A NOVEL GAUSSIAN FITTING APPROACH FOR 2D GEL

ELECTROPHORESIS SATURATED PROTEIN SPOTS

Massimo Natale

1,2

, Alfonso Caiazzo

, Enrico M. Bucci

2,4

and Elisa Ficarra

Department of Control and Computer Engineering, Politecnico di Torino, Torino, Italy

BioDigitalValley srl, via Carlo Viola 78, Pont Saint Martin (AO), Italy

WIAS Berlin, Mohrenstrasse 39, 10997, Berlin, Germany

Istituto di Biostrutture e Bioimmagini, Via Mezzocannone 16, 80134, Naples, Italy

Keywords: Image analysis, Bi-dimensional electrophoresis, Proteomics, Software tools.

Abstract: Analysis of 2D-GE images is a hot topic in bioinformatics research, since currently available commercial

and academic software has proven to be not really effective and not completely automatic, often requiring

manual revision of spots detection and refinement of computer generated matches. In this work, we present

an effective technique for the detection and the reconstruction of over-saturated protein spots.

Firstly, it reveals overexposed areas where spots may be truncated, and plateau regions caused by smeared

and overlapped spots. As next, the correct distribution of pixel values in the overexposed areas and plateau

regions is recovered by a two-dimensional fitting based on a generalized Gaussian distribution approximat-

ing the spots volume. Pixel correction according to the generalized Gaussian curve in saturated and smeared

spots allows more accurate quantifications, providing more reliable image analysis results.

As validation, we process highly exposed 2D-GE image, containing saturate spots, with respect to the corre-

sponding non-saturated image, confirming that the method can effectively fix the saturated spots and enable

correct spots quantification.

1 INTRODUCTION

In the post-genomic era, two-dimensional gel elec-

trophoresis (2D-GE) is a powerful and widely used

method for the analysis of complex protein mixtures

extracted from cells, tissues, or other biological

samples. In 2D-GE proteins are separated according

to their charge (pI) by isoelectric focusing in the first

dimension, and according to their molecular weight

(MW) by SDS-PAGE in the second dimension. Each

resulting 2D-GE contains a few hundred up to sev-

eral thousands of protein spots whose volume corre-

lated with the protein expression in the sample. The

main goal of comparative proteomics is to match

protein spots between gels and define differences in

the expression level of proteins at different biologi-

cal states using image analysis software.

Good image capture is critical to guarantee opti-

mal performance of automated image analysis pack-

ages and generate reliable scientific data. It should

allow for detection from very low to high abundant

protein amounts. Through digitalization, a gel is

represented by a two-dimensional matrix of squares

or pixels. Each pixel of the generated image is de-

fined by its coordinates (x,y) and by its signal inten-

sity I encoded as greyscale level. The spatial coordi-

nates are defined by image resolution, while the

signal intensity is defined by dynamic range.

Saturation occurs when grey levels exceed the

maximum representable. When a spot becomes satu-

rated, the spot appears truncated, and any differences

in high pixel intensities cannot be resolved. No reli-

able quantitative data will be generated from a satu-

rated spot, and different authors recommend to

manually deleting the saturated spots, before analyz-

ing the gels with the available software (Berth,

2007).

Where different experimental states are being

compared the inclusion into the analysis of saturated

spots have the potential to bias normalization, in

particular if they have a variance that is a significant

proportion of the total spot volume (Miller, 2006).

Currently available commercial software (as

Delta2D, ImageMaster, PDQuest, Progenesis) are

not able to deal with specific protein spot distortions

found in the gel images (Maurer, 2006). Automatic

335

Natale M., Caiazzo A., M. Bucci E. and Ficarra E..

A NOVEL GAUSSIAN FITTING APPROACH FOR 2D GEL ELECTROPHORESIS SATURATED PROTEIN SPOTS.

DOI: 10.5220/0003789803350338

In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS-2012), pages 335-338

ISBN: 978-989-8425-90-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

reconstruction of over saturated protein spots is not

possible using available protein analysis software.

The only option suggested by the producers of soft-

ware for 2D-GE analysis is to rescan the gel decreas-

ing the exposure (Nonlinear, 2011). Most of the

time, this is not possible because gel staining are

photosensitive, and loss intensity in few minutes.

Moreover, an image acquired with the largest

exposure also contains the highest number of spots

and thus also the lower-abundance protein spots.

Thus, decreasing the exposure causes the lower-

abundance protein spots to be neglected.

In this work, we present a novel algorithm for the

detection and the reconstruction of over-saturated

protein spots. Firstly, the algorithm reveals overex-

posed areas where spots may be truncated. Secondly,

this method reconstructs the over-saturated protein

spots through a Gaussian mathematical model that

simulates the distribution of the greyscale values in

the saturated spots. Furthermore, the algorithm will

be validated processing highly exposed 2D-GE im-

age, containing saturate spots, to the corresponding

non-saturated image.

2 METHODS AND RESULTS

2.1 Despeckle

After image scanning the 2D-GE are noisy, with

artifacts as scratches, air bubbles, and spikes.

Figure 1: A) Portion of 2D-GE gel where the spikes are

marked with black arrows. B) Portion of 2D-GE gel after

the 3x3 median filter. C) , D) 3D view of the portion of

gels

The aim of reducing speckles in a 2D-GE image

is to remove the noise without introducing any dis-

tortion in quantitative spot volume data.

We evaluated the filter size from 3x3 to 7x7. We

chose a 3x3 filter because it is effective in removing

most of the spikes with minor smoothing effects that

reduce the accuracy in the spot volume computation.

The result of 3x3 median filter is shown in figure 1.

In figure 1A is shown a portion of gel where the

spikes are marked with black arrows. In Figure 1C is

shown the portion of gel in 3D view where a spike is

marked with a red arrow. In Figure 1B and 1D are

shown the 2D-GE image and the 3D view after ap-

plying the 3x3 median filter.

2.2 Find Plateau Regions

The commercial software are able to detect a satu-

rated area when a region of the image reaches the

maximum value of greyscale. However, in most

cases a saturated area looks like a plateau zone,

where the pixels have similar intensity, but they do

not reach the maximum value of greyscale.

In these cases the commercial software not only

are unable to correct this aberration but they also fail

to detect it, inducing the operator to underestimate

the problem.

In order to identify plateau regions, we imple-

mented a morphological filter inspired by the Roll-

ing Ball algorithm (Sternberg, 1983). We designed

structural elements as ball of circular shape with

radius (RD) and height defined by greyscale value

tolerance (GVT). The RD represents the number of

pixels of the circle radius (Figure 2A). The GVT

represents the rate of gray values of the pixel in the

centre of the structural elements (Figure 2B).

Figure 2: A) The radius defines the pixels that are included

into the structural element. B) The greyscale value toler-

ance defines the variation within the gray values are con-

sidered to plateau.

BIOINFORMATICS 2012 - International Conference on Bioinformatics Models, Methods and Algorithms

336

Figure 3: Saturation zone detected from our algorithm.

The figure shows the same gel acquired with three differ-

ent exposure. 2D-GE gel acquired with A) high, B) me-

dium, and C) low exposure.

The RD and the GVT are defined by a single pa-

rameter so that if the user sets, for example, 10 as

parameter, the RD will set of 10 pixels and the GVT

of the 10% of gray values of the pixel in (x,y) posi-

tion. The centre of the structural element is moved

along each pixel across the image. For each point the

maximum and minimum gray value within the given

RD is calculated. When the difference between

maximum and minimum is less than the GVT, the

area defined by local operator is considered as a

plateau area.

In order to test our procedure, we ran the method

on more than 50 2D-GE images, each acquired at 3

different expositions. An example is shown in fig-

ures 3A, 3B and 3C. These gels provide us the op-

portunity to see how the gray values are distributed

in the same spot. The plateau areas found by our

algorithm are filled in red.

Figure 3A contains a larger number of spots, but

some of them are saturated. In this case, only image

in figure 3C could be correctly analyzed by available

software. The other two images would be discarded

because of the large saturated areas that prevent

accurate protein expression measures. However,

researchers would be often interested in analyzing

the image acquired with the largest exposure (figure

3A), which also contains the highest number of spots

(and thus also the lower-abundance protein spots).

For this purpose we developed a refined algorithm

capable of calculating the original non-saturated

distribution of the gray values within the saturated

zone of the spot.

2.3 Gaussian Fitting

To determine the unknown distribution of gray val-

ues in the saturated area, we firstly assumed that the

intensity values distribution in the spot is described

by a Gaussian function of the form (1):



(

,,

)



√

2

exp −





2σ





(1)

where σ and M are, respectively, the standard devia-

tion and the average of intensity values, while x is a

pixel coordinate in the image. To determine σ and

M, we search the optimal fitting of the Gaussian

function in (1) with the values of the unsaturated

spot. In other words, given a set of m points with

coordinates (x

), for j = 1, ..., m, the problem is to

find the couple of parameters (σ,M), such that the

differences (2)

f(x

, σ, M) - I

(2)

are small, where I is the pixel intensity. Choosing

the approximation criterion is equivalent to define an

error function, describing how far is the Gaussian

approximation from the original dataset in the unsa-

turated region. As error function we selected the sum

of the squared differences:



(

,

)

=(



(







,,)−



)



(3)

Other possibilities consist in taking different powers

of the differences, or including a set of weights, e.g.

to give different relevance to the point closer to the

saturation.

However, once the error function is chosen, the

problem results in finding the couple (σ,M) that

minimize the error function itself. A possible ap-

proach is to perform an exhaustive search on (σ,M)

values.

Figure 4: A) Portion of 2D-GE where all spots are cor-

rectly acquired. B) Portion of 2D-GE where two spots are

saturated. C) Plot profile of gray value found along the

green line as shown in 4A). D) Plot profile of gray value

found along the yellow line as shown in 4B). In red are

shown the saturated zone.

However, if the size of the parameters space is

too big, a more effective Newton-Raphson algorithm

to find the zero of the gradient can be employed. In

figure 4 we show the distribution of gray values in

non saturated spots (figure 4A) and in saturated

spots (figure 4B).The figure 4C and 4D show the

A NOVEL GAUSSIAN FITTING APPROACH FOR 2D GEL ELECTROPHORESIS SATURATED PROTEIN SPOTS

337

intensity distribution profiles. In figure 4B and 4D

are underlined the saturated value by red lines. In

figure 5A we show as our mathematical model

where the parameters have been obtained through

the minimization of (3), is able to accurately de-

scribe the distribution of values of a 2D-GE spot.

Figure 5: A) In red is plotted the Gaussian distribution, in

green is plotted the spot non-saturated profile. B) In blue

is plotted the Gaussian distribution while in yellow is

plotted the spot saturated spot.

Finally, in figure 5B we show how the method

can effectively enable correct spots values recon-

struction fixing the spot saturation issue.

The procedure ran on more than 50 2D-GE im-

ages, each of them acquired at three different exposi-

tions (i.e. acquisition parameters).

3 CONCLUSIONS

Saturation of abundant spots is a general problem in

2-DE evaluation, in particular working with complex

samples like serum or plasma, which have a very

uneven protein distribution.

Currently available commercial software are not

able to perform 2D-GE image analysis in presence

of saturated spots. The only alternatives are to re-

move the saturated spots or rescan the gel image

with different acquisition parameters.

In this paper is presented a new approach for

treatment of over-saturated protein spots in 2D-GE.

Using experimental 2D-GE images we have demon-

strated that saturated protein spots can be found by

our algorithm.

Subsequently, we applied a Gaussian function to

calculate the real experimental spot volume (and

thus the correct protein expression) through the

reconstruction of intensity distribution of non-

saturated spots. The accuracy of reconstruction was

verified by comparing the same gel acquired with or

without saturated spots.

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