Técnicas de análisis de microarrays -...

Post on 03-May-2020

10 views 0 download

Transcript of Técnicas de análisis de microarrays -...

Técnicasdeanálisisdemicroarrays

AntonioGómezTato

EtapasenelanálisisdeMicroarrays• Segmentaciónyextraccióndedatos.

• Filtradoytransformacióndedatos.

• Normalización.

• AnálisisestadísAcoenfuncióndelobjeAvo– Análisisclusteryclasificación

– Patronesdeexpresióntemporalparabuscargenescorregulados.

– Búsquedadegenesexpresadosdeformadiferencial

– .....

Segmentaciónyextraccióndedatos

3

4

Diferentes tipos de microarrays

5

6

7

Primera microarray de rodaballo

8

Imágenes de microarrays

La imagen de un microarray que obtiene un scanner no es más que una colección de números.

La imagen de un microarray que obtiene un scanner no es más que una colección de números.

La imagen de un microarray que obtiene un scanner no es más que una colección de números.

Etapasdelanálisisdelasimágenes

• Localizarlosdiferentesspots(segmentación).

• Decidirquépixelsformanpartedelspotycuálesno.

• Calcularunvalor“representaAvo”delasintensidadesdecadaspot.

• Calcularelruidodefondo(background)

12

13

Se coloca una primera rejilla sobre la imagen de la microarray para dividirla en regiones, una por cada una de la agujas del robot de impresión.

Primer paso de la segmentación

Segundopasodelasegmentación

14

Localizar la región que sólo contenga al spot que queremos analizar.

15

Tercerpaso:Decidirquéesspotyqué

background

16

17

Intensidades de un spot representadas en tres dimensiones

gen 1,3 canal 2

510

15

20

5

10

15

Intensidad

0

5000

10000

15000

20000

Tercerpaso:Decidirquéesspotyquébackground

18

Programasdeextraccióndedatosdemicroarrays

• Spo\inder(TIGRsuite)

• Genepix

• Spot

• FeatureextracAon(Agilent)

• ...

19

EjemplosegmentaciónautomáAca

20

Con Feature extraction de Agilent y una microarray de oligos.

Cada esquina tiene un patrón diferente

EjemplosegmentaciónautomáAca

21

Localizadas las esquinas y conociendo la estructura de la microarray estima la posición de los centros de los spots

EjemplosegmentaciónautomáAca

22

En cada centro hipotético coloca tres “galletas” concéntricas radios prefijados.

Los pixels dentro de la primera galleta son los del spot.

Los pixels que sólo están en la galleta más grande son el background local

Resultadodelprocesodesegmentaciónyextraccióndedatos

23

Un archivo, para cada microarray, de (en nuestro caso) 13544 filas por 67 columnas, que hay que depurar y analizar.

Filtradoytransformacióndedatos

24

• Seeliminanlosspotsdebajacalidadatendiendoadiferentescriterios.– Formairregulardelspot

– Spotmuydiferentedelasotrasréplicasdelmismogenenlamismamicroarray.

– SpotconintensidadnosignificaAvamentediferentedelbackground.

– Etc.

25

Ejemplo:Genesfiltradoenunamicroarrayderodaballo

26

● ●

●●●●

●● ●●●● ●

● ● ●●●●●

●● ●●●●

● ●●●● ●●

● ● ●

● ●

●●

● ●● ●●●

●● ●●●● ●● ● ●

● ●●●● ● ●● ●

●●

●●●

●●●

●● ●

●●●● ●

●● ● ●●●● ● ●●

●● ●●

●●

●●●●●

●●●● ●●

●● ●●

●●

●●●

●●

●●●

●●

●● ●● ● ●

● ●●

●●●●

● ●● ●●

●●

●● ●●● ●● ●

●●● ● ●●●●

● ● ●●●● ●●

●●

●● ●●

●● ●

●●

●●

● ●●

●●●

●●●

● ● ●●

● ●● ●●●●

● ●●

●●

● ●●

● ●●

●●

● ●● ●●

● ●● ● ● ●●●●

●● ●●

●● ●●●

● ●●

●● ●● ●● ●●

●●

●●

● ●●●

●●

● ●●

●●

●●

● ●● ● ● ●●●

●● ● ●●

●● ●●

●● ●

● ● ●

●●● ●

● ●●●

●● ●● ●●●

●●

●●

●● ● ● ●●●● ● ●● ●●● ●●

●● ●●● ●

●●

●●●●

●● ●

●● ●●●

● ●

● ● ● ●●●

● ●

●● ●

●●

●●

●● ●

●●●

●●●

●●●

●●● ●●

●●

●●

●●

● ●

●● ●

●● ●●

●●● ●

●●

●● ●● ●

●●● ●● ●●●

● ●● ●● ● ●●● ●●

●●●

●●

●●

● ●

●●

●● ●●● ●

●● ●● ●●

●● ●● ●●

●●●

●● ●●

●●

● ●

●● ●● ●

●●● ● ●●● ●

● ●●●● ●●

●● ● ●

● ● ●●●●

●●●●●●

●●

● ●

●● ●●

●●

●●

●● ●●

●●

●● ● ●

●●

●●

● ●●●

● ●● ●● ●

●●●

●● ●

●●●●

●●

●● ●●●

●● ●

● ● ●●

●●

●● ●

●●

●●

●● ●● ● ●●

●●

●●●●

●●

●●

● ●●

● ●●

●● ● ●● ● ● ●● ●● ●

●●

●●

●● ●●

●● ● ●

●●●

●●

●●●●● ●●● ●

●●

●●●● ●●● ●

● ● ●●

●●

●●●

●●

●●●●●● ● ●●

●●●

●●

●●

●● ● ●● ● ●

●●

●●

●● ●●●●

● ●●●

●●

●●

●●●●● ●

●●●

●●

●●

● ●

●● ●

●● ● ●●

●●●● ●

●●

●●

●●●

●●

● ●● ●

●●●

●●●

● ●●

●● ●●

●●

●●●●● ●

● ● ●●● ●●

●●

●●

●●

● ●●

●● ●

●● ●● ●

●● ●●● ●

●●

●● ●●●

● ●

● ●●●

●●●● ●●●● ●●●

●● ●● ●

● ●●

●●●

●●

●●●●

● ●●● ●●●

●●

●●● ●

●● ●●

● ●●●

●● ●●● ● ●●

●●

●●

● ● ●● ●●

● ●● ● ● ● ●

●● ●●●

●●

●●● ●●●●

●●

● ●●

● ●●●● ●● ●

●●●●

● ●●●

●●●●

●● ● ●●●

●●

●●

●● ●● ●● ●●●●● ●●●●

●●

●●● ●●

● ●

●●

●● ●●

●●●● ● ●● ●●

●●●

● ●● ●● ●●●●●

●●

● ●●●

● ●

●●● ●●

● ●●● ●

● ●●●

●●

● ●●

●●

●● ●●

●●

●●

●● ●● ●●● ●●

● ●●●

● ● ●

●●

●● ●●● ●

●●

●●

● ●●●● ●● ● ●

●●

● ●

●●

●●●

●●●●● ●● ●● ● ●●

●●●

●●●

● ●

●●

●●

●●●●●

● ●●

● ●●

●●●

●●●

●●● ●

●●● ●●●

●●

●●

●● ●● ●●● ●

● ● ●

●●● ●

●●

●●

●●●●● ●●●

●●

●●●●

● ●

●● ● ●●● ●● ●

●●●

●●

●●●●●

●● ●

●● ●

●● ●●

●●

● ●

●● ● ●● ●●

●●● ●● ●●

●●●

●●●

●●●● ●

● ●●● ●●

●●●●●● ●

●●

●●●

● ●● ●● ●●

●●

●● ●●●

●●●

●●

●●

●●

●●●

● ●●● ●● ●

●● ●● ●

●● ●

●●●

● ●●

●●

●●● ● ●

●●●

●●

●● ●

● ●●

●● ●● ●

●● ●

●●

●●● ●● ● ●●●

●● ●●

●● ●● ●

● ●

● ● ●

●●●

● ●

●●●

●●

●●

●●

●● ●

●● ●●

●● ●

● ●●●

●● ●●

● ●●●●

●● ●

●●

●●

●●●

● ● ●

● ●●

●●● ●● ●

●●

●● ●●

●●

●● ● ●● ●

●●● ● ●●●●

●● ● ●●●●

●● ●

●● ●

● ●●●

● ●

●●

●● ●●●

●●

● ●● ●● ● ●

● ● ●●

●●● ●

●● ● ●● ● ● ●

● ●●● ● ●●

●● ● ●

●●●

●●

● ●● ●● ●

●●

● ● ●

●●

●●

● ●●

●●

●●●

●●

●●● ●

●●●●

●●

● ●●● ● ●●●●

● ●●

● ●●● ●● ●

●●

● ● ●●● ●

●● ●

● ● ● ●●●● ●

●●● ●● ●●● ●

●●●

●●

● ● ●● ●●

●● ●

●●● ●● ● ●●●●

●●

● ●

●●

●●

●●

●●● ●●● ●● ●●

●●●●

●●

●● ●

●●

●●

● ●

● ● ● ●

●●●

● ● ●●

●●●● ●

●●

●● ●

● ●●●

●●●

●●

● ●● ●● ● ●

●● ● ●●

●●

●●●●

●●●

● ● ●● ●

●●●

●●

●● ●●● ●●

● ●● ●● ●● ●

●●

●●

●● ●●

●● ●

●●

●●●●

●●

●●●

● ● ●●

● ●● ●●●● ●●● ●

●●

●●●

●●●●

●● ●● ●●

●●● ● ● ●● ● ●●● ●●

●●●

● ●● ●●● ●

●●● ●

●●

●●

●●● ●● ● ●●

●●

●● ●●

●●●

● ●●● ●●● ●● ●

●●

●●●●

● ●●● ●● ●●

● ●●● ●●● ●● ●

● ●●

●● ● ●●

●● ●●

●●

●● ● ●●●● ●

●● ●● ●

● ●

●●● ●●

●●

●● ●●● ● ●●

●● ●● ●

● ●●

●●

● ● ● ●● ●●

●●●● ● ●● ●

● ●●

● ● ●●● ●● ●●●● ● ●●

●● ●●● ● ●●●●

●●

●●

●● ● ●

●●● ●●●

●●

●●

● ●● ●●● ●●

●●

●●

●●

●● ●

●● ●● ●● ●

●●●

●●

● ●●●

●● ● ●

● ● ●● ● ●

●●

●● ●

● ●

●●● ●●

●● ● ●● ●

●●

●● ●

●● ●●

●●●

●●

●●●

●●●

●● ●●

●●●

●●● ●●● ●●●●

●●● ●●

●● ●

●● ●● ●

●●

●●

● ●●●● ●●

● ●●

●● ●●

●●

●●

● ●

●●

●● ●● ●●●

●●

●●

●●● ●●●●

●● ●●● ●●●● ●●● ● ●●

● ● ●

●● ●● ●●●

●●●

● ●●

● ●

● ●●●

●●

●●

●●●

●●●

●●

●●

●●● ●●

●● ● ●●●

● ●●●

●●●● ●●●

●●● ● ●●

●●● ●●●

●●● ●

● ●●

●●●●●

●●

●● ●●●

●●

●●

●●

●●

●● ●

●●●

● ●

●●

●●●●● ●

●● ●

●●●●

●● ●●●

● ●

●●

●●●

●●

●●

●●

●●

● ● ●●

●● ●

●●

●●

●●

●●●●

● ●●●

●●●

●●● ●

●●●

● ●

●●●

●●●●

● ●●

●● ●

●● ●

●●●

●●

●●

●●●

●●● ●●●

●●

●●●●

●● ● ●●● ●●● ● ● ●

●●●

●●●● ●● ● ●

●● ●●● ●● ●●

● ●●● ●● ●●

● ●● ●●

● ● ● ●●● ●● ●

●●● ●●

●●●●

●● ●●● ●●

●●● ● ●

●●

●● ●

1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

log(mean)

sd

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

Eliminados por filtradoNo eliminados por filtrados

Desviaciones típicas de las réplicas frente a logaritmo de sus medias para los genes de la micro Cal_B12C.txt

27

●●●●●

●●●●

●●

●●●●●

●●●

●●●

●●●●●

●●●●

● ●●

●●●●●

●●●●

●●●●

●●●●

●●●

●●●●●●●

●●●●

●●

●●●●●●●●

●●●●●●●●

●●

●● ●

●●

●●

●●

●●

●●●●●●●●

●●

●●●

●●●

●●●●●●●●

●●

●●●

●●●●●

●●●●●●●

●●

●●●●

●●

●●

●●●●●●●●

●●●

●●

●●

●●●●●●

●●

●●●●

●●●●●

●●

●●●●●●●●●

●●●●

● ●●●

●●●

●●●

●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●●

●●●●

●●●

●●

●●●●●●●●●

●●● ●●●

●●● ●●●●●●●●●●●●

●●●

●●●●●●●●●

●●

● ●

●●● ●●

●●●

●●

●●

●●

●●●●

●●●●●

●●●●●

●●

●●●●●

●●

●●

●●●●●●●●

●●●●

●●

●●

● ●

●●●

●●●●●

●●

●●●●●●●●

●●

●●

●●

●●●

●●

●●

●●●

●●●●

●●

●●

●●●●

●●

●●

●●●●●●●●

●●

●●●●●●●

●●●●●

● ●●●

●●●●●●●●●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●●●●●●●

●●

●●●●

●●

●●

●●●●

●●●●●●

●●●

●●●●

● ●●

●●●

●●

●●●●●●●●

●●

●●●●●●●

●●●●●

●●●●

●●

●●

●●●●●●

●●

●●●●

●●●●●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

● ●●●●●●

●●●

●●●●●●●

●●●●●●●●

●●

●●●●●●●

●●●●●

●●●●●●

●●

●●●●●●

●●●●

●●●●●

●●

●●●●●

● ●●●●●

●●●

●●

●●●

●●

●●

●●●●

●●●●●

●●●●

●●●●●●●●●●●●●●●●●●

●●●●

●●●

●●

●●●●●●●

●●●

●●●●

●●●

●●●●

●●●

●●

●●●

●●

●●●●●●●●●

●●●●

●●

●●●●●●●

●●●●●●

●●

●●●●●●●

●●●

●●●

●●●●

●●

●●●●●

●●

●●

●●

●●●●

●●●●

●●●

●●●●●●●●

●●●●●●●●

●●●

●●●●●●●●

●●●●●●●●●●

●●●●

●●

●●●

●●

●●●

●●●●●●●

●●

●●●●●●

●●●●●

●●

●●●●

●●

●●●

●●●●●

●●●●

●●●●

●●●●●●●

●●●●

●●●

●●

●●●●●●●

●●●●●

●●●●●●●

●●●

●●●

●●

●●●

●●

●●

●●●

●●

●●●●●●

●●

●●●●●●●

●●

●●●●

●●

●●

●●●●

●●

●●●●

●●●●●

●● ●●

●●●●

●●

●●●●●

●●●●●●

●●●●●

●●

●●●●●●●●

●●●●●●●●

●●●●●●●●●●●

●●●●

●●●

●●●●●●●

●●●●●●●●●●

●●●●●

●●

●●●●●●

●●

●●

●●●

●●●

●●●●

●●●● ●●●●●●●

●●

●●●●●●●●

●●●●

●●●●

●●●

●●●●●●●

●●●

●●

●●●●●●●

●●●

●●●●●●

●●

●●●●●●

●●●●●●●●●

●●

●●

●●

●●●●

●●

●●●

● ●

●●

●●●●

●●

●●●

●●●●●●

●●●●●●●●

●●

●●●●●●●

●●

●●●●●

●●●

●●●

●●●●●

●●●●●●

●●●

●●

●●

●●

●●●●●●●● ●●●●●

●●

●●

●●●

●●●

●●●●●●●

●●●

●●●

●●

●●

●●

●●

●●●●●

●●●● ●●●

●●

●●●

●●●●●

●●●● ●●●●

●●●●●

●●●●

●●● ●

●●●●●

●●

●●

●●●

●●●●

●●● ●

●●

●●●●●●

●●

●●●●●●●●

●●

●●●●●

●●●●

● ●

●●●

●●●

●●

●●

●●●●●●

●●

●●●●●

●●●

●●

●●●

●●

●●●●

●●●

●●

●●●●

●●

●●●

●●●●●●●●●●

●●

●●●●●

●●

●●●●●●

●●

●●

●●●●●●●●

●●● ●●

●●●

●●●●●●●●●●●●

●●

●●●●

●●

●●

●●●

●●●●●●

●●●

●●●●●●●●●●●

● ●

●●●

●●

●●●●

●●●

●●

●●●●●●●●●●●●●

●●

●●●● ●●

●●●

●●●●

●●

●●●

●●●

●●●●

●●●

●●

●●● ●●●

● ●●

●●

●●

●●●●●

●●

●●

●●

●●●

●●●

●●●●

●●●

●●

●●●●●

●●●

●●●●●●●

●●

●●●

●●

●●

●●●

●●

●●●●●●●

●●

●●●

●●●●●

●●

●●●●

●●

●●●●

●●●●●

●●

●●

●●

●●●

●●●●●●

●●

●●●●●

●●●●●●

●●

●●●●●●

●●●●●●

●●●

●●●●●●●●●●●●

●●●●●●●●

●●

●●●

●●

●●

●●

●●●●

●●●●●●●

●●

● ●

●●●●●●

●●

●●●●●

●●

●●● ●●

●●

●●●●●

●●

●●

●●

●●●●●●●●●

●●

●●●●●

●●●●●

●● ●●●●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●●●●●●

● ●●●●●●

●●

●●

●●●●

●●●●●●●●●●

●●●●●

●●●●●●

●●●●●●●●

●●●●●●

●●●●●●●●●

●●

●●●

●●

●●●

●●●

●●

●●●●

●●

●●

●●● ●●●●●

●●

●●●●●

●●

●●●

●●●

●●

●●●

●●●●●

●●●●●●●●●●

●●●●●

●●

●●●●

●●●

●●

●●●●●●

●●

●●●●●●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●●

●●●

●●●●

●●●

●●

●●● ●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●

●●

●●●●●●●●

●●●●●

●●●

●●

● ●

●●●

●●●●

●●●●

●●●●●●●

●●●●●●●●●

●●●

●●●●

●●●

● ●●

●●●●●●

●●●

●●●

●●●●

●●

●●

●●●●

●●

●●●●●

●●

●●

●●●●

●●●●●●

●●● ●

●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●

●●●●

●●●●●●●●

●●

●●●

●●

●●

●●●●●● ●●●●

●●●

●●●●●●

●●●●●●

●●● ●●

●●

●●

●●

●●●●●

●●●

●●●

●●●●●●●

●●●●●●

●●

●●●●●

●●●●●

●●

●●●

●●●●●●●●

●●●●●●●

●●

●●●

●●●●

●●●●●●●

●●

●●

●●●

●●●●●

●●●●

●●

●●

●●●●●●

●●●

●●●

●●

●●●●●

●●●●●

●●

●●

●●●

●●●●

●●

●●●●

●●●

●●

● ●●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●●●

●●●

●●●●●●

●●

●●

●●

●●●●●

●●●

●●●

●●●

●●

●●

●●●●●●●●●

●●●●

●●●

●●●●●●●●●

●●

●●●●

●●●

●●●●

●●●

●●

●●●

●●●●●● ●●●●● ●●

●●

●●●●●●

●●●●

●●●

●●●●

●●●●●●

●●

●●

●●●

●●●●●

●●●●

●●●●

● ●●

●●●

●●●●

●●●●

●●

●●●●●●●●●●●●●●

●●●●

●●●●●●

●●●●●

●●●

●●

●●●●

●●

●●●

●●●

●●●●

●●●●●●

●●●

●●●

●●

●●●●●●

●●

●●

●●●

●●●●

●●●

●●●

●●● ●●●●●

●●●●●

●●●●

● ●●●

●●●●●●●●●●

●●

●●●

●●●●●

●●

●●●●●●●●●

●●●●●●●●●

●●●●●●●●

●●●

●●

●●

●●●●●●●●

●●●

●● ●●

●●●●●

●●●●●●●●●●

●●

●●●●

●●

●●●

●●●

●●

●●●

●●●

●●

●●●

●●

●●●

● ●

●●

●●

●●●●●

●●●●●●●●●●●●

●●

●●

●●●

●●●

●●●●●

●●

●●

●●●●

●●●

●●●

●●

●●

●●

●●●●

●●●●

●●

●●●

●●●●

● ●●

●●●●

●●●●

●●●

●●●●●●

● ●

●●

●●●●

●●●

●●●●

● ●●●● ●●●●●●●

●●●●

●●

●●

●●●●●●●

●●●●●

●●●

●●●

●●●●●●

●●

●●●

●●●●●●

●●●●

●●

●●●●

●●●

●●

●●

●●●●●

●●●●●●●●●●

●●●●●

●●●●

●●●●

●●

●●

●●●●●●●●

●●

●●●●●●

●●●●●●●●●●●●●●●●●

●●●

●●●

●●●●

●●

●●●●●

●●●●●●

●●●

●●

●●

●●

●●

●●

●●●●●

●●●●●●●●●

●●

●●

●●●●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●●●●●● ●

●●●●●

●●

●●

●●

●●●●●●●

●●

●●●

●●●●●

●●

●●●●

●●

●●●●●● ●

●●●●●●●

●●

●●●●●●●●

●●●●●

●●●●●

●●

●●

●●

●●

●●

●●●●

●●●●●●●

●●●

●●●

●●●●●●●

●●

●●●

●●

●●●●

●●●

●●●●●●

●●●

●●●

●●●

●●●●●●●

●●

●●

●●●

●●

●●●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●

●●

●●●

●●

●●●●●

●●

●●●

●●

●●●

●●●●●●

●●●●

●●●●

●●

●●●●

●●●

●●●●

●●●●●●●

●●

●●●

●●

●●●●●●●●

●●●

●●

●●●

●●●●●●●

●●

●●●

● ●

●●

●●

●●●●●●●

● ●

●●

●●●●●● ●

●●●●●●

●●●●●

●●●

●●

●●

●●

●●

●●

●●

●●●●●●●

●●●●

●●●●●●●●●●

●●●●●

●●

●●●●●●●●●●

● ●

●●●●

●●

●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●●●

●●●●●●●●●●●

●●

●●

●●●

●●●

●●

●●

●●●●●●

●●●●

●●

●●

●●●● ●

●●●●●

●●

●●●

●●●●●

●●

●●●●

●●●●●●

●●●●

●●●

●●

●●●●

●●

●●

●●● ●●●●●

●●●

●●

●●

●●●●

●●●

●●●●●

●●●●

●●●

●●●●

●●

●●●

●●●●●●

●●● ●●●●●●●

●●●●

●●

●●●

●●

●●●●●●●●●●

●●●●

●●●

●●●●●

●●●●●●

●●●●●●

●●●

●●●●

●●●

●●

●●●●●

●●●●

●●●●

●●●●

●●●●

●●●

●●●●●●

●●●

●●●●●

●●

●●●●●

●●

●●

●●

● ●

●●

●●

●●

●●●●

●●●

●●

●●

●●●●●

●●●

●●●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●●●●●●●●

●●

●●●

● ●●●●●●

●●●

●●

●●●●●●●●●●

●●●●●

● ●

●●

●●●●

●●●●●●

●●●

●●●●●

●●

●●

●●●

●●

●●●

●●●●

●●

●●●●●●

●●

●●●

●●

●●●

●●●●

●●

●●●●

●●

●●●●●●●

●●

●●●

●●●

●●●●

●●

●●●●

●●●●●●

●●●●●●

●●●

●●

●●

●●

●●●●●

●●●●

●●●

●●●●●●●

●●●●●

●●●●●●●●●●

●●●

●●

●●

●● ●

●●

●●●

●●

●●●

●●

●●●●

●●●

●●

●●●●●●●●●

●●

●●●

●●●

●●

●●

●●●●●

●●●●●

●●●

●●

●●

● ●

●●

●●●●

●●

●●

●●

●●

●●●●●●●

●●●

●●●●●●

●●

●●●●

●●● ●●●

●●

●●

●●●●

●●●●●

●●●

●●

●●●

●●●

●●●●●●

●●

●●●

●●

●●●●●

●●●●

●●●●

●●

●●

●●●

●●

●●

●●

●●●●

●●●

●●●●●●

●●●

●●●

● ●●●●●

●●●●

●●

●●

● ●●●●●●●

●●

●●●●●●●●● ●●●

●●●

●●●●●●

●●●

●●●●

●●●●

●●●

●●●●

●●●●●●●●

●●●●●

●●●

●●●●

●●

●●

●●●●

●●●●●●●

●●●●●

●●

●●

●●●●●●●●●

●●●

●●●●

●●

●●

●●

●●●

●●●●●●● ●●●

●●

●●●●●●●

●●●●●

●●●

●●●●●●

●●

●●●●

●●●

●●●

●●●●

●●●

●●●

●●●●●●

●●

●●●●●●●●●●

●●

●●●

●●●

●●

●●●●●●●●●●●

●●●●●●●●●●●●

●●

●●

●●●●

●●●

●●

●●●

●●●

●●●●

●●● ●

●●●●●

●●

●●●

●●●●●●

●●●

●●

●●●

●●●●●●●●

●●●

●●

●●●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●●●●

●●●●●

●●

● ●●●●●●●

●●●

●●●●

●●●●●●

●●●●●●●

●●

●●

●●●●●●●

●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●●●●●

●●●●●●

●●●

●●

●●

●●

●●●●

●●

●●●●●●●●●●

●●

●●

●●

●●●

●●●●

●●●●●●●

●●●●

●●

●●

●●●●●

●●

●●●●●●●

●●

●●

●●

●●●●●●●

●●●

●●●

●●●

●●

●●

●●

●●

● ●

●●●

●●

●●●●●●●●●

●●●

●●

●●●

●●●●

●●

●●●●

● ●●●

●●●●●

●●●●●●●●●

●●●●

●●●●●●●

●●

●●●

●●●

●●●●

●●●●

●●

●●●●●

●●●●

●●●

●●

●●●

●●●●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●

●●●

●●

●●

●●●●●

●●

●●●●

●●●●

●●●

●●●

●●

●●●●

●●

●●●

●●●

●●●

●●

●●●

●●●●●●●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●●●●●

●●●

●●●●

●●●

●●●

●●●

●●●●●●●

●●

●●●●

●●

●●●●

●●●●●●●

●●

●●●

●●●

●●

●●●

●●●●

●● ●

●●●●

●● ●●●

●●

●●●●●

●●

●●●

●●

●●●

●●

●●●●

●●●●

●●●

●●●

●●●

●●●●

●●●●

●●●

●●●●●

●●

●●

●●●●●●

●●

●●●●●●

●●

●●

●●

●●

●●

●●●●●●

● ●●

●●●

●●

●●

●●●

●●●●●●

●●●●●

●●

●●●●

●●●

● ●●●●

●●

●●

●●

●●●●●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●● ●●●

●●●●

●●

●●●●

●●

●●

●●●●●●●●●

●●●●

●●

●●

●●●●●

●●●●

●●●

● ●

●●

●●●●●

●●

●●●●

●●●

●●●●

●●●●●●●●●●

●●●●●●●●

●●●

● ●●●●

●●●

●●●

●●

●●●●●●●●

●●●

●●●

● ●

●●●●●

●●●

●●●

●●

●●

●●

●●●●●

●●●●●●●●●

●●

●●●

●●

●●

●●●

●●

●●●●

●●●

●●

●●

●●●●

●●●

●●●●●

●●●●●

●●

● ●

● ●

●●●●

●●●

●●●●●●

●●●●

●●●●●

●●●●

●●●●●

●●●

●●●●●

●●●

●●

●●●

●●●●●●

●●

●●● ●●●

●●●●

●●●

●●●

●●●

●●

●●●

●●●●

●●●●●●●

●●●●

●●●

●●●●

●●

●●●

●●

●●●●●●●

●●●●●

●●●●●●●

●●●●●

●●●●●● ●

●●●● ● ●●●●●●●●●●●●●

●●●

●●

●●

●●●

●●●●●●

●●●●

●●●●

●●●●●●●●

●●

●●

●●●

●●●●

●●●●

●●●●

●●●

●●●●●

● ●

●●●

●●

●●●●●●

●●●

●●

●●●●●

●●●

●●

●●●●●

●●

●●

●●

●●●●●●●●●●●●

●●

●●

●●

●●

●●

●●●●

●●●●●●●

●●

●●●●●●

●●●●●●●●●

●●●●●

●●

●●●●

●●●●

●●

●●●●●

●●

●●●●●●●●●

●●●●●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●●●●●●

●●●●

●●●●

●●

●●●

●●

●●●

●●

●●●

●●●

●●●●●●●●

● ●●●●

●●

●●●● ●●●●●●●●●

●●●

●●●

●●●●

● ●

●●●

●●●●●

●●

●●● ●●●●

●●

●●●●●●●●●● ●●

●●●●●●

●●

●●●●

●●●

●●●

●●

●●

●●

●●●

●●

●●●

●●●●

●●

●●●

●●●

●●●●

●●●●●

●●

●●●●●

●●

●●●●● ●●

●●●●

●●

●●

●●

●●●●●

●●

●●

●●

●●●

●●●●

●●●●

●●

●●●●

●●

●●

●●●●

●●

●●●●●●

●●

●●●●●●●●

●●

●●●

●●●●●

●●●●●●

●●●●●

●●

●●

●●●●●

●●●●

●●●●●●●

●●●●●●

●●

●●●

●●●

●●●

●●●

●●●●●

●●●●●

●●●●●●●

●●●●

●●●

●●

●●●●

●●●●

●●●●

●●●

●●●●●

●●●●

●●●●

●●●●●●●●

●●

●●

●●●●

●●●●

●●●

●●●●●

●●●

●●●

●●●●●

● ●

●●●●●●●●●●●

●●

●●

●●

●●●●

●●

●●●

●●●●

●●

●●

●●●

●●●●●●

●●

●●

●●●●●

●●●●●

●●

●●●

●●●

●●●●●

●●●

●●

●●

●●

●●

●●●●●●●●●●●●●●

●●

●●

●●●●●●●

●●●●●

●●●

●●●●●●●

●●●●●

●●●

●●●

●●● ●

●●●●●●

●●●●●

●●

●●●●●●

●●

●●●●

●●●

●●

●●●●

●●●

●●●●●

●●

●●

●●●●

●●●

●●●

●● ●

●●

●●●●

●●●

●●●

●●

●●●●●● ●●●●

●●●●●●

●●

●●

●●●●●●●●●●●●●●●●●

●●●●

●●●●●●●●●

●●

●●●

●●●

● ●●

●●

●●●●●●●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●

●●●●●

●●●●●●●●

●●

●●●

●●

●●●

●●●

●●

●●●

●●●●●

●●●

●●

●●

●●●

●●

●●●●

●●●●

●●

●●

●●

● ●

●●

●●

●●●●●●●●

●●●●●

●●●

●●

●●●●●

●●●

●●●●●●●●●●●●

●●●

●●●●

●●●●●●●●●●

●●●●●●●

●●●●

●●●●

●●●●●●

●●

●●●

●●●

●●●●●●

●●●●●●●●●

●●

●●

●●

●●●●●

●●●●

●●●●●

●● ●●

●●●●●●●●●●

●●●●●

●●●

●●●●●

●●●●●●●

●●●●●●●●●●

●●●

●●

●●●

●●●●●

●●

●●●

●●

●●

●●

●●●●●●●

●●●●

●●●●●●

●●●●●●●

●●●

●●●●●●●

●●●●●

●●

●●● ●●

●●●

●●

●●●

●●●●●●

●●●●●●

●●●●●●●●●●●

● ●●●●

●●●●●●●●●

●●●●

●●●

●●●●

●●●●

●●

●●●

●●●●●●●●●●●●

●●●●

●●

●●●

●●

●●●●●●●●

●●

●●●●

●●●●

●●●

●●●●●●●●●

●●

●●

●●●●

●●●●

●●

●●●●

●●●●●●●●

●●●●● ●

●●●

●●●

●●

●●●●●●●●●

●●●

●●●●●●●●●●●●●

●●●

●● ●

●●●●●

●●●

●●

●●

●●●●●●●

●●

●●●

●●●

●●

●●●●

●●●●

●●●

●●●●

●●

●●●

●●●●

●●

●●●●●●

●●

●●

●●

●●●●●●●

●●

●●

●●

●●

●●●●●

●●●

●●●

●●

●●●

●●●●●●●●

●●●●●●●●●

●●●

●●

●●

●●●

●●●●●●●●●●

●●

●●●

●●●●●●●●

●●●●

●●●

●●●●●●

●●

● ●

●●●

●●●

●●●●●●●●●●●

●●●●●●●

●●●●●●

●●

●●

●●

●●

●●●● ●●●●●●●●

●●●●●●●

●●●●

●●●

●●

●●

●●

●●●

●●●●●●●●●●●●

●●

●●●●●●●

●●●●●

●●●

●●

●●

●●

●●●●

●●●●

●●●●●

●●

●●●● ●●●●●●

●●●

●●●

●●●●●

●●●●

●● ●

●●●

●●

●●●●●

●●●●

●●●

●●●●

●●●●●●●●●●

●●●●●

●●●

●●●

●●●●●

●●●●●●

●●

●●

●●

●●●●●

●●●●●●●●

●●

●●●

●●●

●●

●●

●●●

●●●●

●●

●●

●●

●●●●●●●

●●

●●

●●●

●●

●●

●●●●

●●●

●●

●●●●

●●●●

●●

●●●

●●

●●

●●

●●●●●●

●●●

●●

●●●

●●●●

●●●●●

●●●●●●●

●●●●●●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●●●●●●●●●

●●

●●●●●●●

●●●

●●●●

●●

●●

●●

●●●●●●●

●●●●●●

●●●●●

●●●●●●

●●

●●

●●

●●●●

●●●●●●●●●

●●●

●●

●●●●

●●●

●●●●

●●●●●●

●●●

●●

●●●●

●●

●●●●●

●●●

●●●●

●●

●● ●●

● ●●

●●●

●●●

●●●●●●●

●●●●

●●●●●

●●

●●●

●●●

●●●●●●

●●●

●●●●

●●●●

●●●

●●●●

●●●●●●●●●

●●

●●

●●●●

●●

●●●

●●●●●●●

●●●●●

●●●

●●●

●●●●●●

●●

●●●

●●●

●●●●●

●●

●● ●●●●●●

●●●

●●●

●●●●●●●

●●●●●●●

●●

●●●

●●●

●● ●●●

●●●●

●●●

●●

●●

●●

●●

●●●●

●●●

●●●

●●

●●●

●●●●

●●●

●●●

●●●●●

●●

●●

●●

●●●●●●

●●

●●●●●

●●●●

●●●●●●

●●●●●●

●●

●●●●

●●

●●●

●●●●

●●●●●●●●●●●●

●●●●

●●●●●

●●●●●●

●●●●●

●●

●●●●●

●●

●●●●

●●●●●●

●●●●●

●●●●●

●●

●●●●

●●●●●●

●●●●

●●●●●

●●●●●●●

●●●

●●●●●

●●●

●●●●●●●●●●

●●●

●●

●●●●

●●

●●●●●

●●●●●●

●●●

●●●●

●●●●●●● ●

●●●●●

●●

●●

●●●

●●●●

●●●

●●●●●●●●

●●●●

●●●●●●●●

●●●

●●●

●●●●●●

●●

●●

●●

●●●●

●●●

●●

●●●

●●

●●●●●

●●●●

●●●●●●

●●●

●●●●

●●

●●●

●●●

●●

●●

●●●●

●●

●●●●●

●●

●●

●●●●●●●●●●

●●●

●●●●●

●●●●●●●●●●●

●●

●●●

●●

●●●●

●●●●●●

●●●

●●

●●●●●

●●●

●●●●

●●●

●●

●●●

●●

●●●●●

●●

●●●●●

●●

●●

●●●●●●

●●●

●●

●●●

●●●●●

●●●

●●●

●●●●●

●●●●

●●●●

●●●

●●

●●●●●●●

●●●● ●●●●●●

●●●●

●●

●●

●●●

●●●●

●●●

●●

●●●●●

●●●●

●●

●●●

●●●

●●

●●●●●●●●●

●●●●●●●●

●●●

●●●●●

●●

●●●●●●

●●●

●●

●●●●

●●●

●●●

●●●

●●●●●

●●

●●●●●

●●●●●●

●●●●●

●●●●●●

●●●

●● ●

●●

●●

●●●

●●●●●●

●●●●

●●●

●●●●

●●

● ●

●●

●●

●●

●●

●●●●●

●● ●● ●

●●●●●●●

●●●●●

●●● ●●●●●●●●●

●●

●●

0e+00 1e+05 2e+05 3e+05 4e+05 5e+05 6e+05

0e+00

1e+05

2e+05

3e+05

4e+05

5e+05

6e+05

Intensidades de los dos canales

intensidades control

Inte

nsid

ades

infe

ctad

o

Enfrentar las intensidades de un canal frente al otro tiene dos aspectos negativos

1. Casi todos los valores se encuentran concentrados en la esquina inferior izquierda

2. La variabilidad aumenta con la intensidad. ●

●●●●●

●●●●

●●

●●●●●

●●●

●●●

●●●●●

●●●●

● ●●

●●●●●

●●●●

●●●●

●●●●

●●●

●●●●●●●

●●●●

●●

●●●●●●●●

●●●●●●●●

●●

●● ●

●●

●●

●●

●●

●●●●●●●●

●●

●●●

●●●

●●●●●●●●

●●

●●●

●●●●●

●●●●●●●

●●

●●●●

●●

●●

●●●●●●●●

●●●

●●

●●

●●●●●●

●●

●●●●

●●●●●

●●

●●●●●●●●●

●●●●

● ●●●

●●●

●●●

●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●●

●●●●

●●●

●●

●●●●●●●●●

●●● ●●●

●●● ●●●●●●●●●●●●

●●●

●●●●●●●●●

●●

● ●

●●● ●●

●●●

●●

●●

●●

●●●●

●●●●●

●●●●●

●●

●●●●●

●●

●●

●●●●●●●●

●●●●

●●

●●

● ●

●●●

●●●●●

●●

●●●●●●●●

●●

●●

●●

●●●

●●

●●

●●●

●●●●

●●

●●

●●●●

●●

●●

●●●●●●●●

●●

●●●●●●●

●●●●●

● ●●●

●●●●●●●●●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●●●●●●●

●●

●●●●

●●

●●

●●●●

●●●●●●

●●●

●●●●

● ●●

●●●

●●

●●●●●●●●

●●

●●●●●●●

●●●●●

●●●●

●●

●●

●●●●●●

●●

●●●●

●●●●●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

● ●●●●●●

●●●

●●●●●●●

●●●●●●●●

●●

●●●●●●●

●●●●●

●●●●●●

●●

●●●●●●

●●●●

●●●●●

●●

●●●●●

● ●●●●●

●●●

●●

●●●

●●

●●

●●●●

●●●●●

●●●●

●●●●●●●●●●●●●●●●●●

●●●●

●●●

●●

●●●●●●●

●●●

●●●●

●●●

●●●●

●●●

●●

●●●

●●

●●●●●●●●●

●●●●

●●

●●●●●●●

●●●●●●

●●

●●●●●●●

●●●

●●●

●●●●

●●

●●●●●

●●

●●

●●

●●●●

●●●●

●●●

●●●●●●●●

●●●●●●●●

●●●

●●●●●●●●

●●●●●●●●●●

●●●●

●●

●●●

●●

●●●

●●●●●●●

●●

●●●●●●

●●●●●

●●

●●●●

●●

●●●

●●●●●

●●●●

●●●●

●●●●●●●

●●●●

●●●

●●

●●●●●●●

●●●●●

●●●●●●●

●●●

●●●

●●

●●●

●●

●●

●●●

●●

●●●●●●

●●

●●●●●●●

●●

●●●●

●●

●●

●●●●

●●

●●●●

●●●●●

●● ●●

●●●●

●●

●●●●●

●●●●●●

●●●●●

●●

●●●●●●●●

●●●●●●●●

●●●●●●●●●●●

●●●●

●●●

●●●●●●●

●●●●●●●●●●

●●●●●

●●

●●●●●●

●●

●●

●●●

●●●

●●●●

●●●● ●●●●●●●

●●

●●●●●●●●

●●●●

●●●●

●●●

●●●●●●●

●●●

●●

●●●●●●●

●●●

●●●●●●

●●

●●●●●●

●●●●●●●●●

●●

●●

●●

●●●●

●●

●●●

● ●

●●

●●●●

●●

●●●

●●●●●●

●●●●●●●●

●●

●●●●●●●

●●

●●●●●

●●●

●●●

●●●●●

●●●●●●

●●●

●●

●●

●●

●●●●●●●● ●●●●●

●●

●●

●●●

●●●

●●●●●●●

●●●

●●●

●●

●●

●●

●●

●●●●●

●●●● ●●●

●●

●●●

●●●●●

●●●● ●●●●

●●●●●

●●●●

●●● ●

●●●●●

●●

●●

●●●

●●●●

●●● ●

●●

●●●●●●

●●

●●●●●●●●

●●

●●●●●

●●●●

● ●

●●●

●●●

●●

●●

●●●●●●

●●

●●●●●

●●●

●●

●●●

●●

●●●●

●●●

●●

●●●●

●●

●●●

●●●●●●●●●●

●●

●●●●●

●●

●●●●●●

●●

●●

●●●●●●●●

●●● ●●

●●●

●●●●●●●●●●●●

●●

●●●●

●●

●●

●●●

●●●●●●

●●●

●●●●●●●●●●●

● ●

●●●

●●

●●●●

●●●

●●

●●●●●●●●●●●●●

●●

●●●● ●●

●●●

●●●●

●●

●●●

●●●

●●●●

●●●

●●

●●● ●●●

● ●●

●●

●●

●●●●●

●●

●●

●●

●●●

●●●

●●●●

●●●

●●

●●●●●

●●●

●●●●●●●

●●

●●●

●●

●●

●●●

●●

●●●●●●●

●●

●●●

●●●●●

●●

●●●●

●●

●●●●

●●●●●

●●

●●

●●

●●●

●●●●●●

●●

●●●●●

●●●●●●

●●

●●●●●●

●●●●●●

●●●

●●●●●●●●●●●●

●●●●●●●●

●●

●●●

●●

●●

●●

●●●●

●●●●●●●

●●

● ●

●●●●●●

●●

●●●●●

●●

●●● ●●

●●

●●●●●

●●

●●

●●

●●●●●●●●●

●●

●●●●●

●●●●●

●● ●●●●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●●●●●●

● ●●●●●●

●●

●●

●●●●

●●●●●●●●●●

●●●●●

●●●●●●

●●●●●●●●

●●●●●●

●●●●●●●●●

●●

●●●

●●

●●●

●●●

●●

●●●●

●●

●●

●●● ●●●●●

●●

●●●●●

●●

●●●

●●●

●●

●●●

●●●●●

●●●●●●●●●●

●●●●●

●●

●●●●

●●●

●●

●●●●●●

●●

●●●●●●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●●

●●●

●●●●

●●●

●●

●●● ●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●

●●

●●●●●●●●

●●●●●

●●●

●●

● ●

●●●

●●●●

●●●●

●●●●●●●

●●●●●●●●●

●●●

●●●●

●●●

● ●●

●●●●●●

●●●

●●●

●●●●

●●

●●

●●●●

●●

●●●●●

●●

●●

●●●●

●●●●●●

●●● ●

●●●●●●

●●●●●●

●●●●●●●●●●●●●●●●●

●●●●

●●●●●●●●

●●

●●●

●●

●●

●●●●●● ●●●●

●●●

●●●●●●

●●●●●●

●●● ●●

●●

●●

●●

●●●●●

●●●

●●●

●●●●●●●

●●●●●●

●●

●●●●●

●●●●●

●●

●●●

●●●●●●●●

●●●●●●●

●●

●●●

●●●●

●●●●●●●

●●

●●

●●●

●●●●●

●●●●

●●

●●

●●●●●●

●●●

●●●

●●

●●●●●

●●●●●

●●

●●

●●●

●●●●

●●

●●●●

●●●

●●

● ●●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●●●

●●●

●●●●●●

●●

●●

●●

●●●●●

●●●

●●●

●●●

●●

●●

●●●●●●●●●

●●●●

●●●

●●●●●●●●●

●●

●●●●

●●●

●●●●

●●●

●●

●●●

●●●●●● ●●●●● ●●

●●

●●●●●●

●●●●

●●●

●●●●

●●●●●●

●●

●●

●●●

●●●●●

●●●●

●●●●

● ●●

●●●

●●●●

●●●●

●●

●●●●●●●●●●●●●●

●●●●

●●●●●●

●●●●●

●●●

●●

●●●●

●●

●●●

●●●

●●●●

●●●●●●

●●●

●●●

●●

●●●●●●

●●

●●

●●●

●●●●

●●●

●●●

●●● ●●●●●

●●●●●

●●●●

● ●●●

●●●●●●●●●●

●●

●●●

●●●●●

●●

●●●●●●●●●

●●●●●●●●●

●●●●●●●●

●●●

●●

●●

●●●●●●●●

●●●

●● ●●

●●●●●

●●●●●●●●●●

●●

●●●●

●●

●●●

●●●

●●

●●●

●●●

●●

●●●

●●

●●●

● ●

●●

●●

●●●●●

●●●●●●●●●●●●

●●

●●

●●●

●●●

●●●●●

●●

●●

●●●●

●●●

●●●

●●

●●

●●

●●●●

●●●●

●●

●●●

●●●●

● ●●

●●●●

●●●●

●●●

●●●●●●

● ●

●●

●●●●

●●●

●●●●

● ●●●● ●●●●●●●

●●●●

●●

●●

●●●●●●●

●●●●●

●●●

●●●

●●●●●●

●●

●●●

●●●●●●

●●●●

●●

●●●●

●●●

●●

●●

●●●●●

●●●●●●●●●●

●●●●●

●●●●

●●●●

●●

●●

●●●●●●●●

●●

●●●●●●

●●●●●●●●●●●●●●●●●

●●●

●●●

●●●●

●●

●●●●●

●●●●●●

●●●

●●

●●

●●

●●

●●

●●●●●

●●●●●●●●●

●●

●●

●●●●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●●●●●● ●

●●●●●

●●

●●

●●

●●●●●●●

●●

●●●

●●●●●

●●

●●●●

●●

●●●●●● ●

●●●●●●●

●●

●●●●●●●●

●●●●●

●●●●●

●●

●●

●●

●●

●●

●●●●

●●●●●●●

●●●

●●●

●●●●●●●

●●

●●●

●●

●●●●

●●●

●●●●●●

●●●

●●●

●●●

●●●●●●●

●●

●●

●●●

●●

●●●●●●●●●●●●●

●●●●●●

●●●●●●●●●●●

●●

●●●

●●

●●●●●

●●

●●●

●●

●●●

●●●●●●

●●●●

●●●●

●●

●●●●

●●●

●●●●

●●●●●●●

●●

●●●

●●

●●●●●●●●

●●●

●●

●●●

●●●●●●●

●●

●●●

● ●

●●

●●

●●●●●●●

● ●

●●

●●●●●● ●

●●●●●●

●●●●●

●●●

●●

●●

●●

●●

●●

●●

●●●●●●●

●●●●

●●●●●●●●●●

●●●●●

●●

●●●●●●●●●●

● ●

●●●●

●●

●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●●●

●●●●●●●●●●●

●●

●●

●●●

●●●

●●

●●

●●●●●●

●●●●

●●

●●

●●●● ●

●●●●●

●●

●●●

●●●●●

●●

●●●●

●●●●●●

●●●●

●●●

●●

●●●●

●●

●●

●●● ●●●●●

●●●

●●

●●

●●●●

●●●

●●●●●

●●●●

●●●

●●●●

●●

●●●

●●●●●●

●●● ●●●●●●●

●●●●

●●

●●●

●●

●●●●●●●●●●

●●●●

●●●

●●●●●

●●●●●●

●●●●●●

●●●

●●●●

●●●

●●

●●●●●

●●●●

●●●●

●●●●

●●●●

●●●

●●●●●●

●●●

●●●●●

●●

●●●●●

●●

●●

●●

● ●

●●

●●

●●

●●●●

●●●

●●

●●

●●●●●

●●●

●●●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●●●●●●●●

●●

●●●

● ●●●●●●

●●●

●●

●●●●●●●●●●

●●●●●

● ●

●●

●●●●

●●●●●●

●●●

●●●●●

●●

●●

●●●

●●

●●●

●●●●

●●

●●●●●●

●●

●●●

●●

●●●

●●●●

●●

●●●●

●●

●●●●●●●

●●

●●●

●●●

●●●●

●●

●●●●

●●●●●●

●●●●●●

●●●

●●

●●

●●

●●●●●

●●●●

●●●

●●●●●●●

●●●●●

●●●●●●●●●●

●●●

●●

●●

●● ●

●●

●●●

●●

●●●

●●

●●●●

●●●

●●

●●●●●●●●●

●●

●●●

●●●

●●

●●

●●●●●

●●●●●

●●●

●●

●●

● ●

●●

●●●●

●●

●●

●●

●●

●●●●●●●

●●●

●●●●●●

●●

●●●●

●●● ●●●

●●

●●

●●●●

●●●●●

●●●

●●

●●●

●●●

●●●●●●

●●

●●●

●●

●●●●●

●●●●

●●●●

●●

●●

●●●

●●

●●

●●

●●●●

●●●

●●●●●●

●●●

●●●

● ●●●●●

●●●●

●●

●●

● ●●●●●●●

●●

●●●●●●●●● ●●●

●●●

●●●●●●

●●●

●●●●

●●●●

●●●

●●●●

●●●●●●●●

●●●●●

●●●

●●●●

●●

●●

●●●●

●●●●●●●

●●●●●

●●

●●

●●●●●●●●●

●●●

●●●●

●●

●●

●●

●●●

●●●●●●● ●●●

●●

●●●●●●●

●●●●●

●●●

●●●●●●

●●

●●●●

●●●

●●●

●●●●

●●●

●●●

●●●●●●

●●

●●●●●●●●●●

●●

●●●

●●●

●●

●●●●●●●●●●●

●●●●●●●●●●●●

●●

●●

●●●●

●●●

●●

●●●

●●●

●●●●

●●● ●

●●●●●

●●

●●●

●●●●●●

●●●

●●

●●●

●●●●●●●●

●●●

●●

●●●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●●●●

●●●●●

●●

● ●●●●●●●

●●●

●●●●

●●●●●●

●●●●●●●

●●

●●

●●●●●●●

●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●●●●●

●●●●●●

●●●

●●

●●

●●

●●●●

●●

●●●●●●●●●●

●●

●●

●●

●●●

●●●●

●●●●●●●

●●●●

●●

●●

●●●●●

●●

●●●●●●●

●●

●●

●●

●●●●●●●

●●●

●●●

●●●

●●

●●

●●

●●

● ●

●●●

●●

●●●●●●●●●

●●●

●●

●●●

●●●●

●●

●●●●

● ●●●

●●●●●

●●●●●●●●●

●●●●

●●●●●●●

●●

●●●

●●●

●●●●

●●●●

●●

●●●●●

●●●●

●●●

●●

●●●

●●●●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●

●●●

●●

●●

●●●●●

●●

●●●●

●●●●

●●●

●●●

●●

●●●●

●●

●●●

●●●

●●●

●●

●●●

●●●●●●●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●●●●●

●●●

●●●●

●●●

●●●

●●●

●●●●●●●

●●

●●●●

●●

●●●●

●●●●●●●

●●

●●●

●●●

●●

●●●

●●●●

●● ●

●●●●

●● ●●●

●●

●●●●●

●●

●●●

●●

●●●

●●

●●●●

●●●●

●●●

●●●

●●●

●●●●

●●●●

●●●

●●●●●

●●

●●

●●●●●●

●●

●●●●●●

●●

●●

●●

●●

●●

●●●●●●

● ●●

●●●

●●

●●

●●●

●●●●●●

●●●●●

●●

●●●●

●●●

● ●●●●

●●

●●

●●

●●●●●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●● ●●●

●●●●

●●

●●●●

●●

●●

●●●●●●●●●

●●●●

●●

●●

●●●●●

●●●●

●●●

● ●

●●

●●●●●

●●

●●●●

●●●

●●●●

●●●●●●●●●●

●●●●●●●●

●●●

● ●●●●

●●●

●●●

●●

●●●●●●●●

●●●

●●●

● ●

●●●●●

●●●

●●●

●●

●●

●●

●●●●●

●●●●●●●●●

●●

●●●

●●

●●

●●●

●●

●●●●

●●●

●●

●●

●●●●

●●●

●●●●●

●●●●●

●●

● ●

● ●

●●●●

●●●

●●●●●●

●●●●

●●●●●

●●●●

●●●●●

●●●

●●●●●

●●●

●●

●●●

●●●●●●

●●

●●● ●●●

●●●●

●●●

●●●

●●●

●●

●●●

●●●●

●●●●●●●

●●●●

●●●

●●●●

●●

●●●

●●

●●●●●●●

●●●●●

●●●●●●●

●●●●●

●●●●●● ●

●●●● ● ●●●●●●●●●●●●●

●●●

●●

●●

●●●

●●●●●●

●●●●

●●●●

●●●●●●●●

●●

●●

●●●

●●●●

●●●●

●●●●

●●●

●●●●●

● ●

●●●

●●

●●●●●●

●●●

●●

●●●●●

●●●

●●

●●●●●

●●

●●

●●

●●●●●●●●●●●●

●●

●●

●●

●●

●●

●●●●

●●●●●●●

●●

●●●●●●

●●●●●●●●●

●●●●●

●●

●●●●

●●●●

●●

●●●●●

●●

●●●●●●●●●

●●●●●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●●●●●●

●●●●

●●●●

●●

●●●

●●

●●●

●●

●●●

●●●

●●●●●●●●

● ●●●●

●●

●●●● ●●●●●●●●●

●●●

●●●

●●●●

● ●

●●●

●●●●●

●●

●●● ●●●●

●●

●●●●●●●●●● ●●

●●●●●●

●●

●●●●

●●●

●●●

●●

●●

●●

●●●

●●

●●●

●●●●

●●

●●●

●●●

●●●●

●●●●●

●●

●●●●●

●●

●●●●● ●●

●●●●

●●

●●

●●

●●●●●

●●

●●

●●

●●●

●●●●

●●●●

●●

●●●●

●●

●●

●●●●

●●

●●●●●●

●●

●●●●●●●●

●●

●●●

●●●●●

●●●●●●

●●●●●

●●

●●

●●●●●

●●●●

●●●●●●●

●●●●●●

●●

●●●

●●●

●●●

●●●

●●●●●

●●●●●

●●●●●●●

●●●●

●●●

●●

●●●●

●●●●

●●●●

●●●

●●●●●

●●●●

●●●●

●●●●●●●●

●●

●●

●●●●

●●●●

●●●

●●●●●

●●●

●●●

●●●●●

● ●

●●●●●●●●●●●

●●

●●

●●

●●●●

●●

●●●

●●●●

●●

●●

●●●

●●●●●●

●●

●●

●●●●●

●●●●●

●●

●●●

●●●

●●●●●

●●●

●●

●●

●●

●●

●●●●●●●●●●●●●●

●●

●●

●●●●●●●

●●●●●

●●●

●●●●●●●

●●●●●

●●●

●●●

●●● ●

●●●●●●

●●●●●

●●

●●●●●●

●●

●●●●

●●●

●●

●●●●

●●●

●●●●●

●●

●●

●●●●

●●●

●●●

●● ●

●●

●●●●

●●●

●●●

●●

●●●●●● ●●●●

●●●●●●

●●

●●

●●●●●●●●●●●●●●●●●

●●●●

●●●●●●●●●

●●

●●●

●●●

● ●●

●●

●●●●●●●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●

●●●●●

●●●●●●●●

●●

●●●

●●

●●●

●●●

●●

●●●

●●●●●

●●●

●●

●●

●●●

●●

●●●●

●●●●

●●

●●

●●

● ●

●●

●●

●●●●●●●●

●●●●●

●●●

●●

●●●●●

●●●

●●●●●●●●●●●●

●●●

●●●●

●●●●●●●●●●

●●●●●●●

●●●●

●●●●

●●●●●●

●●

●●●

●●●

●●●●●●

●●●●●●●●●

●●

●●

●●

●●●●●

●●●●

●●●●●

●● ●●

●●●●●●●●●●

●●●●●

●●●

●●●●●

●●●●●●●

●●●●●●●●●●

●●●

●●

●●●

●●●●●

●●

●●●

●●

●●

●●

●●●●●●●

●●●●

●●●●●●

●●●●●●●

●●●

●●●●●●●

●●●●●

●●

●●● ●●

●●●

●●

●●●

●●●●●●

●●●●●●

●●●●●●●●●●●

● ●●●●

●●●●●●●●●

●●●●

●●●

●●●●

●●●●

●●

●●●

●●●●●●●●●●●●

●●●●

●●

●●●

●●

●●●●●●●●

●●

●●●●

●●●●

●●●

●●●●●●●●●

●●

●●

●●●●

●●●●

●●

●●●●

●●●●●●●●

●●●●● ●

●●●

●●●

●●

●●●●●●●●●

●●●

●●●●●●●●●●●●●

●●●

●● ●

●●●●●

●●●

●●

●●

●●●●●●●

●●

●●●

●●●

●●

●●●●

●●●●

●●●

●●●●

●●

●●●

●●●●

●●

●●●●●●

●●

●●

●●

●●●●●●●

●●

●●

●●

●●

●●●●●

●●●

●●●

●●

●●●

●●●●●●●●

●●●●●●●●●

●●●

●●

●●

●●●

●●●●●●●●●●

●●

●●●

●●●●●●●●

●●●●

●●●

●●●●●●

●●

● ●

●●●

●●●

●●●●●●●●●●●

●●●●●●●

●●●●●●

●●

●●

●●

●●

●●●● ●●●●●●●●

●●●●●●●

●●●●

●●●

●●

●●

●●

●●●

●●●●●●●●●●●●

●●

●●●●●●●

●●●●●

●●●

●●

●●

●●

●●●●

●●●●

●●●●●

●●

●●●● ●●●●●●

●●●

●●●

●●●●●

●●●●

●● ●

●●●

●●

●●●●●

●●●●

●●●

●●●●

●●●●●●●●●●

●●●●●

●●●

●●●

●●●●●

●●●●●●

●●

●●

●●

●●●●●

●●●●●●●●

●●

●●●

●●●

●●

●●

●●●

●●●●

●●

●●

●●

●●●●●●●

●●

●●

●●●

●●

●●

●●●●

●●●

●●

●●●●

●●●●

●●

●●●

●●

●●

●●

●●●●●●

●●●

●●

●●●

●●●●

●●●●●

●●●●●●●

●●●●●●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●●●●●●●●●

●●

●●●●●●●

●●●

●●●●

●●

●●

●●

●●●●●●●

●●●●●●

●●●●●

●●●●●●

●●

●●

●●

●●●●

●●●●●●●●●

●●●

●●

●●●●

●●●

●●●●

●●●●●●

●●●

●●

●●●●

●●

●●●●●

●●●

●●●●

●●

●● ●●

● ●●

●●●

●●●

●●●●●●●

●●●●

●●●●●

●●

●●●

●●●

●●●●●●

●●●

●●●●

●●●●

●●●

●●●●

●●●●●●●●●

●●

●●

●●●●

●●

●●●

●●●●●●●

●●●●●

●●●

●●●

●●●●●●

●●

●●●

●●●

●●●●●

●●

●● ●●●●●●

●●●

●●●

●●●●●●●

●●●●●●●

●●

●●●

●●●

●● ●●●

●●●●

●●●

●●

●●

●●

●●

●●●●

●●●

●●●

●●

●●●

●●●●

●●●

●●●

●●●●●

●●

●●

●●

●●●●●●

●●

●●●●●

●●●●

●●●●●●

●●●●●●

●●

●●●●

●●

●●●

●●●●

●●●●●●●●●●●●

●●●●

●●●●●

●●●●●●

●●●●●

●●

●●●●●

●●

●●●●

●●●●●●

●●●●●

●●●●●

●●

●●●●

●●●●●●

●●●●

●●●●●

●●●●●●●

●●●

●●●●●

●●●

●●●●●●●●●●

●●●

●●

●●●●

●●

●●●●●

●●●●●●

●●●

●●●●

●●●●●●● ●

●●●●●

●●

●●

●●●

●●●●

●●●

●●●●●●●●

●●●●

●●●●●●●●

●●●

●●●

●●●●●●

●●

●●

●●

●●●●

●●●

●●

●●●

●●

●●●●●

●●●●

●●●●●●

●●●

●●●●

●●

●●●

●●●

●●

●●

●●●●

●●

●●●●●

●●

●●

●●●●●●●●●●

●●●

●●●●●

●●●●●●●●●●●

●●

●●●

●●

●●●●

●●●●●●

●●●

●●

●●●●●

●●●

●●●●

●●●

●●

●●●

●●

●●●●●

●●

●●●●●

●●

●●

●●●●●●

●●●

●●

●●●

●●●●●

●●●

●●●

●●●●●

●●●●

●●●●

●●●

●●

●●●●●●●

●●●● ●●●●●●

●●●●

●●

●●

●●●

●●●●

●●●

●●

●●●●●

●●●●

●●

●●●

●●●

●●

●●●●●●●●●

●●●●●●●●

●●●

●●●●●

●●

●●●●●●

●●●

●●

●●●●

●●●

●●●

●●●

●●●●●

●●

●●●●●

●●●●●●

●●●●●

●●●●●●

●●●

●● ●

●●

●●

●●●

●●●●●●

●●●●

●●●

●●●●

●●

● ●

●●

●●

●●

●●

●●●●●

●● ●● ●

●●●●●●●

●●●●●

●●● ●●●●●●●●●

●●

●●

0e+00 1e+05 2e+05 3e+05 4e+05 5e+05 6e+05

0e+00

1e+05

2e+05

3e+05

4e+05

5e+05

6e+05

Intensidades de los dos canales

intensidades control

Inte

nsid

ades

infe

ctad

o

28

Histograma de las intensidades del canal rojo

Intensidades

Frequency

0 50000 100000 150000 200000 250000 300000 350000

02000

4000

6000

8000

10000

Histograma de los logaritmos de las intensidades del canal rojo

Log de las intensidades

Freq

uenc

y

6 8 10 12 14 16 18

0

500

1000

1500

Histogramas de las intensidades antes y después de aplicar log en base 2.

Sin el logaritmo las intensidades se acumulan en los valores bajos

Con el logaritmo las intensidades aproximan a una normal aunque aún presenta diferencias

29

●●

●●

●●

●●

●●

●●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●●

● ●

●●

●●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●●

● ●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●●

●●

●●

●●

●●

● ●●●

●●

● ●

●●

●●

●●

● ●

●●

● ●●

●●

●●

●●

●●

●● ●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

● ●

● ●●

●●

● ●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●●

●●

●●

● ●●

●●● ●

● ●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

● ●

●●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

● ●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

● ●

●●

● ●

●●

● ●

● ●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●●

● ●

●●

●●

●●

●●

● ●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●●

●●

●●

● ●

● ●

●●

● ●

●●

●●

●●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ● ●

●●

●●

●●

●●

●● ●

●●

●●

● ●

●●

●●

●●

●●

● ●

● ●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

● ●

●●

●●

●●

●●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●● ●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●●

●●

●●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

● ●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●●

●●

●●

●●

●●

● ●

●●

● ●

●●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●● ●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

● ●●

●●

●● ●

●●●

● ●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●●

● ●

● ●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●● ●

●●

● ●●

●●

●●

●●

●●

0 5 10 15 20

05

1015

20

log Intensidades de los dos canales

log intensidades control

log

Inte

nsid

ades

infe

ctad

o

Este gráfico es mejor.

Los datos están distribuidos a lo largo del rango de intensidades y la variabilidad es la misma en la mayor parte de dicho rango

Después de aplicar logaritmos en ambos canales

Podemosgirarelgráfico

30

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●●

●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ● ●●

●●

● ●

● ●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●●

● ●

●●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●● ●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

● ●

● ●

● ●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

● ●

●●

● ●●

●●

●●

●●

● ●

● ●●

●●

●●

●●

●●●

●● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

● ●

●●●

● ●

●●

●●

●●

● ●● ● ●

●● ●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

● ●●●

●●

●●

● ●●

● ●●

●●

● ●

●●

● ●

●●

●●

●●

● ●

●●●

●●

●●

●●

●●

● ●

●●

● ●

● ●

●●

●●

●●

●● ●

● ●

●●

●●●

●●

●●

●● ●

● ●

●●

●●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

● ●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●●

● ●●

●●

●●

●●

● ●

●●

● ●

●●

● ●

●●

●●

●● ●

●●

●● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

● ●

●●

●●

● ●

●● ●

●●●

●●

●●

● ●

●●

● ●

●●

● ●

● ●

●●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●●

●●

●●

● ●

● ●●

●●

●●

●●

● ●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

● ●

●●

●●

● ●●

●●

●● ●● ●

● ●●

●●

●●

● ●

●●

●●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●● ●

●●

●●

●● ●

● ●

●●

●● ●

● ●

●●

●●

●●

● ●

●●

●●

● ●●

●●

●●

●●

●●

● ●

●●

●●

●●●

● ●

●●

●●●

●●

●● ●

●●

●● ●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

● ●

●●

● ●

●●

●●

●● ●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

● ●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●●

●●

●● ●

●●

●●

●●

●●

●●

● ●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

● ● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

● ●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●●●

● ●

● ●

●●

●●

● ●●

●●

●●

● ●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●●

●●

● ●

●●

●●

● ●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●

●●

● ●

●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

● ●

●●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

● ●

● ●

●● ●

●●

●●

●●

●●●

●●

●●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

● ●

●●

●●

●●

●●

● ●

● ●

●●

●●●

●●

●●

●●

●●

●●

● ● ●

●●

●●

●● ●

● ●

●● ●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●●

● ●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

● ●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

● ●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●●

●●●

●●

● ●

●●

●●

●●

●●

●● ●

●●

● ●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●●

●●

●●

● ●

●●

●● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●●

● ●

●●

●● ●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●● ●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

● ●

●●

● ●

●●

● ●

●●

● ●●

●●

●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●●

● ●●

●●

● ●

●●

●●

●●

●●

●●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●●

●●

5 10 15

−5

0

5

Plot MA

A

M

Normalización

31

Necesidaddenormalizarcadamicroarray

• EncadamicroarraysetratadecompararlaexpresióndelosgenesenmuestrasbiológicassomeAdasadoscondicionesdiferentes.

• Lahipótesis(biológica)inicialesquelamayoríadelosgenesnosevanaexpresardemaneradiferenteendichascondiciones.

• LadistribucióndeloslogaritmosdelosraAosdeberíasersimétricaconrespectoalcero.

32

33

La regresión LOESS realiza una gran (o pequeña) cantidad de regresiones locales sobre ventanas que se superponen y se van desplazando recorriendo todo el rango de una de las variables.

La unión de todas estas pequeñas curvas locales da lugar a una curva de regresión no lineal.

Es una técnica relativamente sofisticada pero que está implementada en R y Matlab. El ancho de la ventana puede variar bastante la bondad del ajuste.

34

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●●

●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ● ●●

●●

● ●

● ●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●●

● ●

●●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●● ●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

● ●

● ●

● ●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

● ●

●●

● ●●

●●

●●

●●

● ●

● ●●

●●

●●

●●

●●●

●● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

● ●

●●●

● ●

●●

●●

●●

● ●● ● ●

●● ●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

● ●●●

●●

●●

● ●●

● ●●

●●

● ●

●●

● ●

●●

●●

●●

● ●

●●●

●●

●●

●●

●●

● ●

●●

● ●

● ●

●●

●●

●●

●● ●

● ●

●●

●●●

●●

●●

●● ●

● ●

●●

●●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

● ●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●●

● ●●

●●

●●

●●

● ●

●●

● ●

●●

● ●

●●

●●

●● ●

●●

●● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

● ●

●●

●●

● ●

●● ●

●●●

●●

●●

● ●

●●

● ●

●●

● ●

● ●

●●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●●

●●

●●

● ●

● ●●

●●

●●

●●

● ●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

● ●

●●

●●

● ●●

●●

●● ●● ●

● ●●

●●

●●

● ●

●●

●●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●● ●

●●

●●

●● ●

● ●

●●

●● ●

● ●

●●

●●

●●

● ●

●●

●●

● ●●

●●

●●

●●

●●

● ●

●●

●●

●●●

● ●

●●

●●●

●●

●● ●

●●

●● ●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

● ●

●●

● ●

●●

●●

●● ●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

● ●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●●

●●

●● ●

●●

●●

●●

●●

●●

● ●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

● ● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

● ●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●●●

● ●

● ●

●●

●●

● ●●

●●

●●

● ●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●●

●●

● ●

●●

●●

● ●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●

●●

● ●

●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

● ●

●●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

● ●

● ●

●● ●

●●

●●

●●

●●●

●●

●●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

● ●

●●

●●

●●

●●

● ●

● ●

●●

●●●

●●

●●

●●

●●

●●

● ● ●

●●

●●

●● ●

● ●

●● ●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●●

● ●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

● ●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

● ●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●●

●●●

●●

● ●

●●

●●

●●

●●

●● ●

●●

● ●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●●

●●

●●

● ●

●●

●● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●●

● ●

●●

●● ●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●● ●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

● ●

●●

● ●

●●

● ●

●●

● ●●

●●

●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●●

● ●●

●●

● ●

●●

●●

●●

●●

●●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●●

●●

5 10 15

−5

0

5

Plot MA

A

M

MAPlot con la curva obtenida por regresión no lineal antes y después de normalizar

●●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ● ●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

● ●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●● ●

● ●

● ●

●●

●●

●●

●●

● ●

●●

● ●

● ●

● ●

● ●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●● ●

●●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

● ●

● ●

● ●

●●

●●

●●

● ●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

● ●

● ●

● ●

●●

●●

●●

●●

● ● ●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●●

● ●

● ●

●●

●●

●●

●●

●● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●● ●

● ●

●● ●

● ●

●●

● ●

● ●●

●●

●● ●

● ●

●●

●●

● ●

●●

● ●

● ●

● ●

●●●

●●

●●

●●

● ●●

●●

●●

● ●

●●

●●

● ●●

● ●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●●

●●

● ●●

●●

●●

●●

● ● ●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

● ●●●

● ●

●●

●● ● ●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

● ●

● ●

●●

● ●

●●

●●

●●

● ●

●●●

●●

●●

● ●

●●

●●

● ●

●●

● ●

●●

●●

● ●●

●●

●●

●●●

●●

● ●

●●

●●

●●

●●

● ●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●● ●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●●

● ●

● ●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

● ●

●●

●●

● ●

●● ●

●●

● ●

●●

● ●●

●●

●●

●●●

●●

●●

● ●

●●

● ●

●●

●●●

● ●

● ●

●●

●●

● ●

●●

●●

●●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●●

●● ●

●● ● ●

● ●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●● ●

●●

●●

●●●

● ●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●

● ●● ●

●●

●●

●●

●●

●●

●●

●●

●● ●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

● ●

● ●●

●●

● ●

● ●

● ●

● ●●

●●

●●

● ●●

●●

●●

● ●

● ●●

●●

●●

●●

●●

●●

●●●

● ●

●●

●●

●●

●●

● ●

●●

●● ● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●●

●●

● ●●

●●

●●

● ●

●●

● ●

●●

● ●●

●●

●●

●●

● ●

●●●

● ●

●●

●● ●

●●●

●●

●●

●●

●●

● ●

●●

● ●

● ●

●●

● ●

●●

●●

●●

●●

●●●

●●

●●

● ●

●●

●●

● ●

●●

●● ●

● ● ●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●●

●●

● ●

●●

● ●

●●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●●

● ●

●●

● ●

● ●

●●

●●

● ●

●●●

●●

● ●●

●●

●●

●●

●●

●●

●●

● ●

●●●

●●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

● ●●

●●

●●

●● ●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●● ●

●●

●● ●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

● ●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

● ●

● ●

● ●●

●●

●●

●●

●●

●●

●●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

● ●

●●

●●

●●

● ●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

● ●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

● ●

●●

● ●

●●

●●

●●●

● ●

● ●●

●● ●

● ●

●●

●●●

●●

● ●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●●

●●

●●

●●

● ●

●●●

● ●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●● ●

●●

●●

●●

●●

●● ●

● ●●●

●●

●●

● ●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

● ●

●●

● ●

●●

● ●

●●

●●

●● ●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●●

●●

●●

8 10 12 14 16 18

−6

−4

−2

0

2

4

Plot MA normalizado

A

M

NecesidaddenormalizarlasdisAntasmicroarraysentreellas

• Lasdiferentesetapasdelprocesointroducenerrores(“ruido”)quedanlugaradiferencias“globales”entrelasdisAntasmicroarrys.

• Elprocesodenormalizaciónentrelasmicroarraysintentareduciralmínimoesasdiferencias“globales”.

• Losmecanismosfundamentalesenlanormalizaciónentremicroarrayssonelescalado,elcentrado.

35

36

●●●●

●●

●●●●●●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●●●●

●●

●●

●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●

●●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●●

●●

●●●

●●

●●●

●●●●

●●●●

●●●●

●●

●●

●●●

●●●●●●

●●

●●

●●

●●●●

●●●

●●

●●●●●●

●●

●●

●●

●●●●●●

●●

●●

●●●●

●●●

●●

●●●

●●●●●

●●

●●●●●

●●●●●●●●●

●●●

●●

●●

●●●●●●

●●●●

●●

●●●●●

●●

●●

●●

●●

●●●●

●●●●●●●

●●●

●●

●●●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●●●●

●●●

●●

●●●

●●●●●●●

●●●

●●●

●●●●●●

●●

●●●

●●●

●●●

●●

●●

●●

●●

●●●●●●

●●●●

●●

●●●●●●●

●●●

●●●

●●

●●

●●●

●●

●●●●

●●

●●

●●●●

●●

●●

●●●

●●

●●●●●

●●

●●●

●●●●

●●●

●●●

●●

●●●●●●

●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●●

●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●●

●●●

●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●●

●●●●

●●●●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●●●

●●●

●●

●●

●●●

●●●●

●●●

●●

●●

●●●●

●●

●●

●●●

●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●●●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●●●

●●

●●

●●●

●●

●●●

●●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●

●●●

●●●

●●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●●

●●●●

●●

●●

●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●●●

●●●

●●●

●●●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●●●

●●●

●●●

●●

●●●

●●●●

●●●

●●

●●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●●●

●●

●●●●

●●

●●●●

●●●

●●●

●●

●●●

●●●

●●

●●

●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●●

●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●

●●

●●●

●●●

●●

●●

●●●●

●●

●●

●●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●

●●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●

●●

●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●●●●

●●

●●

●●

●●

●●

●●●

●●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

micro1 micro3 micro5 micro7

−10

−50

5

Logaritmos de los ratios de las intensidades.

●●●

●●●

●●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●●●●●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●●●

●●

●●●●

●●

●●●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●●

●●●●

●●

●●●

●●

●●●●●

●●

●●●●

●●

●●●

●●

●●●●●●●

●●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●

●●

●●●

●●

●●

●●●●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●●●●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●●

●●

●●

●●●●

●●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●●●●

●●

●●

●●

●●●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●

●●●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●●

●●●

●●●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●

●●●

●●

●●●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●●●

●●

●●●

●●

●●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●

●●●

●●●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●●

●●

●●

●●●●●

●●

●●

●●

●●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●●●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●

●●●●

●●

●●●●●

●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●●

●●

●●

●●●

●●

●●

●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●

●●●●

●●

●●

●●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●

●●●●

●●

●●●

●●●●●

●●

●●

●●●

●●

●●

●●●●

●●●

●●

●●

●●●

●●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●●●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●

●●●●

●●

●●

●●

●●●

●●●●●

●●●

●●

●●●

●●

●●

●●

●●●●●

●●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●●●●●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

micro1 micro2 micro3 micro4 micro5 micro6 micro7

−50

5

Logaritmos de los ratios de las intensidades. Cada array normalizada

37

●●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●●●●●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●●

●●

●●●●●●●

●●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●

●●

●●●

●●

●●

●●●●●

●●

●●●

●●

●●●

●●

●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●●

●●●●

●●●

●●●●●●

●●●●●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●●●

●●

●●●

●●●

●●●

●●

●●●●

●●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●●●

●●●

●●●●●●●

●●●●●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●●●

●●●●●

●●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●●

●●

●●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●●●

●●

●●

●●

●●

●●●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●●●●

●●

●●

●●

●●●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●

●●●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●●●●

●●●

●●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●●●●

●●

●●

●●●

●●

●●●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●●●

●●

●●●

●●

●●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●●

●●●●

●●

●●

●●●●

●●

●●

●●●

●●●●●

●●

●●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●

●●●●●●●●

●●

●●●

●●

●●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●

●●●

●●

●●

●●●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●●●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●●

●●●●

●●

●●●●●

●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●

●●

●●

●●

●●●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●●

●●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●●

●●

●●

●●

●●●●

●●

●●

●●●●

●●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●●●

●●

●●

●●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●●●

●●

●●●●

●●●●●

●●

●●

●●●

●●

●●

●●●●

●●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

● ●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●●●

●●

●●

●●

●●●

●●●●●

●●●

●●

●●●

●●

●●

●●

●●●●●

●●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●●●●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

micro1 micro2 micro3 micro4 micro5 micro6 micro7

−50

5

Logaritmos de los ratios de las intensidades. Normalización entre micros

●●●●

●●

●●●●●●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●●●●

●●

●●

●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●

●●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●●

●●

●●●

●●

●●●

●●●●

●●●●

●●●●

●●

●●

●●●

●●●●●●

●●

●●

●●

●●●●

●●●

●●

●●●●●●

●●

●●

●●

●●●●●●

●●

●●

●●●●

●●●

●●

●●●

●●●●●

●●

●●●●●

●●●●●●●●●

●●●

●●

●●

●●●●●●

●●●●

●●

●●●●●

●●

●●

●●

●●

●●●●

●●●●●●●

●●●

●●

●●●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●●●●

●●●

●●

●●●

●●●●●●●

●●●

●●●

●●●●●●

●●

●●●

●●●

●●●

●●

●●

●●

●●

●●●●●●

●●●●

●●

●●●●●●●

●●●

●●●

●●

●●

●●●

●●

●●●●

●●

●●

●●●●

●●

●●

●●●

●●

●●●●●

●●

●●●

●●●●

●●●

●●●

●●

●●●●●●

●●

●●

●●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●●

●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●●

●●●

●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●

●●●

●●●●

●●●●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●●●

●●●

●●

●●

●●●

●●●●

●●●

●●

●●

●●●●

●●

●●

●●●

●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●●●

●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●●●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●●●

●●

●●

●●●

●●

●●●

●●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●

●●●

●●●

●●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●●

●●●●

●●

●●

●●

●●

●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●●●

●●●

●●●

●●●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●●●

●●●

●●●

●●

●●●

●●●●

●●●

●●

●●●

●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●●

●●

●●

●●●●

●●

●●●●

●●

●●●●

●●●

●●●

●●

●●●

●●●

●●

●●

●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●●

●●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●●

●●

●●●

●●●

●●

●●

●●●●

●●

●●

●●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●●●

●●

●●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●

●●●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●●

●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●

●●

●●●●

●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●●

●●

●●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●●●

●●

●●●

●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●●●●

●●

●●

●●●

●●

●●

●●●

●●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●

●●

●●

●●

●●

●●●●

●●●●

●●

●●

●●●

●●

●●

●●

●●

●●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●●

●●●●

●●

●●

●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●●

●●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●●

●●

●●

●●●

●●

●●●

●●●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●●

●●●

●●●●●

●●

●●

●●

●●

●●

●●●

●●●●●

●●●

●●

●●

●●●

●●

●●

●●

●●

●●

●●

●●●

●●●●●●●

●●

●●

●●

●●

●●

●●●

●●●

●●

●●

●●

●●●●●

●●●

●●

●●

●●

●●

●●●●

●●

●●●

●●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

micro1 micro3 micro5 micro7

−10

−50

5

Logaritmos de los ratios de las intensidades.

Análisisdelosdatos

38

• AntesdeempezarhayquepreguntarseparaquésequierenuAlizarlosmicroarrays.

• Comoesobvio,elestudioestadísAcodependerádedichoobjeAvo.

• LoquenoestanobvioesqueeldiseñoexperimentalpreviotambiéndependedelobjeAvobuscado.

• VeamosdosejemplosclásicoscondisAntosobjeAvos.

39

Primerasmicroarrays

• Las primeras pruebas de la potencia de los microarrays surgieron en el estudio de la levadura, ya que fue el primer genoma secuenciado y ensamblado.

• EntrelosprimerostrabajossesuelecitareldeSchena(Science1995)sobrelamonotorizacióndeexpresióngénica.

• Sin embargo el más citado es el de DeRissi y sus colaboradores (Science 1997)

40

41

Diferentes patrones de expresión de genes de la levadura en respuesta a la disminución de la concentración de glucosa.

Uso de análisis cluster

Usodemétodosdeclasificación

42

Ejemplo: Golub 1999

Eltrabajoqueimpulsóalasmicroarrays

• EltrabajodeGolubysuscolaboradoresen1999,enelqueusanmicroarraysparadiagnosAcardosAposdecancer,impulsadefiniAvamenteelusodelasmicroarrayscomoinstrumentodediagnósAcoeinvesAgaciónenelcampodelosestudiossobreelcancer.

43

44

• Golub parte de dos tipos de cancer:ALL (acute lymphoblastic leukemia) y AML(acute myeloid leukemia).

• Los métodos de diagnóstico eran sólidos pero costosos. Requerían varias pruebas e involucraban a numerosas especialidades médicas.

45

•Obtuvieron muestras de 38 pacientes (27 ALL y 11 AML) (acute myeloid leukemia).

•El RNA obtenido se hibridó en microarrays de affimetrix que contenían “probes” para 6817 genes.

•Diseñaron un algoritmo de predicción que era capaz de diagnosticar correctamente con 50 genes.

46

47

•El test asignaba correctamente 36 de los 38 casos y los otros dos los dejaba como inciertos.

•Sobre una colección independiente de 34 muestras, predecía correctamente 29 casos

Descubrimientodeclases

• Aplicaron la técnica de “self-organizing maps” (SOMs).

• LatécnicapredijodosclasesA1yA2con24(de25)ALLenA1y10(de13)ALMenA2.

48

Búsquedadegenesexpresadosdiferencialmente

• Siestamosenunasituaciónsimpledondesólohayunfactorcondosniveles(porejemplo:infectadoonoinfectado)podemostrabajarconlostestsdehipótesishabituales.

• Sólohayquetenerencuentaqueseestánhaciendomilesdeellossimultáneamenteyhayquehacerlacorrecciónadecuadaenlosp‐valores

49

Busquedadegenesexpresadosdeformadiferencial

• Encasosmáscomplejoshayquerecurriramétodosmáscomplejoscomoelanálisisdelavarianzaoelusodemodeloscomoenelpaquete“limma”deBioconductor.

50

51

52

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

● ●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

● ●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

● ●

●●

●●

●●

●●

●●

−2 0 2 4

020

4060

8010

0

Los resultados de B1 en la primera slide,grupo1=B11,13,14,grupo2=B12A,B,C

Log Fold Change

Log

Odd

s

R1__610

R1__421 R1__450R1__397R1__1072R1__295R1__891R1__2884 R1__499R1__1125

53

Los resultados del factor slide, normalizados Between

(Intercept) Slideslide2

Slideslide3 372

54

42

57

1065

330

354

442

Apéndice

• LasmicroarrayssonuninstrumentovaliosoenlainvesAgaciónenbiológicaymedicina.

• Lastécnicasnecesariasparasuestudiosonconocidasperonotriviales.

• ParaellosepuedenusarlacoleccióndepaquetesestadísAcos(libres)desarrolladosenelproyectoBioconductor.

• http://www.bioconductor.org/54