Sequence logo and PWM

PWM for DNA sequences has four rows, each representing a nucleotide, multiple columns, each representing a TFBS position. Figure 1 shows an example of PWM and its corresponding sequence logo. Here we denote the PWM as P. Each element P _ij represents the probability of nucleotide i∈{A,C,G,T} in position j, where the sum probability of each column is 1. To convert a PWM to sequence logo, for each letter column j, the height of the whole letter stack is determined by the information content I of the column, which is calculated by

$$\begin{array}{*{20}l} I_{j} &= H_{j, max}\left(P_{1}, P_{2}, P_{3}, P_{4}\right) - H_{j}\left(P_{1j}, P_{2j}, P_{3j}, P_{4j}\right) \\&= 2 + \sum_{i=1}^{4}P_{ij}\cdot log_{2}{P_{ij}} \end{array} $$

where H _j represent the entropy of position j, and 1 to 4 represents nucleotide A, C, G and T [3, 8]. Then, the height for each nucleotide is calculated by P _ij ·I _j . For the color denotation, usually green, blue, yellow and red represent A, C, G and T respectively.

Reconstruction of the probabilities for nucleotides A, C, G and T from the sequence logo is not as straight forward as it looks. Here we only focus on logo image of one logo-column j.

First of all, directly measuring the proportion of each letter of the whole letter-stack at position j does not work - the lower the letter stack, the lower the resolution, and therefore the harder to measure the proportion of the letter height. For the cases that one big letter dominates a position, such as logo-columns on position 1, 3, 4, 6 and 9 in Fig. 1, a few pixel difference of the bottom letters will severely influence the accuracy. This phenomenon is worse for the cases that have two similar sized letters and have lower information content, such as column 2, 5, 7, where directly measuring the letter height for probability would cause the reconstructed PWM to have much higher information content. This influence is even worse when the resolution of image is low.

In order to speed up the slow computational time of solving the above formula, we pre-calculated a I to p _1st lookup table, B, with p _1st interval 0.01 from 0 to 1.

Concatenating the estimated probabilities for all positions, we obtained the reconstructed PWM.

Algorithm

Figure 2 shows the workflow of the mian algorithm. Firstly,The image pre-processing module converts the image file to a common three-channel RGB formatted file. Current supported file format includes ‘png’, ‘jpg’, ‘jpeg’ and ‘gif’, except ‘png’ file with alpha channel (transparent channel).

Secondly, the algorithm determines if the logo contains X and Y coordinates using the black pixel feature. We assume that the coordinates in the image are black. If the logo has X and Y coordinates, the algorithm determines the full length and height of the logo, then cuts the pure logo area. If the logo image does not contain X and Y coordinates, the algorithm uses the logo boundary to cut the pure logo area and assume that the highest letter has maximum information content - 2 bits. If the logo image contains Y coordinate, then the height of Y coordinate is used to estimate the information content later. Then the program cuts the pure logo region and removes noise in the image, such as horizontal dashed lines of background patterns in some logo images.

Then for each pixel in the image, the algorithm determines its color by finding its nearest color central point. White pixel is for background, black pixel is for axis and labels/marks, the other four color pixels are for the four nucleotides in DNA sequences. We use consensus voting to determine the color of the letter sub-image. We do not choose to use ‘optical character reader (OCR)’ for the letter recognition task because OCR has low recognition speed and low accuracy for this case, especially due to the uncommon shape of font and the variety of colors.

Implementation

Stand-alone application The core functions of logo2PWM is written in MATLAB 8.6 with image processing toolbox. The complete MATLAB program requires as input the file name of the sequence logo image, and outputs three files in the same folder of the original logo image file: the reconstructed PWM in.csv format, the reconstructed PWM in enologo format, and the Position-specific Scoring Matrix (PSSM) file for MEME suite. The program can also provide the flexibility to accept an optional parameter - the ‘number of columns’, therefore has a higher chance to return a good result.

The source code of stand-alone application can be accessed at http://www.cs.utsa.edu/~jruan/logo2pwm_sa.

Web-based service As shown in Fig. 3, the software architecture for the web-based service has four layers. From bottom to top, these layers are MATLAB source code, MATLAB compiler runtime executable, web framework, and deployment.

logo2PWM is available at http://www.cs.utsa.edu/~jruan/logo2pwm.

Evaluation

We evaluate our algorithm by computing the correlation between estimated and true PWMs, and visually examining the original sequence logos and sequence logos regenerated with the estimated PWMs. Three systematic evaluations have been performed on 1946 TFBS logos from - Zhu et al. [9], MacIsaac et al. [10], and, JASPAR-2016 database [11, 12]. There are 179 sequence logo-PWM pairs from Zhu et al. [9], 124 sequence logo-PWM pairs from MacIsaac et al. [10], and 1643 available logo-PWM pairs from the JASPAR-2016 database respectively.

Evaluation on 179 logos from Zhu et al. [9]

On 179 logos from Zhu et al. [9], our estimated PWMs has high correlation of the original PWMs all-across the sequence logo images (Fig. 5). For all logos, the estimated PWM correlation is greater than 0.94, and the median is above 0.97. Visual comparison between re-generated and original logos on arbitrarily selected logos is almost identical, shown in Fig. 6.

Evaluation on 124 logos from MacIsaac et al. [10]

Figure 7 shows the distribution of correlation between 124 estimated PWMs and their original PWMs. Our algorithm works well on most of logos. The median correlation is 0.98. The outliers shown by the red ‘+’ signs on the boxplot indicates the failed cases. Actually, most of the failed cases are due to bad logo images - such logo images cannot even read by human. For example, sequence logos with letter width less than one pixel (multiple cases in this dataset). Visual comparison between re-generated and original logos on arbitrarily selected logos shows no obvious flaw (Fig. 8).

Evaluation on 1,643 logos from the JASPAR-2016 database

The JASPAR-2016 database provides entries for 2049 TFs of variety kinds of species. Within the 2049 TF-entries, 1643 of them have their sequence logo available. Figure 9 shows the distribution of correlation between the 1643 estimated PWMs and their original PWMs. Our algorithm still works fluently on most of logos. The median correlation is 0.99. Visual comparison on Fig. 10 shows that our logo2PWM tool also handles the JASPAR logo format well.

To accurately estimated PWMs from a large variety of sequence logo images is a challenging task, and sometimes the automatic option of our tool fails. Usually, passing the number of letter-columns parameter n and carefully cropping the pure logo region of the logo image solve most of problems. Figure 11 shows four examples of failures using the default options of logo2PWM. Figure 11 a shows a good example of a sequence logo with a long gap, which make the pattern complex and the PWM hard to be reconstructed. Our solution is to crop the region of interest. Note that logo2PWM works best with no left and right margin on the logo image. Sometimes, the resolution of the image is so low (Fig. 11 b) that the number of letters cannot be correctly counted by program. In this case, we simply need to input a letter count parameter n to the tool. There are also several cases just like Fig. 11 c, where bad logos cause the failure of the tool, which lower down the overall evaluation accuracy shown in Fig. 7. Figure 11 d shows an example of logo2PWM’s failure dues to incompatible logo format, which can be easily solved by cropping logo image.