1 Introduction

1.1 Biological Data Analysis

The primary goal of bioinformatics is developing computational techniques to analyze and understand biological data, especially genomic data. However, it is difficult to define the goal of analyzing and understanding biological data.

This dilemma is common to all fields of natural science. In natural science, we usually do not have "ground truth" data to evaluate the accuracy of methods. This is because we analyze scientific data when we do not know the "ground truth".

Obviously, because we want methods that lead to new biological discoveries, the goal of computational techniques to analyze biological data is to make a biological discovery. This is correct; we need to have deep expertise in biology to decide the goals of computational methods for biological data analysis. However, it is preferable that we have another strategy to determine the goals, because it is efficient to evaluate computational techniques before we conduct biological experiments based on the results of the computational analysis. In this respect, I propose that we should focus on human perception, our way of seeing.

1.2 Human Perception

To understand our way of seeing, it is useful to consider it in terms of psychology of vision. Figure 1(a) shows the well-known image of "Dalmatian dog" proposed by R. Gregory. If we are unfamiliar with this picture, it is likely that it will not make sense. Once the dog silhouette has been seen as shown in Figure 1(b), it becomes clear that there is a dog in the original image. This example illustrates the amazing ability of the human visual system to find meaningful objects in images by using prior knowledge of what we see in them. The important point here is that this is not a particular case; this is our basic visual capability. We can recognize local features (e.g. fragments of silhouette of a dog) only by knowing that they consist in an overall structure (e.g. a dog). Without the prior knowledge of the overall structure, it is difficult to distinguish between a local meaningful object and a noise.

1.3 Goal of This Study

Therefore, I define my goal of this study as achieving a computational technique that mimics our way of seeing biological data. More specifically, the purpose of this study is developing a method to analyze biological data by using prior knowledge of what it analyzes. For this reason, I developed a detection method that uses prior knowledge of the structure of the data by using a marked point process.

2 Expression Patterns of the Distributions of Transcription Start Sites Using Marked Point Process

In this study, I propose a novel method to detect expression patterns of the distri-butions of transcription start sites (TSSs). Figure 2.1 (a) shows a toy example of TSSs distribution. When we see this type of data, we usually put arbitrary "hills" into the data, as shown in Figure 2.1 (b), to interpret them. In other words, we use our prior knowledge of the structure of the data to understand them; we use our prior knowledge that the TSSs distributions can be approximated by a mixture of some simple functions, such as Gauss functions, to see the data. From this viewpoint, I present a method that mimics our way of seeing the data by using prior knowledge of the data structure and applying Gauss functions to the data.

I model the distributions of TSSs by using a marked point process and present a method to detect expression patterns of TSSs. In my methodology, each point corre-sponds to each nucleotide, and points have attributes to represent the prior knowledge of data structure. The attribute of the point is called mark in the field of point processes; thus, it is a marked point process that I use in this study. Because I employ Gauss functions as the marks, my method puts Gauss functions into TSSs data to detect their patterns, as shown in Figure 2.1 (c). To search good configurations of Gauss functions, I define a Gibbs energy consisting of two terms: data energy and prior energy. The data energy measures consistence of Gauss functions to the TSSs data; the prior energy incorporates some constraints on interactions of Gauss func-tions. The Gibbs energy can be minimized by using a multiple birth-and-death dy-namics coupled with the traditional simulated annealing to find the optimum configuration of the marked points.

The proposed method was tested on synthetic and real-world data. The synthetic data is composed of three Gauss functions, and random noise is added to the mixture. In Figure 3, histogram is the synthetic data, and plotted curves are the results of pat-tern detections of the synthetic data by my method. In Figure 3(a), the leftmost and central functions overlap moderately. It is difficult to definitely decide the number of Gauss functions; there seems to be two functions, and there seems to be three func-tions at the same time. The proposed method detects two Gauss functions when the data and prior energy terms are equally contributed to the global energy function, as shown in Figure 3(b). It also detects three functions when we increase the weight of data energy, as shown in Figure 3(c). In other words, if we want to undervalue "re-pulsive power" between adjacent functions, my method can detect functions in such a way. This result demonstrates that the proposed method is useful in that it detects patterns in a way preferred by us.

3 Discussion

Improving our understandings of promoters is one of the most important goals to analyze the distributions of transcription start sites. Because promoters are responsi-ble for transcriptional regulation, we can make a hypothesis that promoters decide expression patterns of the TSSs distributions in the downstream sequence. In other words, expression patterns of the TSSs distributions might be determined by the type of promoter sequences. For this purpose, we need to classify the TSSs data, and one of the most straightforward approaches is using machine learning techniques. In this classification, training data is a set of known promoter sequences and their down-stream TSSs distributions, and we can classify TSSs distribution data that is not relat-ed with the known promoters on the basis of the training. Although we can perform this classification by using raw TSSs data, we can also utilize the patterns of the TSSs distributions that my method detects. Using the results of my method has an ad-vantage over using raw data, because we can incorporate our assumption of the data into this classification. For example, the distribution in Figure 3(a) is obscure in that deciding the number of Gauss functions in the distribution is difficult. However, we can use Figure 3(b) for the classification, if we think this distribution consists of two Gauss functions based on the knowledge of biology. We can also use Figure 3(c) for the classification, if we think this distribution consists of three Gauss functions based on the knowledge of biology. More specifically, if we think the promoter sequence upstream the distribution in Figure 3(a) has an effect on two points in the downstream region, we should use Figure 3(b) for the classification. If we think the promoter sequence upstream the distribution in Figure 3(a) has an effect on three points in the downstream region, we should use Figure 3(c) for the classification. In this respect, the proposed approach is useful for biologists because they can test their hypotheses by using it.

Figure 1 Dalmatian dog proposed by R. Gregory (a) obscure image (b) dog silhouette

Figure 2 Illustrative diagrams of my method. (a) Toy example of transcription start sites data. (b) An example of our way of seeing: We see four "hills", such as Gauss functions. (c) My method: In my method, each point has Gauss functions; Red point has red function. Yellow function is removed because it overlaps the red function, depending on a parameter. Blue function is removed because it is too small, depend-ing on another parameter.

Figure 3 (a) A synthetic data composed of three Gauss functions.

(b) Pattern detection of (a) using the proposed method 1. The data and prior energy terms are equally considered in the global energy function.

(c) Pattern detection of (a) using the proposed method 2. The data energy is more overvalued than the prior energy in the global energy function.

本論文は五章からなり、以下のような構成を持っている。第一章は生物学データを解釈するための計算機論的手法、第二章は、生物学的画像データについての背景説明、第三章はショウジョウバエの羽根画像データから翅脈及び羽根の細胞数を認識する研究、第四章は、転写開始点データからピークの形状を推定する研究、第五章は結論、第六章は謝辞が述べられている。

論文の主となる部分は第三章で、そこではショウジョウバエの網羅的な遺伝子変異体の羽根画像データを計算機で解析するための手法の開発と、それを用いた画像の解析結果について述べている。第三章の前半では、羽根画像データから、翅脈を抽出し、羽根の領域分割を行うアルゴリズムの開発と計算機実験の結果が示されている。具体的には、まずActive Contour Model 法を用いて、羽根の輪郭を認識し、その後Texture Feature分析と呼ばれるWaveletを用いる手法により翅脈上の点列を求める。その後既知の翅脈モデルとの対応関係をGeometric Branch Bound アルゴリズム用いて計算することにより、画像中の翅脈の完全な認識が行われる。このアルゴリズムを1000枚の画像データに適用し、大部分の場合に数ピクセルの誤差で翅脈を正しく認識できることを示した。

第三章の後半では、羽根の細胞に生えている翅毛の画像を頼りに、羽根を構成する細胞の数や密度を計測する手法の開発と、それを用いて、羽根の細胞密度の自動計測について述べている。方法は、翅毛の位置を表現する画像中の点集合に対して、点の間の距離や画像濃度の整合性を評価するギブスエネルギーを定義し、点の生成消滅を繰り返すランダムプロセスを発生させることにより、最適な細胞集合を計算するというものである。これを羽根画像に適用し細胞数を計測したところ、人の目で数えた細胞数とほぼ同じ細胞数が得られ、提案手法が十分に実用的なものであることが示された。

第四章では、羽根の細胞数を数える手法を、ゲノム上の転写開始点のクラスタリングに応用し、人の目で行ったクラスタリングにどの程度近いものが得られるかについて比較検討を行った。

なお本論文第三章は、村松圭吾、板垣敏郎、森下真一との共同研究であるが、論文提出者が主体となって分析及び検証を行ったもので、論文提出者の寄与が十分であると判断する。

したがって、博士(科学)の学位を授与できると認める。