Abstract:
A method for correcting microarray data for the effects of cross-hybridization comprising multiplication of microarray probe hybridization intensities with the inverse or pseudoinverse of a matrix of cross-hybridization potentials between probes and targets. This matrix of cross-hybridization potentials may be determined experimentally by repeating a microarray experiment with each of the targeted genes individually present to determine the cross-hybridization of that targeted gene to each probe, or alternatively, computational models of hybridization may be employed. This represents a new paradigm for handling the problem of cross-hybridization and also can be used in probe-set design strategies.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]    This is a continuation-in-part of application Ser. No. 11/473,472, Filed Jun. 24, 2006. 
     
     FEDERALLY SPONSORED RESEARCH  Not Applicable 
     SEQUENCE LISTING OR PROGRAM  
       [0002]    Not Applicable 
       BACKGROUND OF THE INVENTION  
       [0003]    1. Field of the Invention 
         [0004]    This invention relates to DNA microarrays. More specifically this invention relates to a method of manipulating the data produced by such microarrays. The methods of the present invention are also applicable to the analysis of other nucleotide-nucleotide interactions as well as all nucleic acid-nucleic acid, DNA-protein, RNA-protein, and protein-protein interactions. 
         [0005]    2. Description of Prior Art 
         [0006]    DNA microarrays are known in which genetic probes are affixed to a substrate at discrete locations for binding with a sample containing labeled genetic material. Terminologies used to describe this technology include biochip, DNA chip, DNA microarray and gene array. DNA microarrays allow massively parallel gene expression studies. 
         [0007]    In one type of study employing DNA microarrays the genetic composition of one or more samples is investigated. In the case of samples containing messenger RNA, for instance, a microarray is provided to have a set of cDNA spots for binding. These cDNA spots are referred to as probes. Messenger RNA polynucleotides in the samples being investigated that are complementary to these cDNA probes hybridize with said probes. After hybridization has occurred images of the microarray are obtained using a laser scanner designed to induce fluorescence in markers previously bound to the sample mRNA. In the resulting image the genetic composition of the sample investigated is indicated by the measured intensities of probe locations on the microarray. Such microarray experiments have found a broad range of uses especially in comparative studies between diseased and healthy organisms. 
         [0008]    DNA microarrays, while providing a wealth of data from a massively parallel design, are prone to distortions of various kinds. In many assays there may be one or more nucleic acids present that have a nucleotide sequence closely related to that of one or more of the target sequences being investigated and that differ by only a few nucleotides (one to five for example). In such cases the non-target nucleic acid or nucleic acids may then interfere with the assay by hybridizing with at least some of the probes to produce false qualitative or quantitative results. This problem is particularly acute where the probe sequence is selected to permit assaying of various genes within a multigene family, each member of which contains a sequence closely related to another target nucleotide sequence. 
         [0009]    Thus, in analysis by array technology there is the concern that cross-hybridization may occur—i.e., hybridization of certain sample polynucleotides to probes designed to measure other sample polynucleotides. This could result in false positive signals. This is especially relevant in the field of immunology for example where antibody genes that have high degrees of homology between them are often the subjects of investigation. An effective means of disambiguating intended hybridization and cross-hybridization in such microarrays of high-homology genes would prove highly useful both in research and also in medical diagnostics. This is especially the case for diagnostics relating to autoimmune diseases. Autoimmune diseases such as systemic lupus erythematosus, for instance, are often idiosyncratic in terms of the specific auto-antibody repertoire expressed. For such diseases, as well as for many others, detailed knowledge of the patient-specific manifestation of the disease can valuably inform treatment strategies. An effective array of highly homologous antibody genes could be part of an efficient means to detect the patient-specific auto-antibody repertoire that characterizes a given disease state. 
         [0010]    Approaches have been suggested for alleviating some of the above concerns of specificity and cross-hybridization. One technique involves placing on an array control probes intentionally mismatched with respect to the targets under investigation as well as probes targeting with perfect complementarity the target segments of interest. A mismatched probe differs from a fully complementary probe in that it has one or more base substitutions. By comparing the hybridization signal for the original probe with that of the mismatched probes it is assumed that one can gauge specificity and perhaps even correct for cross-hybridization by subtracting some fraction of the mismatch probe signal from the signal generated by the probe of interest. 
         [0011]    There are some shortcomings to this approach. While the difference between matched and mismatched probes tracks target concentration fairly well when hybridizing to the intended target there is evidence that this correspondence is poorly defined for cases of cross-hybridization (Wu et. al.). This flaw has lead some investigations to the conclusion that it is better to ignore the mismatched probes altogether in estimations of gene expression (Wu et. al.). 
         [0012]    Another approach to resolving the problem of cross-hybridization involves the design and use of cross-hybridizing probes to identify cross-hybridization events. This approach is outlined in U.S. Pat. No. 6,461,816. These cross-hybridizing probes are meant to identify “cross-hybridization events” of a “predetermined probability” to identify the effect of “interfering” targets. This means including additional probes in a microarray experiment to target genes that may cross-hybridize to the original intended probe set. The claimed use of the data gathered from these cross-hybridizing probes is for “selecting or rejecting” a given probe based on its determined risk for distortion due to interference by cross-hybridizing targets. This method recognizes the possibility that untargeted genes in an experimental sample could hybridize to probes targeting other sample genes. It does not though solve the problems of dealing with a large number of highly homologous, potentially cross-hybridizing, targets of interest. It is specified that if a high probability of cross-hybridization is identified, “then the probe is not specific and should not be used without using the results of the cross-hybridization target experiment to correct for cross-hybridization.” This method amounts to an analysis of the specificity of a probe, and though it suggests when correction for cross-hybridization may be necessary, no way of effectively achieving this is specified. 
         [0013]    There are additional methods in the prior art for determining specificity and relative potentials for cross-hybridization of probe and target sets. These include comparing the free-energies of hybridization for gene-specific or cross-hybridizing targets or probes. Computational methods for estimating the free-energy of polynucleotide annealing such as the models of Zucker based on the nucleotide nearest-neighbor thermodynamic studies of SantaLucia are known in the prior art (Rouillard, et. al, 2003; SantaLucia, J, Jr. 1998). Additionally U.S. Pat. No. 6,551,784 discloses a neural network method of predicting hybridization and cross-hybridization intensities in order to chose probes with the least cross-hybridization potential. 
         [0014]    Still other methods have been disclosed for determining the cross-hybridization potential of a set of polymers (DNA, RNA, or Polypeptides). U.S. Pat. No. 6,403,314 discloses one such method in which a matrix of all possible interactions is created and analyzed to identify appropriate probe/target combinations that minimize cross-hybridization within the probe set. This method relies on methods of scoring cross-hybridization potential including thermodynamic calculations. Rouillard, et. al. also describe the use of a matrix to keep a record of “all similarities between the current oligonucleotide sequence and other sequences.” These similarities are used to compute thermodynamic values to distinguish probes with minimal or no cross-hybridization potential. 
         [0015]    While methods have been disclosed in the prior art for identifying potentially cross-hybridizing probes, there remains a need for a method of quantitatively and reliably distinguishing the contributions of cross-hybridization and intended hybridization in the data produced by microarray experiments. This is especially the case in microarray experiments that seek to investigate highly homologous genes. The methods for resolving problems of cross-hybridization that dominate the prior art are generally dominated by efforts to minimize the occurrence of cross-hybridization by choosing probes that target maximally characteristic segments of targets—those with least homology to regions in other targets. While this remains important, a method for distinguishing highly homologous targets has been wanting due to the effects of cross-hybridization. Nevertheless there remains great potential utility for such a method especially in the fields of research and medical diagnostics. 
         [0016]    Therefore, in light of the severe shortcomings of previous approaches towards resolving the problem of cross-hybridization in microarray experiments, the method of this invention is disclosed. 
         [0017]    3. Objects and Advantages 
         [0018]    Thus, the objects of the invention of the microarray analysis method disclosed herein are:
       (a) to provide a method for correcting microarray data for the effect of cross-hybridization;   (b) to provide a method for analyzing microarray data that will allow clear results to be obtained in experiments comparing highly homologous sequences;   (c) to further provide such a method that can yield quantitative results;       
 
         [0022]    Further objects and advantages will become apparent from a consideration of the following descriptions and drawings. 
       SUMMARY OF THE INVENTION 
       [0023]    Briefly, these and other objects of my invention are achieved by the use of a matrix to represent the cross-hybridization potential of each target to every probe, the inverse or pseudoinverse of which matrix is then determined and a vector of experimental results is multiplied by this inverse or pseudoinverse matrix to yield a resultant vector in which the effect of cross-hybridization has been mitigated. This matrix of cross-hybridization potentials may be determined experimentally by repeating a microarray experiment with each of the targets individually present to determine the cross-hybridization of that targeted gene to each probe, or alternatively, computational models of hybridization may be employed. This represents a new paradigm for handling the problem of cross-hybridization and also can be used in probe-set design strategies. 
       DRAWINGS—FIGURES 
       [0024]      FIG. 1  is a schematic illustration of the interaction between a set of targets and a single probe. 
         [0025]      FIG. 2  is a schematic illustration of the interaction between a set of targets and a single probe including a vector representative of interaction potentials. 
         [0026]      FIG. 3  is an illustration of the multiplication of two vectors. 
         [0027]      FIG. 4  is a schematic illustration of the interaction between a set of targets and a set of probes. 
         [0028]      FIG. 5  is an illustration of an example of a matrix generated from hybridization and cross-hybridization potentials. 
         [0029]      FIG. 6  is an illustration of the multiplication of a vector of target concentrations and a matrix of hybridization potentials to yield a vector of hybridization intensities. 
         [0030]      FIG. 7  is an illustration of the multiplication of a vector of target concentrations and a matrix of hybridization potentials to yield a vector of hybridization intensities in which illustration the number of probes is less than the number of targets. 
         [0031]      FIG. 8  is an illustration of the multiplication of a vector of target concentrations and a matrix of hybridization potentials to yield a vector of hybridization intensities in which illustration the number of probes exceeds the number of targets. 
     
     DRAWINGS—REFERENCE NUMERALS 
       [0032]      10  probe 
         [0033]      15  set of five probes 
         [0034]      20  lines representing hybridization potential between each target and a single probe 
         [0035]      25  column vector of values representing hybridization potential between each target and a single probe 
         [0036]      27  lines representing hybridization potentials between each target and each probe 
         [0037]      30  target maximally complementary to probe  10   
         [0038]      35  vector of target concentrations in experimental sample 
         [0039]      37  vector of target concentrations in experimental sample 
         [0040]      38  total hybridization intensity at probe  10   
         [0041]      40  set of targets which may hybridize to probe  10  but which are not maximally complementary to probe  10   
         [0042]      45  set of targets each matched to a probe in the set of probes  15   
         [0043]      50  vector of values representing hybridization potentials between each target in  45  and first probe in  15   
         [0044]      52  vector of values representing hybridization potentials between each target in  45  and second probe in  15   
         [0045]      54  vector of values representing hybridization potentials between each target in  45  and third probe in  15   
         [0046]      56  vector of values representing hybridization potentials between each target in  45  and fourth probe in  15   
         [0047]      58  vector of values representing hybridization potentials between each target in  45  and fifth probe in  15   
         [0048]      60  the matrix composed of vectors  50 ,  52 ,  54 ,  56 , and  58   
         [0049]      65  the non-square matrix composed of vectors  50 ,  52 ,  54 , and  56   
         [0050]      67  the non-square matrix composed of the first four rows of matrix  60   
         [0051]      70  vector of overall hybridization intensities at each probe 
         [0052]      75  vector of overall hybridization intensities at each probe 
         [0053]      77  vector of overall hybridization intensities at each probe 
       DETAILED DESCRIPTION 
       [0054]    In the following description, the invention is described in connection with a preferred embodiment. References are made to accompanying figures. Values used are for purely illustrative purposes and are not representative of any limiting implementation. 
         [0055]    Terminology has been a contentious issue in the prior art. The following terminology will be used in the descriptions that follow. 
         [0056]    “Target” shall refer to the polynucleotide or other sample molecule of interest being investigated in a given experiment. For instance an experiment may include investigating a messenger RNA sample taken from an experimental organism in order to identify the levels of target polynucleotide present in said sample. 
         [0057]    “Probe” shall refer to a known polynucleotide fragment or other known molecule used to investigate a target. In an example experiment investigating mRNA for instance the probes would constitute the various polynucleotide fragments immobilized on a solid support. 
         [0058]    “Microarray” shall refer to the tool comprised of a spatially organized collection of probes and the solid support on which these are immobilized. 
         [0059]      FIG. 1  is a schematic representation of the interaction between a set of target polynucleotides  30  and  40 , and a probe  10 . The relative interaction strength between probe  10  and each of the target polynucleotides in the set of targets  30  and  40  is represented by the collection of lines  20  connecting the target polynucleotides  30  and  40 , and the probe  10 . In this schematic representation the thickness of each line in the group of lines  20  is related to the magnitude of the hybridization potential that line represents. Broken lines in the set of lines  20  represent zero hybridization potential. In one possible experiment target polynucleotides  30  and  40  represent a potential set of polynucleotides which may be present in a sample being investigated. These target polynucleotides can be messenger RNAs for example, and probe  10  can represent a known cDNA fragment immobilized on a microarray chip as described in Lockhardt, et. al. 
         [0060]      FIG. 2  is a schematic representation similar to  FIG. 1 . In  FIG. 2  the relative hybridization potential between the polynucleotide targets  30  and  40 , and probe  10  are represented as a collection of values—i.e. vector  25 —superimposed upon the set of lines  20  representing hybridization potentials. 
         [0061]    The invention disclosed herein recognizes the fact that the hybridization intensity observed on probe  10  in the example experiment described, and on potentially any probe in an actual experiment, is representative not only of the target  30  for which probe  10  is intended but also of other cross hybridizing targets  40  to varying degrees; the degree to which a cross-hybridizing target is represented in the overall hybridization intensity of a given probe being proportional to the hybridization potential between said target and said probe. Thus the signal that would be observed in a hypothetical experiment at probe  10  can be represented as the dot product of a vector  35  representing the concentrations of each target present in the experimental sample and a vector  25  representing the cross hybridization potential of each of these targets to probe  10 . This holds for potentially any probe in any microarray experiment, especially those subject to cross-hybridization. This amounts to taking the sum across all targets of the product of target concentration and the hybridization potential of that target for a given probe. This multiplication is illustrated in  FIG. 3 . 
         [0062]    A more complete example of a microarray experiment incorporates multiple probes—often one or more probes for each intended target though it may also be the case that fewer probes are used than the number targets.  FIG. 4  shows a schematic illustration similar to  FIG. 2 . In  FIG. 4  each of the targets in the set of targets  45  is designed to hybridize most strongly, or when possible exclusively, with one of the probes in the set of probes  15 . As in  FIG. 2  the cross hybridization potentials between each target and each probe are represented by lines of varying thicknesses  27  with broken lines representing zero hybridization potential. Thus just as the schematic representation of  FIG. 2  is analogous to the matrix multiplication operation of  FIG. 3 , the schematic of  FIG. 4  can be represented as a matrix multiplication operation illustrated in  FIG. 6 . 
         [0063]    In  FIG. 6 , the matrix  60 , like the vector  25  in  FIG. 3 , represents the cross hybridization potentials of each target for each given probe. Matrix  60  is made up of five vectors  50 ,  52 ,  54 ,  56 , and  58 , as shown in  FIG. 5 . Each of these column vectors represents the hybridization potential of each target in the set of targets  45  for one probe in the set of probes  15 . The number of elements in each column vector in the matrix  60  is therefore equal to the number of targets in the experiment. This can represent a situation in which each target is assigned one probe. Other situations also occur though, involving an unequal number of targets and probes. One such situation is described in conjunction with  FIG. 7  below. In these cases a non-square matrix of hybridization potentials is generated. 
         [0064]    In  FIG. 6 , vector  70  represents the overall hybridization intensities that are expected at each probe. These overall hybridization intensities incorporate the contribution of the target for which each specific probe is intended as well as the cross hybridizing targets to varying degrees proportional to their cross hybridization potentials represented in matrix  60 . 
         [0065]      FIG. 7  shows a similar situation to  FIG. 6 , though  FIG. 7  illustrates a situation in which the number of probes is less than the number of targets. 
         [0066]      FIG. 8  shows a situation similar to  FIG. 6 , though  FIG. 8  illustrates a situation in which the number of probes exceeds the number of targets. 
         [0067]    The invention disclosed herein recognizes in this representation the potential for the resolution of cross-hybridization in a microarray experiment—i.e. mitigating or removing from the measured hybridization intensity at each probe the contribution of cross-hybridizing targets. It is one object of the invention disclosed herein to calculate indicators of original target concentrations when presented with experimental results in which a measured hybridization intensity at each probe represents the combined contributions of intended target and cross-hybridizing targets. The matrix multiplication of  FIG. 6 ,  FIG. 7 , or  FIG. 8  can be represented by equation  1 , in which I represents the row vector of original target concentrations present in the experimental sample (i.e. vector  35  in  FIG. 6  and  FIG. 7 , and vector  37  in  FIG. 8 ), C represents the matrix with a number of rows equal to the number of elements in I (i.e. matrix  60  in  FIG. 6 , matrix  65  in  FIG. 7 , and matrix  67  in  FIG. 8 ), and O represents the row vector with the same number of elements as columns in C and which represents the overall hybridization intensities at probes on the microarray (i.e. vector  70  in  FIG. 6 , vector  75  in  FIG. 7 , and vector  77  in  FIG. 8 ). 
         [0000]        I*C=O    (Equation 1) 
         [0068]    It is an objective of the invention disclosed herein to recover the vector I when presented with the vector O. The matrix C can be determined in multiple ways, discussed below. Once C is known its inverse or pseudoinverse may be calculated using methods known in the prior art. When the vector O and the inverse or pseudoinverse of the matrix C are known, I can be determined by equation 2, in which Ĉ-1 represents the inverse or pseudoinverse of the matrix C. In the preferred embodiment Ĉ-1 represents the inverse of C when C is an invertible matrix and the pseudoinverse of the matrix C when only the psuedoinverse of the matrix C can be determined. 
         [0000]        I=O*Ĉ -1   (Equation 2) 
         [0069]    The effect of the multiplication of O and Ĉ-1 is further clarified by equation 3. Equation 3 reflects the substitution of O in equation 2 by the product of I and C described in equation 1. 
         [0000]        I=I*C*Ĉ -1   (Equation 3) 
         [0070]    While not wishing to be bound by theory, it is therefore believed that the vector I can be determined as described in equation 2, so long as Ĉ-1 is chosen such that it satisfies equation 3. As described above the inverse and pseudoinverse of C can be suitable choices. 
         [0071]    Thus, a method has been disclosed herein for determining indicators of the concentrations of a set of targets present in an experimental sample from a set of probe hybridization intensities and a matrix describing the hybridization potentials of each target for each probe. Thus, the resolution of intended hybridization and cross-hybridization in microarray experiment data can be accomplished. 
         [0072]    The invention disclosed herein makes use of a matrix of hybridization potentials between each target and each probe. This matrix should be determined for each microarray involving new probe/target combinations. Once this matrix has been determined it can be used repeatedly as long as the design of the experiment does not change. This is highly useful in cases where microarrays are used in medical diagnostics. In medical diagnostics there is often much repetition of the same experiments under near identical conditions. For instance, the same matrix may be used for performing the same microarray test on many different individual patients. 
         [0073]    In the preferred embodiment, the matrix of hybridization potentials is determined in the following manner. A microarray is allowed to hybridize with a single target only. The hybridization intensity at each probe is measured. These hybridization intensities are scaled. One method of scaling involves dividing the intensity at each probe by the sum of the intensities at all of the probes. These scaled hybridization intensities may then be used as the hybridization potentials of a target polynucleotide for each probe on the microarray. These values occupy a row vector in the matrix of hybridization potentials (e.g. matrix  60 , matrix  65 , or matrix  67 ). This is then repeated for all of the targets included in the experiment or some subset thereof until the desired matrix is generated. 
         [0074]    An alternative or adjunct method for determining the matrix of hybridization potentials is to use a computational method to determine relative free energies of hybridization of each target for each probe. These free energies of hybridization can then be scaled in a similar manner to that described above to yield a matrix of relative hybridization potentials (e.g. matrix  60 , matrix  65 , or matrix  67 ). 
       Conclusion, Ramifications, and Scope 
       [0075]    Accordingly, the reader will see that the method of this invention can aid in the resolution of cross-hybridization and intended hybridization in microarray experiment data. 
         [0076]    Although the description above contains many specificities, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of this invention. For instance, as described above, the invention disclosed herein functions equally well in cases where multiple probes are designed for each target and in cases where there are fewer probes than targets because effective methods of determining the inverse of a given matrix are known as are methods for determining the pseudoinverse of a given matrix. Thus, the scope of this invention should not be limited by the dimensions of the matrix of cross-hybridization potentials used. A possible ramification involves performing the method of the invention disclosed herein on one or more subsets of microarray data. This may be used to facilitate efficient manipulation of data in such cases, for example, where a large number of probes is used but only limited subsets of these are sufficiently homologous to require resolution of cross-hybridization. Additionally a wide variety of methods for determining the inverse of a matrix may be implemented. Also, subsets of a microarray can be examined independently in order to ensure that the matrix of hybridization potentials used can be inverted or its pseudoinverse taken using favored means. Furthermore, as is common in the prior art, methods may be included to relate hybridization intensities (e.g. vectors  35  and  37  described by equation  2  above) from a microarray experiment to actual target concentrations. This can be accomplished for instance by the use of a control target added to the experimental sample and whose concentration in the experimental sample is known. Additionally, although the illustrations in the above descriptions involve between four and five probes and between four and five targets many fold greater are routinely used in microarray experiments. The invention disclosed herein may be used with all numbers of probes and targets. Furthermore, the implementations and scale of the invention may be varied and other modifications and variations made without affecting the spirit or scope of the invention. Thus the scope of the invention should be determined by the appended claims and their legal equivalents, rather than by the examples given.