BACKGROUND
two-dimensional gel electrophoresis  has been a successful technique for identification and visualization of post-translational modifications  <cit>  , and is increasingly used to determine accessible parts of the proteome in human cells  <cit> .
to a certain extent has 2de been used to propose diagnosis or clinical classification in diseases  <cit> , including differentiating acute myeloid leukemia  from acute lymphoblastic leukemia   <cit> .
the amount and complexity of data obtained from 2de patterns have led to the development of analysis software for digitalized images  <cit> , but human interpretation and validation of the data is usually necessary.
typically, one of the steps in 2de analysis is the selection of spots followed by description of their position, volume and other variables.
current methods for spot detection assume regular spot shapes  <cit>  or model spots as bivariate gaussian densities  <cit> , and therefore cannot discriminate spot shapes and irregularity  <cit> .
in this paper we present a method that omits the spot detection phase and does not require human interpretation on a gel-to-gel basis.
given a set of gel images, the technique measures correlation between every pixel position and an external variable.
this makes it possible to study the 2de protein distribution as well as the actual relation to the external variable.
the method has been rigorously tested on a set of simulated 2de images with different levels of background, additional noise and outliers.
biological evaluation of the technique was performed by testing the correlation analysis on p <dig> protein isoform profiles in cell samples from patients with well-characterized hematological malignancies.
different hematological malignancies, like all and aml  <cit>  are characterized by distinct mutations or expression of genes involved in cell signaling  <cit> .
the tp <dig> gene is frequently mutated in many cancers and mutations in signaling pathways acting on p <dig> protein are found both in sporadic and hereditary cancers  <cit> .
the p <dig> protein is a sequence specific transcription factor that can regulate differentiation, growth and cell death, and is highly regulated by post-translational modifications caused by multiple signaling networks that directly or indirectly target the protein  <cit> .
during differentiation, p <dig> undergoes modifications like phosphorylation and acetylation and is suggested to be involved in differentiation of aml  <cit> .
because of this large range of activities and complex regulatory functions, we relied on analysis of the post-translationally modified p <dig> protein to illustrate our method.
the p <dig> protein biosignatures in  <dig> aml patients and  <dig> all patients were analyzed by 2de immunoblot.
distinct p <dig> biosignatures correlated with cancer type  and, within the aml group, p <dig> biosignatures correlated with the level of differentiation, using the french-american-british  classification.
RESULTS
overview of the method
the presented method relies on the basic assumption that if spots on 2de images have biological relevance, then so must the pixels comprised within those spots.
therefore it must be possible to analyze 2de images for correlation, without performing a spot detection step.
the method requires the availability of a properly aligned stack of gel images.
each of the images must have an associated parameter t. practically, t can represent any biological variable such as life expectancy, differentiation stage of a cell sample, age of an organism, origin of a cancer cell sample, effect of cancer therapy, cell size or even variables such as time, temperature, pressure, and so on.
for every coordinate in the 2de image stack, a correlation analysis is performed between the pixel data gathered at that position and the external variable t. the correlation image is then created by repeating this process at every possible position.
the work-flow and the concept behind the correlation method is illustrated in fig.
<dig>  a movie of the method is available .
to illustrate how the correlation images ought to be interpreted, a simulated gel stack with defined spot characteristics in function of an external variable t was created .
this simulation reassured a controlled environment in which the algorithmic behavior was observed.
simulated gels
altering spot position and sizes
we first verified how the method reacts to spot location, spot size and spot shifts.
the simulated gel stack has various spots behaving differently.
spot α grows and fades out, spot δ shifts from left to right, spot β changes shape and the γ spots have a constant amplitude and width .
fig  <dig> shows various correlation images in which the strength of a correlation is presented in shades of green  and brown .
by design, spots α and β are parametrized by t. in the correlation images  we find them back at the same position, showing that the correlation image offers correct positional information.
the two constant γ-spots are independent of t. this results in no visible correlation in fig.
2bab.
the .
spot shape
all images in fig.
2b show the α-spot to anti-correlate in the middle and to correlate at its periphery.
this is consistent with the creation of the gel-stack in which the amplitude of spot a lowers from  <dig>  to  <dig>  while the spots broadens from  <dig> to  <dig> pixels.
because the central spot widens, higher gel numbers will have relatively more signal in the periphery.
this indicates that spots where diffusion-like alteration dominate can be detected based on the difference in correlation between the inner and outer areas.
similar behavior can be observed in the shape changing β-spot.
the initial vertical shape  anti-correlates  while the later horizontal shape  correlates .
masking the correlation image
in the simulated gel-stack, empty areas have an almost constant intensity.
for those areas, the raw correlation analysis indicates a strong correlation  or anti-correlation .
there are two reasons for this.
first, the area can be constant, resulting in correlations that are +∞, -∞ or nan .
in the correlation image these are represented as +  <dig> or - <dig>  secondly, in areas with very small alterations , the measured correlation is mathematically correct, but the lack in intensity variation offers little information.
after applying various significance masks to the correlation image, we find that only areas with relevant spot modulations are indicated ).
one mask removes non significant correlations and a second mask removes areas without variance .
effect of different normalizations
different background removal and scaling techniques were tested on the simulated gel-stack , including background subtraction and background division.
in all cases, the original information that led to the creation of the gel-stack was retrieved.
the α, δ and β spot correlations were always visualized, indicating that the normalization technique used is of little importance for qualitative analysis.
in the particular case of gel normalization obtained by division through the mean gel intensity, new information was found that did not directly originate from the creation of the simulation .
due to a t-dependent intensity increase in spot α, the mean intensity of the gel increased.
as a result, the original constant γ-spots decreased in intensity .
the γ-spots became t dependent and thus showed up in the correlation image.
when working with real gels this does not hinder qualitative analysis because normalization is performed on an individual gel basis.
therefore, it can always be repeated on any new gel, without taking into account previous gels and the reported correlations can be observed in the normalized images.
quantitatively, normalization factors strongly influence correlation measures.
if the technique is used as a quantitative method, then calibration spots ought to be used and exact understanding of machine specifications and camera properties should be known.
white noise in 2de images
in fig.
2ba-c, the background correlated towards t. adding white noise  <cit>  to the simulated images attenuates the appearance of such non significant background correlations  resulted in weaker correlations, but still important spots were identifiable .
this suggests that small amounts of noise might enhance interpretation of the correlation analysis by automatically introducing a non-correlating variance.
the signal hidden within the noise must now compete against a non-correlating factor, as such, the noise introduces a form of automatic significance measurement.
when the noise amplitude is t dependent, we observe correct information about the negative correlation, but loss of information about the positive correlation .
such a situation could occur if a camera automatically gates images at waning signal strength.
as long as white noise does not relate to the external variable, its presence barely influences the analytical power of the presented correlation test.
effect of randomization of the dataset
two sets of random data were generated to be used as t-value.
instead of testing correlation towards the sequence number t, we now determined the effect of correlation of the images towards a random vector.
the idl function 'randomu'  <cit> , generated the normally distributed random numbers.
in the correlation images we always recognized the same general shapes.
areas that behaved similarly in the gel stack, had the same coloring, regardless of the external variable.
these examples emphasize the robustness of the algorithm to group together regions of interest .
outliers
a test with outliers in the t-values shows limited impact on the interpretation of the gels .
we changed the t-values from { <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>  14} to { <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>  14}, resulting in a slight change in actual correlation magnitude, but the information content was well preserved.
even with 13% outliers { <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>  14}, the original information was recovered.
this is mainly due to the robust correlation which relies on ranking of the dataset instead of the numerical values .
correlation analysis of p <dig> biosignatures in acute leukemia
recently we demonstrated that signaling networks may be altered and potentiated in cancer cells suggesting a prognostic meaningful classification  <cit> .
this includes altered p <dig> map-kinase signaling, known to phosphorylate p <dig>  the application of the presented method was tested on p <dig> biosignatures of human primary cancer cells.
the p <dig> biosignature is probably formed by the combinations of splice forms of p <dig> and various post-translational modifications  <cit> .
the p <dig> protein is also involved in several positive and negative feedback networks  <cit> .
this has ignited the hypothesis that p <dig> integrates information from various signaling networks  <cit> .
we investigate two different relations.
one illustrates a relation between the overall p <dig> intensity and aml/all classification, the other illustrates detection of p53-isoform biosignatures related to the aml fab classification.
correlation of p <dig> protein biosignatures towards aml/all
all and aml comprise different genetic abnormalities  <cit> , and analysis of growth factor receptor expression and global gene expression has pointed out that the expression of receptor tyrosine kinases and signaling modulators are different  <cit> .
therefore, since the p <dig> protein is implied in various cancer related signaling networks, we expected to find distinct correlations between p <dig> expression and the aml/all variable.
gels of aml patients were marked with t =  <dig>  while all variants were marked with t =  <dig>  the correlations are shown in fig.
3a.
it reveals overall intensity increase of p <dig> in aml compared to all.
there is no previous data from acute leukemia that supports this observation.
to examine whether the 2de p <dig> correlations analysis reflected actual p <dig> protein expression differences in the lymphoid and myeloid cell lineages, we examined normal lymphocytes, neutrophile granulocytes and monocytes by 2de  and one-dimensional immunoblot .
this confirmed the intensity-differences detected by the correlation analysis by reflecting actual attenuated p <dig> protein levels in lymphocytes compared to myeloid cells.
the impact of wrong all versus aml diagnosis was examined by random swapping all and aml labels in the aml/all versus 2de image correlations.
this results in lower correlation values as expected .
correlation of p <dig> protein isoforms towards the aml differentiation level
the french-american-british  classification of aml is based on the morphologically determined stage of myeloid maturation and direction of maturation  <cit> .
recent reports indicate that the fab classification, in particular the distinction between m1– <dig> and m4– <dig> in maturation level and direction of maturation, is associated with certain gene classes in unsupervised clustering of gene expression profiles  <cit> .
it is previously described in several reports that p <dig> is involved in leukemic cell differentiation  <cit> .
phosphorylation of p <dig> ser <dig> is necessary for differentiation in mouse embryonic stem cells  <cit> , and p <dig> is able to direct differentiation in aml cell lines  <cit> .
the p53-deficient hl- <dig> cell line has potential for both monocytic and granulocytic differentiation, and introduction of wild type p <dig> directs differentiation in the granulocytic direction  <cit> .
based on these reports we hypothesized that the p <dig> biosignatures should reflect the stage and direction of myeloid differentiation.
therefore, we measured correlations between the established routine morphological differentiation classification of aml   <cit>  and the p <dig> 2de biosignatures of the cancer cells.
we assigned to every class a separate t-value: m <dig> , m <dig> , m <dig> , m <dig> , m <dig>  and m <dig> .
using  <dig> gels we found specific correlations .
image a is the masked correlation landscape, image b is the raw correlation image.
the observations were: a) the tail of the p53-α isoform correlates negatively to the fab classification .
b) the p <dig> area correlates positively towards the fab classification , c) the p53-δ region has four positively correlating articulated spots , d) the p <dig> sub-δ region has two negatively correlating spots .
the combination of a positive correlation at the p53-δ region and a negative correlating sub-δ region indicates a spot shift from one area to another.
additionally, the e) presence of the super-δ negative correlating region indicates that a change of spot shape also occurs.
when the p53-δ spots are larger and diffuse then the patient is classified as m <dig>  m <dig> or m <dig>  if the spots in the δ region are clear articulated and smaller, the patient is either m <dig> or m <dig>  none of the above correlations are strong .
nonetheless they can be observed in the 2de images, which means that they can form an important tool in stratification of patients.
based on these correlation measurements, we performed further tests to verify and confirm the relation between mass-differences and the fab classification .
the presented correlation includes m <dig>  a distinct subgroup of aml with signs of granulocytic differentiation, featuring the translocation t and responsiveness to retinoic acid therapy  <cit> .
fab m <dig> is therefore a separate entity in the recent who classification  <cit> .
the correlations were weaker when m <dig> was removed , which suggests that it is the pre-neutrophile granulocytic differentiation stage of m <dig> that comprises a distinct p <dig> isoform profile from m0/ <dig> p <dig>  thereby contributing to a greater splitting of the patients into subgroups.
discussion
localization, shape and volume of 2de spots
spot detection methods are in general very complex and time consuming tasks.
the correlation technique relies on the assumption that if spots have a biological relevance then so must their individual pixels.
the advantage of approaching gels this way is that we no longer depend on spot detection methods.
one can wonder though, how relations between spot volumes and external variables are assessed.
as it turns out, one can still rely on the correlation image because if a spot its volume changes it means that the amplitude, width  have changed.
as illustrated in fig.
<dig>  both phenomenon are detected.
in general, the analysis does not favor specific shapes , it will equally treat spots, tails and areas.
input quality
most algorithms react differently towards different kinds of input and the quality of the result often depends on the quality of the input.
input images can have many artifacts and with 2de the accuracy of the measurement is often unknown.
we showed that our technique works surprisingly well without calibrated intensities.
the use of mean background division and rms scaling offers the same information quality as relying on exact calibrated intensities.
we also observed that background noise and outliers don't influence the quality of the analysis.
this is logical because we rely on ranking of the data set, therefore outliers  do not attribute any significant impact to the correlation image.
this also means that some misaligned images will not influence the correlation image.
however, when investigating alignment drift on all images, we find that the method quickly looses power with decreasing alignment accuracy.
as the accuracy becomes less than the size of the spots, one looses analytical power .
for this method to work properly, it is thus of great importance to rely on calibration spots and use these to register the images.
especially when working with large images that can contain many thousand spots, alignment is a known problem  <cit> .
certain errors should be expected but as long as the spot jitter is smaller than the size of the spots, our algorithm will be able to provide useful results.
intra-image correlations
a correlation measures indicates whether two data sets relate to each other, not how they relate.
for instance, vectors  <cit>  and  <cit> correlate with a value  <dig>  without revealing the factor  <dig>  as such, correlation should not be confused with up- or down-regulation, nor with a causal relationship.
nevertheless, if the correlation image reveals that one area goes down in pace with the external variable while another area goes up, it is natural to ask whether the relation between these two areas is of importance.
based on the fab/p <dig> correlation, we will give two examples of such intra-image relations and explain how to address them at the pixel level.
does the difference between p53-α and p53-δ regions relate to the fab classification ?
fig.
<dig> reveals that the p53-α intensity increases with higher differentiation while the p53-δ intensity decreases.
therefore, we wondered whether the difference between p53-α and p53-δ areas related to the fab classification.
to answer this question, we preprocessed the images to introduce the 'difference'.
this was achieved by summarizing the areas of interest and then subtracting those areas prior to correlation.
fig.
<dig> shows the bounding boxes of the p53-α and p53-δ areas.
their sizes, respectively  and , were used to smooth the input images .
the shift between the area centers  was used to superimpose the δ region over the α region prior to subtraction.
if i is a 2de image, then iα and iδ represented the two intermediate images
ia,bα=∑x=a−sxαa+sxα∑y=b−syαb+syαix,y
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaacqwgjbqsdaqhaawcbagaemyyaemaeiilawiaemoyaigabaaccigae8xsdegaaogaeyypa0zaaabcaeaadaaewbqaaiabdmeajnaabaaaleaacqwg4baecqggsaalcqwg5bqeaeqaaaqaaiabdmha5jabg2da9iabdkgaijabgkhitiabdohazjabdmha5naabaaameaacqwfxoqyaeqaaawcbagaemoyaimaey4kasiaem4camnaemyeak3aasbaawqaaiab=f7ahbqabaaaniabgghildaaleaacqwg4baecqgh9aqpcqwghbqycqghsislcqwgzbwccqwg4baedawgaaadbagae8xsdegabeaaasqaaiabdggahjabgucariabdohazjabdiha4naabaaameaacqwfxoqyaeqaaaqdcqghris5aaaa@5e5a@
ia+dx,b+dyδ=∑x=a−sxδa+sxδ∑y=b−syδb+syδix,y
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaacqwgjbqsdaqhaawcbagaemyyaemaey4kasiaemizaqmaemieagnaeiilawiaemoyaimaey4kasiaemizaqmaemyeakhabaaccigae8htdqgaaogaeyypa0zaaabcaeaadaaewbqaaiabdmeajnaabaaaleaacqwg4baecqggsaalcqwg5bqeaeqaaaqaaiabdmha5jabg2da9iabdkgaijabgkhitiabdohazjabdmha5naabaaameaacqwf0oazaeqaaawcbagaemoyaimaey4kasiaem4camnaemyeak3aasbaawqaaiab=r7akbqabaaaniabgghildaaleaacqwg4baecqgh9aqpcqwghbqycqghsislcqwgzbwccqwg4baedawgaaadbagae8htdqgabeaaasqaaiabdggahjabgucariabdohazjabdiha4naabaaameaacqwf0oazaeqaaaqdcqghris5aaaa@65d2@
these two images were then subtracted to yield o = iα - iδ, which was subsequently put back into the gel-stack.
if there was a correlation between the α - δ difference and the fab classification then we would find it at observation point o <dig> in fig.
<dig>  we did not find a correlation, indicating that the difference between α-intensity and δ-intensity does not relate to the fab classification.
does mass-difference relate to the fab classification ?
fig.
<dig> shows the sub-δ region correlating negative and the δ region correlating positive, indicating that a mass-difference might be related to the fab classification.
setting up this specific question is similar to the previous, but without summation of regions.
the image pre-processing measures the difference between the intensity at a certain position y and intensities at the same position, but with a lower mass .
if i is an image from the gel stack, then o defines the new image
ox,y = ix,y - ix,y-dm
when using these preprocessed images into a correlation analysis, we found that observation point o <dig> revealed that indeed a mass-difference relates to the fab classification.
remembering the relative weak correlation in the fab classification , we now find a much strong correlation:  <dig> .
this illustrates how the correlation images can be used to naturally explore data sets.
performance
the complexity of the algorithm is linear to the size of the images and the number of images.
if we have n images of width w and height h then the calculation time will be in the order of o. the memory considerations are the same because all images need to be loaded in memory.
e.g;  <dig> images of  <dig> ×  <dig> pixels with  <dig> bit gray values will require around  <dig> mb of internal memory.
more information on complexity measurement can be found at  <cit> .
CONCLUSIONS
the presented results demonstrated that the correlation method can provide valuable information about complexly regulated proteins in biological systems.
the analysis technique can be used to measure and visualize relations between 2de images and external  variables.
the correlation image is calculated based on an aligned stack of 2de images.
the resulting image can be naturally interpreted and offers information that might otherwise be unavailable .
the technique is robust, general applicable to different object types , and allows a natural amount of spot location jitter.
we also investigated calibration factors and it turned out that normalization factors barely influence the analytical power of the method.
the correlation analysis of p <dig> biosignatures on aml and all cancer cells illustrated that the method can measure relations involving the overall intensity of the biosignature.
the novel findings of all- and aml-specific p <dig> bioprofiles were verified on normal cells from the lymphoid and myeloid lineages.
the positive correlation for full-length and δ- p <dig> in all was reflected by the presence of these p <dig> forms in lymphocytes, while these p <dig> forms were absent in the myeloid granulocytes.
this analysis of normal cells suggest that the p53-distinction between all and aml is correct.
a second analysis illustrated that the correlation method differentiates between different protein isoforms.
the relation between p <dig> biosignature and the aml fab classification was more complex, which allowed us to explain how intra-image relations could answer specific questions.
doing so, we observed that a mass-difference in the p <dig> biosignature correlated strongly towards the fab classification, suggesting that post-translational modifications of p <dig> relate to aml differentiation.
future development of the method could include adjustments and corrections for hardware-parameters such as camera warping and different kinds of noise.
canonical correlations could be used to integrate information offered by similar neighboring correlation pixels  <cit> .
it could also be possible to insert clustering algorithms to pseudo-color the final image or use image segmentation algorithms to classify areas automatically  <cit> .
in its present form we believe the method provides a valuable tool to explore and analyze complex biosignatures and responses from signaling networks.

 two-dimensional gel electrophoresis has been a successful technique for identification and visualization of post-translational modifications, and is increasingly used to determine accessible parts of the proteome in human cells. to a certain extent has 2de been used to propose diagnosis or clinical classification in diseases, including differentiating acute myeloid leukemia from acute lymphoblastic leukemia. the amount and complexity of data obtained from 2de patterns have led to the development of analysis software for digitalized images, but human interpretation and validation of the data is usually necessary. typically, one of the steps in 2de analysis is the selection of spots followed by description of their position, volume and other variables. current methods for spot detection assume regular spot shapes or model spots as bivariate gaussian densities, and therefore cannot discriminate spot shapes and irregularity. in this paper we present a method that omits the spot detection phase and does not require human interpretation on a gel-to-gel basis. given a set of gel images, the technique measures correlation between every pixel position and an external variable. this makes it possible to study the 2de protein distribution as well as the actual relation to the external variable. the method has been rigorously tested on a set of simulated 2de images with different levels of background, additional noise and outliers. biological evaluation of the technique was performed by testing the correlation analysis on p protein isoform profiles in cell samples from patients with well-characterized hematological malignancies. different hematological malignancies, like all and aml are characterized by distinct mutations or expression of genes involved in cell signaling. the tp gene is frequently mutated in many cancers and mutations in signaling pathways acting on p protein are found both in sporadic and hereditary cancers. the p protein is a sequence specific transcription factor that can regulate differentiation, growth and cell death, and is highly regulated by post-translational modifications caused by multiple signaling networks that directly or indirectly target the protein. during differentiation, p undergoes modifications like phosphorylation and acetylation and is suggested to be involved in differentiation of aml. because of this large range of activities and complex regulatory functions, we relied on analysis of the post-translationally modified p protein to illustrate our method. the p protein biosignatures in aml patients and all patients were analyzed by 2de immunoblot. distinct p biosignatures correlated with cancer type and, within the aml group, p biosignatures correlated with the level of differentiation, using the french-american-british classification.  overview of the method the presented method relies on the basic assumption that if spots on 2de images have biological relevance, then so must the pixels comprised within those spots. therefore it must be possible to analyze 2de images for correlation, without performing a spot detection step. the method requires the availability of a properly aligned stack of gel images. each of the images must have an associated parameter t. practically, t can represent any biological variable such as life expectancy, differentiation stage of a cell sample, age of an organism, origin of a cancer cell sample, effect of cancer therapy, cell size or even variables such as time, temperature, pressure, and so on. for every coordinate in the 2de image stack, a correlation analysis is performed between the pixel data gathered at that position and the external variable t. the correlation image is then created by repeating this process at every possible position. the work-flow and the concept behind the correlation method is illustrated in fig. a movie of the method is available. to illustrate how the correlation images ought to be interpreted, a simulated gel stack with defined spot characteristics in function of an external variable t was created. this simulation reassured a controlled environment in which the algorithmic behavior was observed. simulated gels altering spot position and sizes we first verified how the method reacts to spot location, spot size and spot shifts. the simulated gel stack has various spots behaving differently. spot α grows and fades out, spot δ shifts from left to right, spot β changes shape and the γ spots have a constant amplitude and width. fig shows various correlation images in which the strength of a correlation is presented in shades of green and brown. by design, spots α and β are parametrized by t. in the correlation images we find them back at the same position, showing that the correlation image offers correct positional information. the two constant γ-spots are independent of t. this results in no visible correlation in fig. 2bab. the. spot shape all images in fig. 2b show the α-spot to anti-correlate in the middle and to correlate at its periphery. this is consistent with the creation of the gel-stack in which the amplitude of spot a lowers from to while the spots broadens from to pixels. because the central spot widens, higher gel numbers will have relatively more signal in the periphery. this indicates that spots where diffusion-like alteration dominate can be detected based on the difference in correlation between the inner and outer areas. similar behavior can be observed in the shape changing β-spot. the initial vertical shape anti-correlates while the later horizontal shape correlates. masking the correlation image in the simulated gel-stack, empty areas have an almost constant intensity. for those areas, the raw correlation analysis indicates a strong correlation or anti-correlation. there are two reasons for this. first, the area can be constant, resulting in correlations that are +∞, -∞ or nan. in the correlation image these are represented as + or - secondly, in areas with very small alterations, the measured correlation is mathematically correct, but the lack in intensity variation offers little information. after applying various significance masks to the correlation image, we find that only areas with relevant spot modulations are indicated ). one mask removes non significant correlations and a second mask removes areas without variance. effect of different normalizations different background removal and scaling techniques were tested on the simulated gel-stack, including background subtraction and background division. in all cases, the original information that led to the creation of the gel-stack was retrieved. the α, δ and β spot correlations were always visualized, indicating that the normalization technique used is of little importance for qualitative analysis. in the particular case of gel normalization obtained by division through the mean gel intensity, new information was found that did not directly originate from the creation of the simulation. due to a t-dependent intensity increase in spot α, the mean intensity of the gel increased. as a result, the original constant γ-spots decreased in intensity. the γ-spots became t dependent and thus showed up in the correlation image. when working with real gels this does not hinder qualitative analysis because normalization is performed on an individual gel basis. therefore, it can always be repeated on any new gel, without taking into account previous gels and the reported correlations can be observed in the normalized images. quantitatively, normalization factors strongly influence correlation measures. if the technique is used as a quantitative method, then calibration spots ought to be used and exact understanding of machine specifications and camera properties should be known. white noise in 2de images in fig. 2ba-c, the background correlated towards t. adding white noise to the simulated images attenuates the appearance of such non significant background correlations resulted in weaker correlations, but still important spots were identifiable. this suggests that small amounts of noise might enhance interpretation of the correlation analysis by automatically introducing a non-correlating variance. the signal hidden within the noise must now compete against a non-correlating factor, as such, the noise introduces a form of automatic significance measurement. when the noise amplitude is t dependent, we observe correct information about the negative correlation, but loss of information about the positive correlation. such a situation could occur if a camera automatically gates images at waning signal strength. as long as white noise does not relate to the external variable, its presence barely influences the analytical power of the presented correlation test. effect of randomization of the dataset two sets of random data were generated to be used as t-value. instead of testing correlation towards the sequence number t, we now determined the effect of correlation of the images towards a random vector. the idl function'randomu', generated the normally distributed random numbers. in the correlation images we always recognized the same general shapes. areas that behaved similarly in the gel stack, had the same coloring, regardless of the external variable. these examples emphasize the robustness of the algorithm to group together regions of interest. outliers a test with outliers in the t-values shows limited impact on the interpretation of the gels. we changed the t-values from { 14} to { 14}, resulting in a slight change in actual correlation magnitude, but the information content was well preserved. even with 13% outliers { 14}, the original information was recovered. this is mainly due to the robust correlation which relies on ranking of the dataset instead of the numerical values. correlation analysis of p biosignatures in acute leukemia recently we demonstrated that signaling networks may be altered and potentiated in cancer cells suggesting a prognostic meaningful classification. this includes altered p map-kinase signaling, known to phosphorylate p the application of the presented method was tested on p biosignatures of human primary cancer cells. the p biosignature is probably formed by the combinations of splice forms of p and various post-translational modifications. the p protein is also involved in several positive and negative feedback networks. this has ignited the hypothesis that p integrates information from various signaling networks. we investigate two different relations. one illustrates a relation between the overall p intensity and aml/all classification, the other illustrates detection of p53-isoform biosignatures related to the aml fab classification. correlation of p protein biosignatures towards aml/all all and aml comprise different genetic abnormalities, and analysis of growth factor receptor expression and global gene expression has pointed out that the expression of receptor tyrosine kinases and signaling modulators are different. therefore, since the p protein is implied in various cancer related signaling networks, we expected to find distinct correlations between p expression and the aml/all variable. gels of aml patients were marked with t = while all variants were marked with t = the correlations are shown in fig. 3a. it reveals overall intensity increase of p in aml compared to all. there is no previous data from acute leukemia that supports this observation. to examine whether the 2de p correlations analysis reflected actual p protein expression differences in the lymphoid and myeloid cell lineages, we examined normal lymphocytes, neutrophile granulocytes and monocytes by 2de and one-dimensional immunoblot. this confirmed the intensity-differences detected by the correlation analysis by reflecting actual attenuated p protein levels in lymphocytes compared to myeloid cells. the impact of wrong all versus aml diagnosis was examined by random swapping all and aml labels in the aml/all versus 2de image correlations. this results in lower correlation values as expected. correlation of p protein isoforms towards the aml differentiation level the french-american-british classification of aml is based on the morphologically determined stage of myeloid maturation and direction of maturation. recent reports indicate that the fab classification, in particular the distinction between m1– and m4– in maturation level and direction of maturation, is associated with certain gene classes in unsupervised clustering of gene expression profiles. it is previously described in several reports that p is involved in leukemic cell differentiation. phosphorylation of p ser is necessary for differentiation in mouse embryonic stem cells, and p is able to direct differentiation in aml cell lines. the p53-deficient hl- cell line has potential for both monocytic and granulocytic differentiation, and introduction of wild type p directs differentiation in the granulocytic direction. based on these reports we hypothesized that the p biosignatures should reflect the stage and direction of myeloid differentiation. therefore, we measured correlations between the established routine morphological differentiation classification of aml and the p 2de biosignatures of the cancer cells. we assigned to every class a separate t-value: m, m, m, m, m and m. using gels we found specific correlations. image a is the masked correlation landscape, image b is the raw correlation image. the observations were: a) the tail of the p53-α isoform correlates negatively to the fab classification. b) the p area correlates positively towards the fab classification, c) the p53-δ region has four positively correlating articulated spots, d) the p sub-δ region has two negatively correlating spots. the combination of a positive correlation at the p53-δ region and a negative correlating sub-δ region indicates a spot shift from one area to another. additionally, the e) presence of the super-δ negative correlating region indicates that a change of spot shape also occurs. when the p53-δ spots are larger and diffuse then the patient is classified as m m or m if the spots in the δ region are clear articulated and smaller, the patient is either m or m none of the above correlations are strong. nonetheless they can be observed in the 2de images, which means that they can form an important tool in stratification of patients. based on these correlation measurements, we performed further tests to verify and confirm the relation between mass-differences and the fab classification. the presented correlation includes m a distinct subgroup of aml with signs of granulocytic differentiation, featuring the translocation t and responsiveness to retinoic acid therapy. fab m is therefore a separate entity in the recent who classification. the correlations were weaker when m was removed, which suggests that it is the pre-neutrophile granulocytic differentiation stage of m that comprises a distinct p isoform profile from m0/ p thereby contributing to a greater splitting of the patients into subgroups. discussion localization, shape and volume of 2de spots spot detection methods are in general very complex and time consuming tasks. the correlation technique relies on the assumption that if spots have a biological relevance then so must their individual pixels. the advantage of approaching gels this way is that we no longer depend on spot detection methods. one can wonder though, how relations between spot volumes and external variables are assessed. as it turns out, one can still rely on the correlation image because if a spot its volume changes it means that the amplitude, width have changed. as illustrated in fig. both phenomenon are detected. in general, the analysis does not favor specific shapes, it will equally treat spots, tails and areas. input quality most algorithms react differently towards different kinds of input and the quality of the result often depends on the quality of the input. input images can have many artifacts and with 2de the accuracy of the measurement is often unknown. we showed that our technique works surprisingly well without calibrated intensities. the use of mean background division and rms scaling offers the same information quality as relying on exact calibrated intensities. we also observed that background noise and outliers don't influence the quality of the analysis. this is logical because we rely on ranking of the data set, therefore outliers do not attribute any significant impact to the correlation image. this also means that some misaligned images will not influence the correlation image. however, when investigating alignment drift on all images, we find that the method quickly looses power with decreasing alignment accuracy. as the accuracy becomes less than the size of the spots, one looses analytical power. for this method to work properly, it is thus of great importance to rely on calibration spots and use these to register the images. especially when working with large images that can contain many thousand spots, alignment is a known problem. certain errors should be expected but as long as the spot jitter is smaller than the size of the spots, our algorithm will be able to provide useful results. intra-image correlations a correlation measures indicates whether two data sets relate to each other, not how they relate. for instance, vectors and correlate with a value without revealing the factor as such, correlation should not be confused with up- or down-regulation, nor with a causal relationship. nevertheless, if the correlation image reveals that one area goes down in pace with the external variable while another area goes up, it is natural to ask whether the relation between these two areas is of importance. based on the fab/p correlation, we will give two examples of such intra-image relations and explain how to address them at the pixel level. does the difference between p53-α and p53-δ regions relate to the fab classification? fig. reveals that the p53-α intensity increases with higher differentiation while the p53-δ intensity decreases. therefore, we wondered whether the difference between p53-α and p53-δ areas related to the fab classification. to answer this question, we preprocessed the images to introduce the'difference'. this was achieved by summarizing the areas of interest and then subtracting those areas prior to correlation. fig. shows the bounding boxes of the p53-α and p53-δ areas. their sizes, respectively and, were used to smooth the input images. the shift between the area centers was used to superimpose the δ region over the α region prior to subtraction. if i is a 2de image, then iα and iδ represented the two intermediate images ia,bα=∑x=a−sxαa+sxα∑y=b−syαb+syαix,y mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaacqwgjbqsdaqhaawcbagaemyyaemaeiilawiaemoyaigabaaccigae8xsdegaaogaeyypa0zaaabcaeaadaaewbqaaiabdmeajnaabaaaleaacqwg4baecqggsaalcqwg5bqeaeqaaaqaaiabdmha5jabg2da9iabdkgaijabgkhitiabdohazjabdmha5naabaaameaacqwfxoqyaeqaaawcbagaemoyaimaey4kasiaem4camnaemyeak3aasbaawqaaiab=f7ahbqabaaaniabgghildaaleaacqwg4baecqgh9aqpcqwghbqycqghsislcqwgzbwccqwg4baedawgaaadbagae8xsdegabeaaasqaaiabdggahjabgucariabdohazjabdiha4naabaaameaacqwfxoqyaeqaaaqdcqghris5aaaa@5e5a@ ia+dx,b+dyδ=∑x=a−sxδa+sxδ∑y=b−syδb+syδix,y mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaacqwgjbqsdaqhaawcbagaemyyaemaey4kasiaemizaqmaemieagnaeiilawiaemoyaimaey4kasiaemizaqmaemyeakhabaaccigae8htdqgaaogaeyypa0zaaabcaeaadaaewbqaaiabdmeajnaabaaaleaacqwg4baecqggsaalcqwg5bqeaeqaaaqaaiabdmha5jabg2da9iabdkgaijabgkhitiabdohazjabdmha5naabaaameaacqwf0oazaeqaaawcbagaemoyaimaey4kasiaem4camnaemyeak3aasbaawqaaiab=r7akbqabaaaniabgghildaaleaacqwg4baecqgh9aqpcqwghbqycqghsislcqwgzbwccqwg4baedawgaaadbagae8htdqgabeaaasqaaiabdggahjabgucariabdohazjabdiha4naabaaameaacqwf0oazaeqaaaqdcqghris5aaaa@65d2@ these two images were then subtracted to yield o = iα - iδ, which was subsequently put back into the gel-stack. if there was a correlation between the α - δ difference and the fab classification then we would find it at observation point o in fig. we did not find a correlation, indicating that the difference between α-intensity and δ-intensity does not relate to the fab classification. does mass-difference relate to the fab classification? fig. shows the sub-δ region correlating negative and the δ region correlating positive, indicating that a mass-difference might be related to the fab classification. setting up this specific question is similar to the previous, but without summation of regions. the image pre-processing measures the difference between the intensity at a certain position y and intensities at the same position, but with a lower mass. if i is an image from the gel stack, then o defines the new image ox,y = ix,y - ix,y-dm when using these preprocessed images into a correlation analysis, we found that observation point o revealed that indeed a mass-difference relates to the fab classification. remembering the relative weak correlation in the fab classification, we now find a much strong correlation:. this illustrates how the correlation images can be used to naturally explore data sets. performance the complexity of the algorithm is linear to the size of the images and the number of images. if we have n images of width w and height h then the calculation time will be in the order of o. the memory considerations are the same because all images need to be loaded in memory. e.g; images of × pixels with bit gray values will require around mb of internal memory. more information on complexity measurement can be found at.  the presented results demonstrated that the correlation method can provide valuable information about complexly regulated proteins in biological systems. the analysis technique can be used to measure and visualize relations between 2de images and external variables. the correlation image is calculated based on an aligned stack of 2de images. the resulting image can be naturally interpreted and offers information that might otherwise be unavailable. the technique is robust, general applicable to different object types, and allows a natural amount of spot location jitter. we also investigated calibration factors and it turned out that normalization factors barely influence the analytical power of the method. the correlation analysis of p biosignatures on aml and all cancer cells illustrated that the method can measure relations involving the overall intensity of the biosignature. the novel findings of all- and aml-specific p bioprofiles were verified on normal cells from the lymphoid and myeloid lineages. the positive correlation for full-length and δ- p in all was reflected by the presence of these p forms in lymphocytes, while these p forms were absent in the myeloid granulocytes. this analysis of normal cells suggest that the p53-distinction between all and aml is correct. a second analysis illustrated that the correlation method differentiates between different protein isoforms. the relation between p biosignature and the aml fab classification was more complex, which allowed us to explain how intra-image relations could answer specific questions. doing so, we observed that a mass-difference in the p biosignature correlated strongly towards the fab classification, suggesting that post-translational modifications of p relate to aml differentiation. future development of the method could include adjustments and corrections for hardware-parameters such as camera warping and different kinds of noise. canonical correlations could be used to integrate information offered by similar neighboring correlation pixels. it could also be possible to insert clustering algorithms to pseudo-color the final image or use image segmentation algorithms to classify areas automatically. in its present form we believe the method provides a valuable tool to explore and analyze complex biosignatures and responses from signaling networks. 
a second correlation analysis revealed a more complex relation between the differentiation stage in acute myeloid leukemia and p protein isoforms. we validated this technique on a set of simulated 2de images, which revealed also correct working under the presence of normalization factors. we developed an analysis technique to measure correlation between 2de images and biological variables on a pixel by pixel basis. this was followed by an analysis of p 2de immunoblots from cancer cells, known to have unique signaling networks. the presented analysis method measures relations between 2de images and external variables without requiring spot detection, thereby enabling the exploration of biosignatures of complex signaling networks in biological systems. two-dimensional gel electrophoresis is a powerful technique to examine post-translational modifications of complexly modulated proteins. since p is altered through these signaling networks, we expected to find correlations between the cancer type and the p profiles.
 two-dimensional gel electrophoresis is a powerful technique to examine post-translational modifications of complexly modulated proteins. currently, spot detection is a necessary step to assess relations between spots and biological variables. this often proves time consuming and difficult when working with non-perfect gels. we developed an analysis technique to measure correlation between 2de images and biological variables on a pixel by pixel basis. after image alignment and normalization, the biological parameters and pixel values are replaced by their specific rank. these rank adjusted images and parameters are then put into a standard linear pearson correlation and further tested for significance and variance.  we validated this technique on a set of simulated 2de images, which revealed also correct working under the presence of normalization factors. this was followed by an analysis of p 2de immunoblots from cancer cells, known to have unique signaling networks. since p is altered through these signaling networks, we expected to find correlations between the cancer type and the p profiles. a second correlation analysis revealed a more complex relation between the differentiation stage in acute myeloid leukemia and p protein isoforms.  the presented analysis method measures relations between 2de images and external variables without requiring spot detection, thereby enabling the exploration of biosignatures of complex signaling networks in biological systems. 