluorescence
 intensity peaks for polynucleotide fragments of a same size. It is also
 desirable to identify any patterns in relative heights of fluorescence
 peaks as indicators of relative numbers of polynucleotide fragments. Thus,
 measures of centrality are formed from experiment specific, inter-trace
 ratios of smoothed versions of size-calibrated fluorescence trace
 envelopes. Such measures of centrality are used to create a central
 character. However, the present invention is not limited to biotechnology
 experimental data, and other experimental data could also be used.
 FIG. 15 is a flow diagram illustrating a Method 220 for normalization of
 experimental data. Sets of processed experimental data are indexed with
 one or more indices to create multiple indexed data sets that are suitable
 for visual display and comparative analysis. However, other data
 organization schemes could also be used and the present invention is not
 limited to using indices for multiple sets of experimental data. At Step
 222, deviations are measured from a determined central character and data
 values from the multiple indexed data sets. In one exemplary preferred
 embodiment of the present invention, the determined central character is a
 "mode" value of an ordered comparison determined from the multiple indexed
 data sets. However, other types of central characters can also be used and
 the present invention is not limited to central character that is a mode.
 At Step 224, deviations between the central character and the multiple
 indexed data sets are removed by comparing the central character to the
 measured deviations from the multiple indexed data sets. Deviations
 between the multiple indexed data sets are reduced and thus,
 experiment-to-experiment variability is reduced between the multiple
 indexed data sets.
 In one exemplary preferred embodiment of the present invention, the
 multiple indexed data sets include polynucleotide data. The polynucleotide
 data includes, but is not limited to, DNA, cDNA or mRNA data. However, the
 present invention is not limited to multiple indexed data sets that
 include polynucleotide data, and other indexed data sets of experimental
 data can also be used.
 Method 220 helps reduce experiment-to-experiment variability by reducing
 deviations between multiple indexed data set introduced into the multiple
 data sets by experimental variability of individual experiments. Method
 220 allows multiple indexed data sets to be visually displayed on the
 windowed display 16 on the display device 14 to be used for comparative
 analysis.
 In one exemplary preferred embodiment of the present invention, at Step 222
 a normalization transform is applied to the multiple indexed data sets to
 utilize data information across indices from the multiple indexed data
 sets. This normalization transform can also be used to determine a central
 character. The normalization transform includes any of a zero-order
 transform or a low-order transform.
 In another exemplary preferred embodiment of the present invention, a
 determined zero-order central character is multiplied across data values
 in the multiple indexed data sets as a data-value-independent constant to
 normalize data points in the multiple indexed data sets. In yet another
 exemplary preferred embodiment of the present invention, a determined
 low-order central character is multiplied across data values in the
 indexed data sets as a data-value-dependent smoothly varying scaling
 function to normalize data points in the multiple indexed data sets. After
 normalizing data points in the multiple indexed data sets with a
 zero-order central character or a low-order central character, data from
 the multiple indexed data sets are further normalized with Method 220 as
 described above. The zero-order and low-order transforms are explained
 below. However, the present invention is not limited to zero-order or low
 order normalization transforms and other normalization transforms can also
 be used to create a central character.
 Zero-order Data Display Normalization
 A zero-order data display normalization includes determining a zero-order
 central character. The transformed data points are used to determine
 deviations from a zero-order central character. The deviations are
 considered to be of "zero-order" because such central character is a
 "constant" that is independent of the indices of data values from the
 multiple indexed data sets.
 FIG. 16 is a flow diagram illustrating a Method 226 for creating a
 zero-order central character. At Step 228, data points from outer
 quantiles of multiple indexed data sets are removed with a smoothing
 window to create multiple smoothed sets of data points for the multiple
 indexed data sets. At Step 230, a set of indexed data set ratios is
 determined from the multiple smoothed sets of data points. The set of
 indexed data set ratios is determined by comparing a selected smoothed set
 of data points from a selected indexed data set to other smoothed sets of
 data points from other indexed data sets from the multiple indexed data
 sets. At Step 232, outer quantiles of ratios are removed from the set of
 indexed data set ratios to create a subset of indexed data set ratios. At
 Step 234, an averaged set of ratios is determined from the subset of
 indexed data set ratios to create a zero-order central character.
 Method 226 is used to create a zero-order central character to reduce
 experiment-to-experiment variability. In one exemplary preferred
 embodiment of the present invention, a created zero-order central
 character is multiplied across data values in the multiple indexed data
 sets as a data-value-independent constant to normalize data points in the
 multiple indexed data sets before removing deviations (e.g., with Method
 220) with the zero-order central character. In another embodiment of the
 present invention, a created zero-order central character is not
 multiplied across data values in the multiple indexed sets, but is still
 used to reduce experiment-to-experiment variability (e.g., with Method
 220).
 In one exemplary preferred embodiment of the present invention, the
 multiple indexed data sets include polynucleotide data. The polynucleotide
 data includes, but is not limited to DNA, cDNA or mRNA data.
 In one exemplary preferred embodiment of the present invention, at Step 228
 data points from outer quantiles of the multiple indexed data sets are
 removed with a smoothing window. As is known in the art, a distribution
 can be summarized in a few numbers, for ease of reporting or comparison.
 One method is to use "quantiles." Quantiles are values that divide a
 distribution such that there is a given proportion of observations below
 the quantile. For example, a median is a quantile. The median is a central
 value or central character of a distribution, such that half the points
 are less than or equal to the central value and half are greater than or
 equal to it.
 In one exemplary preferred embodiment of the present invention, a
 triangular window is used to smooth envelopes of sets of size-calibrated
 data points in a given indexed set of data points. However, other methods
 can also be used to smooth a trace envelope and the present invention is
 not limited to a triangular smoothing window and other smoothing windows
 could also be used.
 In one exemplary preferred embodiment of the present invention, outer
 quantile values are removed from multiple indexed data sets with a
 smoothing window as is illustrated in Equation 13. A smoothing window has
 a width P. In one specific exemplary preferred embodiment of the present
 invention, P is an odd positive integer greater than or equal to three.
 However, the present invention is not limited to a smoothing window with a
 window size of odd positive integer greater than or equal to three and
 other smoothing window sizes could also be used (e.g., even positive
 integers).
 A smoothed version of a trace envelope f**.sub.k is found with a smoothing
 window as illustrated in Equation 13. However, other smoothing windows
 could also be used.
EQU f**.sub.k.ident.[2/(P+2)].SIGMA..sub.p=-[P/2], . . . ,[P/2]
 [((P+2)-.vertline.p.vertline.)/(P+2)]f*.sub.k+p (13)
 At Step 230, a set of indexed data set ratios is determined. At Step 232,
 outer quantiles of ratios are removed from the set of indexed data set
 ratios to create a subset of indexed data set ratios. With g**.sub.k
 generically designating a smoothed envelope for another set of indexed
 data points and D.sub.s (f**) an s-th quantile of the values of a smoothed
 trace envelope f**, ratios r.sub.k (g,f) for multiple indexed data sets
 are formed as illustrated in Equation 14. However, the present invention
 is not limited to the ratios illustrated in Equation 14 and other ratios
 could also be formulated and used.
EQU r.sub.k (g,f).ident.{g**.sub.k /f**.sub.k :D.sub.s
 (f**).ltoreq.f**.sub.k.ltoreq.D.sub.t (f**);D.sub.s
 (g**).ltoreq.g**.sub.k.ltoreq.D.sub.t (g**)} (14)
 At Step 234, an averaged set of ratios is determined from ratios from the
 subset of indexed data set ratios determined with Equation 14. Using
 D.sub.u (r(g,f)) as a u-th quantile of the ratios of smoothed trace
 envelopes f** and g**, a zero-order normalization of a scale factor,
 .lambda..sub.0 (f), for a central character for a trace envelope f**.sub.k
 is an average over inner quantiles of the ratios and over other distinct
 indexed data sets as is illustrated by Equation 15. However, other
 zero-order normalization scale factors for a central character could also
 be used, the present invention is not limited to the zero-order
 normalization scale factor illustrated in Equation 15. Equation 15 removes
 outer quantile values of ratios of the multiple indexed data sets ratios
 and averages the remaining indexed data set ratios not in a removed outer
 quantile to create an average set of ratios at Step 234.
EQU .lambda..sub.0 (f).ident.avg(.A-inverted.k, g.noteq.f){r.sub.k
 (g,f):D.sub.u (r(g,f)).ltoreq.r.sub.k (g,f).ltoreq.D.sub.v (r(g,f))} (15)
 Although s and u or t and v are not directly related, in one specific
 exemplary preferred embodiment of the present invention, it has been
 determined experimentally that percentiles for the outer quantiles are
 reasonably well-defined using s=u=6 and t=v=95, wherein 6 and 95 represent
 a 6.sup.th percentile and a 95.sup.th percentile respectively in an
 indexed set of data points. Thus, the smallest 6% and the largest 5% of
 the ratios are removed. However, other percentile values could also be
 used for s and u and t and v, and the present invention is not limited to
 these specific values for s and u and t and v.
 FIG. 17 is a flow diagram illustrating a Method 236 for normalization of
 display data using a zero-order central character. At Step 238, deviations
 are measured from a zero-order central character and multiple indexed data
 sets. The zero-order central character is determined from the multiple
 indexed data sets (e.g., with Method 226 of FIG. 16). At Step 240,
 deviations are removed between the zero-order central character and the
 multiple indexed data sets with ratios between the zero-order central
 character and the multiple index data sets and with ratios between the
 multiple indexed data sets and an averaged set of ratios for the multiple
 indexed data sets ratios.
 In one exemplary preferred embodiment of the present invention, the
 multiple indexed data sets include polynucleotide data. The polynucleotide
 data includes, but is not limited to, DNA, cDNA or mRNA data.
 In one exemplary preferred embodiment of the present invention, at Step 238
 of Method 236 (FIG. 17) deviations from a zero-order central character are
 determined using a zero-order central character, for example, with
 .lambda..sub.0 (f), from Equation 15. However, other zero-order central
 characters could also be used in Method 236. At Step 240, deviations are
 removed between the central characters and the multiple indexed data sets
 by finding ratios of the multiple index data sets to the zero-order
 central character as is illustrated by Equation 14. Deviations are removed
 using the multiple indexed data sets and an averaged set of ratios as is
 illustrated with Equation 15.
 Method 236 (FIG. 17) with a zero-order central character helps reduce
 experiment-to-experiment variability by reducing deviations between
 multiple indexed data sets introduced into the indexed data sets by
 individual experiments using a central character created by a
 data-value-independent zero-order normalization of multiple indexed sets
 of data.
 Low-order Data Display Normalization
 A low-order display normalization is a generalization of the zero-order
 Method 226 illustrated in FIG. 16. In one exemplary preferred embodiment
 of the present invention, a low-order central character is used instead of
 a zero-order central character. The low-order normalization produces a
 smoothly varying scaling function with a very low-order dependence upon
 indexed data set data values (e.g., polynucleotide fragment sizes). The
 data-value-dependent low-order central character (FIG. 18) can be
 contrasted with a data-value-independent constant scaling factor produced
 by the zero-order Method 226 (FIG. 16).
 FIG. 18 is a flow diagram illustrating a Method 242 for determining a
 low-order central character. At Step 244, data points from outer quantiles
 of the multiple indexed data sets are removed with a smoothing window to
 form multiple smoothed sets of data points for the multiple indexed data
 sets. At Step 246, a set of indexed data set ratios is determined from the
 multiple smoothed sets of data points by comparing a selected smoothed set
 of data points from a selected index data set to other smoothed sets of
 data points from other indexed data sets from the multiple indexed data
 sets. At Step 248, logarithms are created on the set of indexed data set
 ratios to create a set of logarithm ratios. At Step 250, the set of
 logarithm ratios is filtered to create a filtered set of logarithm ratios.
 At Step 252, an exponentiation is applied to an average of the filtered
 set of logarithm ratios to create a low-order central character.
 In one exemplary preferred embodiment of the present invention, the
 multiple indexed data sets include polynucleotide data. The polynucleotide
 data includes, but is not limited to, DNA, cDNA or mRNA.
 In one exemplary preferred embodiment of the present invention, a created
 low-order central character is multiplied across data values in the
 multiple indexed data sets as a data value dependent smoothly varying
 scaling function. The low-order central character may be used to transform
 data points in the multiple indexed data sets before removing deviations
 (e.g., with Method 220) with the low-order central character. In another
 embodiment of the present invention, a created low-order central character
 is not multiplied across data values in the multiple indexed sets, but is
 still used to reduce experiment-to-experiment variability.
 For any given indexed data set, a low-order size-dependent scaling function
 is created by using a smoothing window (e.g., from Equation 13) to smooth
 envelopes of size-calibrated data values at Step 242. In one preferred
 embodiment of the present invention, Step 244 (FIG. 18) is the same as
 Step of 228 of Method 226 (FIG. 16) (See, e.g., Equation 13). However,
 other smoothing windows could also be used. At Step 246, a set of indexed
 data set ratios is determined by comparing a selected smoothed set of data
 points from a selected index data set to other smoothed sets of data
 points from other indexed data sets from the multiple indexed data sets.
 In one preferred embodiment of the present invention, this is the same as
 Step 230 of Method 226 (See, e.g., Equation 14). However, other ratios
 could also be used.
 At Step 248, logarithms for a desired base-x are formed on the set of
 indexed data set ratios to create a set of logarithm ratios. As is known
 in the art, a logarithm (denoted generally as "log(x)") is an exponent or
 a power to which a given base-x must be raised to produce another number.
 In one exemplary preferred embodiment of the present invention, a log to
 the base e is used where e is the well known mathematical irrational
 number 2.718281828459045 . . . At Step 250, the set of logarithm ratios is
 filtered to create a filtered set of logarithm ratios. In one exemplary
 preferred embodiment of the present invention, the filtering includes
 applying a "low pass filter." However, other filters can also be used and
 the present invention is not limited to low pass filters. As is know in
 the art, a low pass filter-.omega..sub.L "passes" data whose frequencies
 .omega. fall within a range 0.ltoreq..omega..ltoreq..omega..sup.c, and
 rejects data whose frequencies are greater than .omega..sub.c, wherein
 .omega..sub.c is a cutoff frequency.
 In one exemplary preferred embodiment of the present invention, a low pass
 filter is achieved by using a tapered notch in a frequency domain, which
 provides an explicit means for manipulating variability demodulated by a
 low-order normalization. For example, the tapered notch provides
 constraints via a size-scale equivalence of a relative placement of a
 center of a frequency-domain filter edge. A filter edge is chosen to
 ensure that the dampened variability is of a size-scale no finer than a
 significant fraction of a full size range on the display device 14. Such
 scaling functions have very smooth and well-behaved dependence upon data
 size (e.g., polynucleotide fragment size). Note that the zero-order Method
 226 occurs as a special case of the low-order method which is obtained by
 setting an edge of the low pass filter to exclude all variation that has
 any dependence upon data size.
 At Step 250, with f**.sub.k a smoothed envelope for one specific indexed
 data set and g**.sub.k, for another indexed data set other than f**.sub.k,
 a filtered set of logarithmic ratios is created as is illustrated in
 Equation 16. In one exemplary preferred embodiment of the present
 invention, the filter is a low pass filter as described above. However,
 other filters could also be used (e.g., high-pass, band-pass, etc). In
 addition, the present invention is not limited to the filtered set of
 logarithmic ratios illustrated in Equation 16 and other filtered ratios
 could also be used.
EQU .rho..sub.k.ident..chi..sub..omega.[log.sub.x (g**.sub.k /f**.sub.k)] (16)
 In one exemplary preferred embodiment of the present invention, a filter
 .chi..sub..omega. is applied in a frequency domain using a discrete
 Fourier transform to create a filtered set of logarithmic ratios
 .rho..sub.k. The filter .chi..sub..omega., is a tapered low-pass filter
 whose notch mask is multiplied into a zero-padded discrete Fourier
 transform of the logarithmic ratios. Significant features of a tapered
 mask are a degree of tapering and placement of an exclusion edge. In one
 exemplary preferred embodiment of the present invention, a conventional
 two-percent "Tukey taper" is applied to an edge whose half-height (a
 so-called `3 dB point`) is set on a ninth-bin of a discrete transform,
 which is zero-padded by a factor of four. A Tukey taper is known to those
 skilled in the filtering arts. However, other tapers and filters could
 also be used for filter .chi..sub..omega. and the present invention is not
 limited to low pass filters or to Tukey tapers of low pass filters.
 At Step 252, an exponentiation for a desired base-x is applied to an
 average of a filtered set of logarithm ratios to create a low-order
 central character, .lambda..sub.k (f). As is known in the art, an
 exponentiation is an "inverse" of a logarithm.
 The low-order central character, .lambda..sub.k (f), is a size-dependent,
 low-order normalization scaling function for a smoothed envelope f*.sub.k.
 The low-order central character, .lambda..sub.k (f), is an exponentiated
 average of the set of filtered logarithmic ratios over all other k.sup.th
 indexed data sets, as is illustrated in the low-order central character of
 Equation 17. However, the present invention is not limited to Equation 17,
 and exponentiations can also be used.
EQU .lambda..sub.k (f).ident.exp.sub.x
 [avg(.A-inverted.k,g.noteq.f){.rho..sub.k (g,f)}/2] (17)
 In one exemplary preferred embodiment of the present invention, the filter
 .chi..sub..omega. restricts a size-scale of variability demodulated by a
 low-order central character, .lambda..sub.k (f), to no smaller than about
 half a full range of a display size-axis on the display device 16. A
 zero-padding with a tapered filter edge enhances the smoothness of a
 resulting low-order central character by including increasingly smaller
 elements of smaller scale variability.
 FIG. 19 is a flow diagram illustrating a Method 254 for normalization of
 display data using a low-order central character. At Step 256, deviations
 are measured from a low-order central character and multiple indexed data
 sets. The low order character is determined from the multiple indexed data
 sets (e.g., with Method 242 of FIG. 18). At Step 258, deviations are
 removed between the low-order central character and the multiple indexed
 data sets with ratios between the low-order central character and filtered
 logarithms of ratios for the multiple indexed data sets and with
 exponentiations of a filtered set of logarithms of ratios.
 In one exemplary preferred embodiment of the present invention, the
 multiple indexed data sets include polynucleotide data. The polynucleotide
 data includes, but is not limited to, DNA, cDNA or mRNA.
 Method 254 (FIG. 19) with a low-order central character helps reduce
 experiment-to-experiment variability by reducing deviations between
 multiple indexed data set introduced into the indexed data sets by
 individual experiments using a central character created by a
 data-value-dependent low-order normalization of multiple indexed sets of
 data.
 Exemplary Normalized Experimental Data Display Output
 FIG. 20A is a block diagram illustrating a portion of an exemplary output
 display 262 for an indexed set of control data for an illustrative
 experiment (e.g., data peaks 180, 182, and 184 of FIG. 13B). The output
 display 262 is not normalized. FIG. 20B is a block diagram illustrating a
 portion of an exemplary output display 264 for an indexed data set for a
 first target for the illustrative experiment (e.g., a first target
 polynucleotide sequence). The output display 264 is not normalized. In a
 preferred embodiment of the present invention, either a zero-order central
 character or a low-order central character is used to normalize
 experimental results.
 FIG. 20C is a block diagram illustrating a portion of an exemplary output
 display 266 for an indexed data set of control data from FIG. 20A
 normalized with a zero-order normalization (e.g., Method 236, FIG. 17).
 FIG. 20D is a block diagram illustrating a portion of an exemplary output
 display 268 for an indexed set of target data from FIG. 20A normalized
 with a low-order normalization (e.g., Method 254, FIG. 19).
 FIG. 20E is a block diagram illustrating a portion of an exemplary output
 display 270 for an indexed data set for the first target from FIG. 20B
 normalized with a low-order normalization (e.g., Method 250 FIG. 19). FIG.
 20F is a block diagram illustrating a portion of an exemplary output
 display 272 for an indexed data set for the first target from FIG. 20B
 normalized with a low-order normalization (e.g., Method 250 FIG. 19). A
 width for data peaks in FIGS. 20A-20F is expanded for the purposes of
 illustration. However, actual display output in the windowed display 16 on
 the display device 14 for data peaks is similar to those in FIG. 13B.
 The four normalized output displays 266, 268, 270 and 272 correspond to a
 normalized control 258 and a normalization of one experimental variation
 260 for a first target. The output in each of the normalized displays 266,
 268, 270 and 272 distinguished by solid and dashed lines respectively,
 represent independent replications of a sample, in general differing at
 least in a physical gel from which they were taken (e.g., a first run and
 a second run). In an exemplary preferred embodiment of the present
 invention, output in an actual normalized display on the display device 14
 typically uses different colors to illustrate display of multiple
 experimental results.
 As is illustrated in FIG. 20A, there is an experiment-to-experiment
 variability in the indexed data set of control data since the two curves
 are separated. If there were no experiment-to-experiment variability, the
 two curves represented by a solid and dashed line in FIG. 20A would be
 superimposed. As is illustrated in FIG. 20C, a zero-order normalization
 reduces the experiment-to-experiment variability of the control data. The
 two curves in FIG. 20C that are normalized are separated by a smaller
 distance between the two curves from FIG. 20A that are not normalized. As
 is illustrated in FIG. 20D, a low-order normalization further reduces the
 experiment-to-experiment variability as can be seen by a smaller distance
 between the two curves compared to the curves in FIG. 20A.
 FIG. 20E and FIG. 20F illustrate a zero-order normalization and a low-order
 normalization respectively for a first target. As illustrated in FIG. 20B,
 the first target includes more of a first type of data (e.g., a first type
 of polynucleotide sequence) as is illustrated by a first data peak closest
 to the vertical axis, and includes less of a second and third type of data
 represented by the next two data peaks (e.g., a second and third type of
 polynucleotide sequences). This can be seen observed by comparing the
 control data in FIG. 20A to the data displayed for the first target in
 FIG. 20B. As is illustrated in FIG. 20E and FIG. 20F, normalization also
 reduces the experiment-to-experiment variability for the first target as
 can be determined by a narrow separation between the two data curves
 represented by the solid and dashed lines in FIGS. 20E and 20F.
 Since a low-order normalization typically provides slightly better results
 than a zero-order normalization, selecting a zero-order normalization or a
 low-order normalization is dependent on a number of factors including
 desired accuracy of display results, type of analysis required,
 computational time, computational environment, type of display device,
 size of processed indexed data set and other factors. However, selecting
 either a zero-order normalization or a low-order normalization helps to
 significantly reduce experiment-to-experiment variability compared with
 non-normalized data.
 Preferred embodiments of the present invention allow a difference in
 experimental data to be determined and reduced for multiple iterations of
 a selected experiment as well as across multiple different iterations of
 experiments. For example, normalized control data in FIG. 20C or FIG. 20D
 for a first experiment could be compared to normalized control data for a
 second experiment (not illustrated in FIG. 20). The second experiment may
 include the same target or a different target than the first experiment,
 but includes the same control. Preferred embodiments of the present
 invention can be used to determine experiment-to-experiment variability
 between the first and second experiment.
 In addition, normalized data for a first target in FIG. 20E or FIG. 20F in
 a first experiment can be compared to a first target in a different second
 experiment to compare results for the first target in the first experiment
 and in second experiment with reduced experiment-to-experiment
 variability. For example, results of the first experiment including FIGS.
 20A, 20B, 20D and 20F are displayed in a first window of the windowed
 display 16 on display device 14, and results of the second experiment in a
 second window of the windowed display 16.
 FIGS. 20A-20F illustrates exemplary output for preferred embodiments of the
 present invention. However, an actual output display for preferred
 embodiments of the present invention typically would include only
 normalized data and use of the present invention would be "invisible" to a
 user. That is, only a final output display with experiment-to-experiment
 variability reduced is presented to a user for comparative analysis. A
 user would not be presented with the un-normalized data on the display
 device 14 that is illustrated in FIGS. 20A and 20B. Also, only one
 normalization, central character, zero-order or low-order is used at any
 one time. However, in another preferred embodiment of the present
 invention, a zero-order central character and a low-order central
 character may be used together to normalize different selected sets of
 indexed data at the same time.
 Preferred embodiments of the present invention allow "intra-experimental"
 (i.e., same experiment) and "inter-experimental" (i.e., different
 experiments) variability to be reduced for comparative analysis. Preferred
 embodiments of the present invention may also be used as an additional
 method to aid in an automated processing of raw experimental data (e.g.,
 in combination with the methods illustrated in FIG. 2, FIG. 4, FIG. 8, and
 FIG. 10, or FIGS. 12A and 12B above).
 Preferred embodiments of the present invention allow data value features
 that are present in processed experimental data sets, that are of a same
 order of magnitude as data values introduced by experiment-to-experiment
 variability to be normalized and used for comparative analysis. Thus,
 comparison of experimental results can be used with a higher degree of
 confidence, and an intended result may be achieved in a quicker and more
 appropriate manner.
 For example, in the case of biotechnology, a new polynucleotide sequence
 may be determined with fewer experiments with a higher level of confidence
 in the obtained results. This new polynucleotide sequence may be used to
 develop new treatment for diseases, improve existing drugs, develop new
 drugs and as be used for other medical applications including developing a
 more thorough understanding of a biological organism including the
 polynucleotide sequence.
 Exemplary preferred embodiments of the present invention have been
 discussed with respect to biotechnology experimental data. However, the
 present invention is not limited to biotechnology experimental data.
 Preferred embodiments of the present invention may be used to reduce
 experiment-to-experiment variably for telecommunications data, electrical
 data, optical data, physical data, or other experimental data with
 experiment-to-experiment variability introduced by an environment used to
 conduct experiments.
 It should be understood that the programs, processes, methods and system
 described herein are not related or limited to any particular type of
 computer or network system (hardware or software), unless indicated
 otherwise. Various types of general purpose or specialized computer
 systems may be used with or perform operations in accordance with the
 teachings described herein.
 In view of the wide variety of embodiments to which the principles of the
 present invention can be applied, it should be understood that the
 illustrated embodiments are exemplary only, and should not be taken as
 limiting the scope of the present invention. For example, the steps of the
 flow diagrams may be taken in sequences other than those described, and
 more or fewer elements may be used in the block diagrams. While various
 elements of the preferred embodiments have been described as being
 implemented in software, in other embodiments hardware implementations may
 alternatively be used and visa-versa.
 The claims should not be read as limited to the described order or elements
 unless stated to that effect. Therefore, all embodiments that come within
 the scope and spirit of the following claims and equivalents thereto are
 claimed as the invention.