Systems and methods for evaluating the significance of differences in biological measurements

• US 20060190191A1
• Filed: 12/12/2005
• Published: 08/24/2006
• Est. Priority Date: 12/28/1998
• Status: Active Grant

• Current Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Original Assignee: Rosetta Inpharmatics LLC (Merck & Co., Inc.)
• Inventors: Stoughton, Roland, Dai, Hongyue
• Granted Patent: US 7,565,251 B2
• Time in Patent Office: Days
• US Class Current: 702/20
• CPC Class Codes: C12Q 1/6837 using probe arrays or probe chips C12Q1/6874 takes precedence
• CPC Class Codes: G16B 25/00 ICT specially adapted for hybridisation; ICT specially adapted for gene or protein expression
• CPC Class Codes: G16B 25/10 Gene or protein expression profiling; Expression-ratio estimation or normalisation
• CPC Class Codes: Y10T 436/10 Composition for standardization, calibration, simulation, stabilization, preparation or preservation; processes of use in preparation for chemical testing

Abstract

A method for fluorophore bias removal in microarray experiments in which the fluorophores used in microarray experiment pairs are reversed. Further, a method for calculating the individual errors associated with each measurement made in nominally repeated microarray experiments. This error measurement is optionally coupled with rank based methods in order to determine a probability that a cellular constituent is up or down regulated in response to a perturbation. Finally, a method for determining the confidence in the weighted average of the expression level of a cellular constituent in nominally repeated microarray experiments.

Claims

1. A method of fluorophore bias removal comprising the steps of:

(a) labeling a first pool of genetic matter, derived from a biological system representing a baseline state, with a first fluorophore to obtain a first pool of fluorophore-labeled genetic matter;

(b) labeling a second pool of genetic matter, derived from a biological system representing a perturbed state, with a second fluorophore to obtain a second pool of fluorophore-labeled genetic matter;

(c) labeling a third pool of genetic matter, derived from said biological system representing said baseline state, with said second fluorophore to obtain a third pool of fluorophore-labeled genetic matter;

(d) labeling a fourth pool of genetic matter, derived from said biological system representing said perturbed state, with said first fluorophore to obtain a fourth pool of fluorophore-labeled genetic matter;

(e) contacting said first pool of fluorophore-labeled genetic matter and said second pool of fluorophore-labeled genetic matter with a first microarray under conditions such that hybridization can occur, and determining a first color ratio between said first pool of fluorophore-labeled genetic matter that binds under said conditions to said microarray and said second pool of fluorophore-labeled genetic matter that binds under said conditions to said microarray;

(f) contacting said third pool of fluorophore-labeled genetic matter and said fourth pool of fluorophore-labeled genetic matter with a second microarray under conditions such that hybridization can occur, and determining a second color ratio between said third pool of fluorophore-labeled genetic matter that binds under said conditions to said microarray and said fourth pool of fluorophore-labeled genetic matter that binds under said conditions to said microarray; and

(g) computing an average color ratio by averaging said first color ratio and said second color ratio.

2-42. -42. (canceled)

43. A method of estimating a significance d in a difference between a measurement of a cellular constituent in a first microarray experiment and a measurement of the cellular constituent in a second microarray experiment comprising computing:

$d=\frac{\left(X-Y\right)}{\sqrt{{\mathrm{\sigma <br><br>}}_X^2+{\mathrm{\sigma <br><br>}}_Y^2+f^2<br><br>\left(X^2+Y^2\right)}}$

wherein

X is a brightness of a probe spot representing said cellular constituent in said first microarray experiment;

Y is a brightness of a probe spot representing said cellular constituent in said second microarray experiment;

σ

_X² is a variance term for X that represents an additive error level in X;

σ

_Y² is a variance term for Y that represents an additive error level in Y;

f is a fractional multiplicative error level;

σ

_X²+f²X² is an estimated variance for X; and

σ

_Y²+f²Y² is an estimated variance for Y.

44. The method of claim 43, wherein the first microarray experiment and the second microarray experiment are performed on the same microarray.

45. The method of claim 43, wherein the first microarray experiment and the second microarray experiment are each performed on a different microarray.

46. The method of claim 43, wherein

the first microarray experiment is repeated a number of times and the brightness of the probe spot X representing said cellular constituent in the first microarray experiment and each of the repeats of the first microarray experiment are combined to form a weighted mean x;

the second microarray experiment is repeated said number of times and the brightness of the probe spot Y representing said cellular constituent in the second microarray experiment and each of the repeats of the second microarray experiment are combined to form a weighted mean y;

$\mathrm{wherein}$$d=\frac{\left(x-y\right)}{\sqrt{{\mathrm{\sigma <br><br>}}_X^2+{\mathrm{\sigma <br><br>}}_Y^2+f^2<br><br>\left(x^2+y^2\right)}},<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{wherein}$$x=\frac{\sum <br><br>\frac{x_i}{{\mathrm{\sigma <br><br>}}_{\mathrm{xi}}^2}}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_{\mathrm{xi}}^2}\right)}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>y=\frac{\sum <br><br>\frac{y_i}{{\mathrm{\sigma <br><br>}}_{\mathrm{yi}}^2}}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_{\mathrm{yi}}^2}\right)},<br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{xi}}^2={\mathrm{\sigma <br><br>}}_X^2+f^2<br><br>X^2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{yi}}^2={\mathrm{\sigma <br><br>}}_Y^2+f^2<br><br>Y^2,$

and wherein when said number of times approaches zero

σ

_x approaches

$\sqrt{\frac{1}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_{\mathrm{xi}}^2}\right)}},$

and σ

_y approaches

$\sqrt{\frac{1}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_{\mathrm{yi}}^2}\right)}},$

and when said number of times approaches a large number

σ

_x approaches observed error from scatter in X, and

σ

_y approaches observed error from scatter in Y.

47. The method of claim 43, wherein said second microarray experiment is a nominal repeat of said first microarray experiment.

48. The method of claim 43, wherein said first microarray experiment represents a baseline state of a biological system and said second microarray experiment represents a perturbed state of said biological system.

49. The method of claim 48, wherein the perturbed state of said biological system is achieved by exposing said biological system, when representing said baseline state, to a pharmacological agent.

50. The method of claim 48, wherein the perturbed state of said biological system is achieved by exposing said first biological system, when representing said baseline state, to a drug candidate.

51. The method of claim 48, wherein the perturbed state of said biological system is achieved by introducing an exogenous gene into the biological system when the biological system represents said baseline state.

52. The method of claim 48, wherein said perturbed state of said biological system is achieved by deleting a gene from said biological system when the biological system represents said baseline state.

53. The method of claim 48, wherein said perturbed state of said biological system is achieved by changing a culture condition of said biological system when the biological system represents said baseline state.

54. The method of claim 48, wherein said perturbed state of said biological system is due to the onset of a disease in said biological system.

55. The method of claim 48, wherein the biological system is a cell line, a cell culture, a tissue sample, an organ, or a multicellular organism.

56. The method of claim 48, wherein the biological system is a mammal.

57. The method of claim 48, wherein the biological system is a Homo sapien.

58. The method of claim 48, wherein the biological system is a yeast that is substantially isogenic to Saccharomyces cerevisia.

59. The method of claim 48, wherein the baseline state represents the wild-type state of the biological system.

60. The method of claim 48, wherein the baseline state represents a different perturbed state of the biological system.

61. A method of estimating a significance d in a difference between a measurement of a cellular constituent in a first microarray experiment and a measurement of the cellular constituent in a second microarray experiment comprising computing:

$d=\frac{\left(X-Y\right)}{{\mathrm{\sigma <br><br>}}_{X-Y}}$

wherein

X is a brightness of a probe spot representing said cellular constituent in said first microarray experiment;

Y is a brightness of a probe spot representing said cellular constituent in said second microarray experiment; and

σ

_X-Y is the combined error in the measurement of said cellular constituent in said first microarray experiment and the measurement of said cellular constituent in said second microarray experiment.

62. The method of claim 61, wherein the first microarray experiment and the second microarray experiment are performed on a single microarray.

63. The method of claim 61, wherein the first microarray experiment and the second microarray experiment are each performed on a different microarray.

64. The method of claim 61, wherein said second microarray experiment is a nominal repeat of said first microarray experiment.

65. The method of claim 64, wherein said first microarray experiment represents a baseline state of a biological system and said second microarray experiment represents a perturbed state of said biological system.

66. The method of claim 65, wherein the perturbed state of said biological system is achieved by exposing said biological system, when representing said baseline state, to a pharmacological agent.

67. The method of claim 65, wherein the perturbed state of said biological system is achieved by exposing said first biological system, when representing said baseline state, to a drug candidate.

68. The method of claim 65, wherein the perturbed state of said biological system is achieved by introducing an exogenous gene into the biological system when the biological system represents said baseline state.

69. The method of claim 65, wherein said perturbed state of said biological system is achieved by deleting a gene from said biological system when the biological system represents said baseline state.

70. The method of claim 65, wherein said perturbed state of said biological system is achieved by changing a culture condition of said biological system when the biological system represents said baseline state.

71. The method of claim 65, wherein said perturbed state of said biological system is due to the onset of a disease in said biological system.

72. The method of claim 65, wherein the biological system is a cell line, a cell culture, a tissue sample, an organ, or a multicellular organism.

73. The method of claim 65, wherein the biological system is a mammal.

74. The method of claim 65, wherein the biological system is a Homo sapien.

75. The method of claim 65, wherein the biological system is a yeast that is substantially isogenic to Saccharomyces cerevisia.

76. The method of claim 65, wherein the baseline state represents the wild-type state of the biological system.

77. The method of claim 65, wherein the baseline state represents a different perturbed state of the biological system.

78. A method of estimating a significance d in a difference between a measurement of a cellular constituent in a plurality of first microarray experiments and a measurement of the cellular constituent in a plurality of second microarray experiments comprising computing:

$d=\frac{\left(x-y\right)}{{\mathrm{\sigma <br><br>}}_{x-y}}$

wherein

the brightness of the probe spot X representing said cellular constituent in the plurality of first microarray experiments are combined to form the weighted mean x;

the brightness of the probe spot Y representing said cellular constituent in the plurality of second microarray experiments are combined to form the weighted mean y;

σ

_x-y is the combined error in the measurement of said cellular constituent in the plurality of first microarray experiments and the measurement of said cellular constituent in the plurality of second microarray experiments;

wherein

${\mathrm{\sigma <br><br>}}_{x-y}=\sqrt{{\mathrm{\sigma <br><br>}}_x^2+{\mathrm{\sigma <br><br>}}_y^2};<br><br>$$x=\frac{\sum <br><br>\frac{x_i}{{\mathrm{\sigma <br><br>}}_{\mathrm{xi}}^2}}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_{\mathrm{xi}}^2}\right)}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>y=\frac{\sum <br><br>\frac{y_i}{{\mathrm{\sigma <br><br>}}_{\mathrm{yi}}^2}}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_{\mathrm{yi}}^2}\right)};<br><br>$

x_i is the observed brightness of probe spot X in a microarray experiment i in the plurality of first microarray experiments;

y_i is the observed brightness of probe spot Y in a microarray experiment i in the plurality of second microarray experiments;

σ

_xi² is the estimated variance in x_i in a microarray experiment i in the plurality of first microarray experiments; and

σ

_yi² is the estimated variance in y_i in a microarray experiment i in the plurality of second microarray experiments;

and wherein when each of said plurality of first microarray experiments and said plurality of second microarray experiments approaches one

σ

_x approaches

$\sqrt{\frac{1}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_{\mathrm{xi}}^2}\right)}},$

and σ

_y approaches

$\sqrt{\frac{1}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_{\mathrm{yi}}^2}\right)}},$

and wherein when each of said plurality of first microarray experiments and said plurality of second microarray experiments approaches a large number

σ

_x approaches observed error from scatter in X, and

σ

_y approaches observed error from scatter in Y.

79. The method of claim 78, wherein each second microarray experiment in the plurality of second microarray experiments is a nominal repeat of a first microarray experiment in the plurality of first microarray experiments.

80. The method of claim 78, wherein each first microarray experiment in the plurality of first microarray experiments represents a baseline state of a biological system and each second microarray experiment in the plurality of second microarray experiments represents a perturbed state of said biological system.

81. The method of claim 80, wherein the perturbed state of said biological system is achieved by exposing said biological system, when representing said baseline state, to a pharmacological agent.

82. The method of claim 80, wherein the perturbed state of said biological system is achieved by exposing said first biological system, when representing said baseline state, to a drug candidate.

83. The method of claim 80, wherein the perturbed state of said biological system is achieved by introducing an exogenous gene into the biological system when the biological system represents said baseline state.

84. The method of claim 80, wherein said perturbed state of said biological system is achieved by deleting a gene from said biological system when the biological system represents said baseline state.

85. The method of claim 80, wherein said perturbed state of said biological system is achieved by changing a culture condition of said biological system when the biological system represents said baseline state.

86. The method of claim 80, wherein said perturbed state of said biological system is due to the onset of a disease in said biological system.

87. The method of claim 80, wherein the biological system is a cell line, a cell culture, a tissue sample, an organ, or a multicellular organism.

88. The method of claim 80, wherein the biological system is a mammal.

89. The method of claim 80, wherein the biological system is a Homo sapien.

90. The method of claim 80, wherein the biological system is a yeast that is substantially isogenic to Saccharomyces cerevisia.

91. The method of claim 80, wherein the baseline state represents the wild-type state of the biological system.

92. The method of claim 80, wherein the baseline state represents a different perturbed state of the biological system.

93. A method of determining an error σ

_x of a weighted mean x for a quantitative measurement of a cellular constituent, the method comprising;

obtaining a plurality of instances N of said quantitative measurement, wherein each instance x_i of said quantitative measurement is from a first microarray experiment or a nominal repeat of said first microarray experiment;

computing

$x=\frac{\sum <br><br>\frac{x_i}{{\mathrm{\sigma <br><br>}}_i^2}}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_i^2}\right)}$

wherein

x is the weighted mean of the quantitative measurement;

σ

_i² is the estimated variance of instance x_i of said quantitative measurement; and

computing said error in the mean such that,

when N approaches 1,

σ

_x approaches

$\sqrt{\frac{1}{\sum <br><br>\left(\frac{1}{{\mathrm{\sigma <br><br>}}_i^2}\right)}}$

and when N approaches a large number of nominal repeats σ

_x approaches observed error from scatter in x.