A NEW CLUSTERING METHOD AND ITS APPLICATION TO PROTEOMIC PROFILING FOR COLON CANCER

Abstract

In this paper, we introduce a new clustering method: quasi-clique merger, and its associated data pretreatment programs. This program constructs non-binary hierarchical trees with much smaller number of clusters in the outputs. And overlapping clusters are also allowed in the outputs. We applied this new method to cluster 60 human cancer cell lines (the NCI-60) using the previously identified proteomic determinants for chemosensitivity of 5-Fluorouracil (5-FU). All colon cancer cell lines were aggregated into a single cluster, indicating that the eight proteomic markers are potential diagnostic markers of colon cancer. The results based on the new clustering method have surpassed those based on previous methods on the same datasets.

1. Introduction

Clustering is one of the most important methods for bioinformatics research, and there are a variety of different clustering algorithms now available. Although all these approaches have clearly demonstrated their usefulness in applications, a number of important questions remain to be addressed, such as, "problems related to robustness, uniqueness, and optimality of linear ordering which complicates the interpretation of the resulting hierarchical relationships", problems of "how to determine the optimal number of clusters" (Lukashin & Fuchs, Bioinformatics 2001 (1)), problems that "none of these algorithms can, in general, rigorously guarantee to produce a globally optimal clustering for non-trivial objective function" (Xu, Olman & Xu, Bioinformatics 2002 (2)) and "there are no completely satisfactory methods for determining the number of population clusters for any type of cluster analysis… …" (SAS/STAT User's Guide (3)).

In this paper, we introduce a new clustering method called "quasi-clique merger" and its associated data pretreatment programs. One of the most significant differences between the new method and other existing methods is that "quasi-clique merger" method constructs a much smaller hierarchical tree, which highlight the meaningful clusters (while the hierarchical trees produced by most existing hierarchical clustering methods are binary). Another special feature of the new method is the property of multi-membership (or, called overlapping clustering), which is a new concept recently introduced by Palla et al. (4), Pereira-Leal, et al. (5), Futschik et al. (6).

We applied this new method to cluster 60 human cancer cell lines (the NCI-60) using the previously identified proteomic determinants for chemosensitivity of 5-Fluorouracil (5-FU). All colon cancer cell lines were aggregated into a single cluster, indicating that the eight proteomic markers are potential diagnostic markers of colon cancer. The results based on the new clustering method have surpassed those based on previous methods on the same datasets.

2. The quasi-clique merger algorithm

Graph/network is one of the most commonly used model for presenting the real-valued relationship of a set of input items. Let G=(V,E) be a graph with the weight w: E(G)→R where w(e) represents the similarity/closeness of the items u and v where e=uv.

Clustering is a processing that detects all denser subgraphs in G, and list their inclusion relation in a hierarchical structure.

The following is the algorithm.

2-1. Subprograms

For a subgraph C, we define the density of C by

$$\mathrm{d}(\mathrm{C})=\frac{2\sum _{\mathrm{e}\in \mathrm{E}(\mathrm{C})}\mathrm{w}(\mathrm{e})}{|\mathrm{V}(\mathrm{C})|(|\mathrm{V}(\mathrm{C})|-1)}.$$

Obviously, (for those who are familiar with graph theory or in computer science), if w(e)=1 for every edge e in C, the subgraph C induces a clique. For a weighted graph, a subgraph C is called a Δ-quasi-clique if d(C) ≥ Δ for some positive real number Δ. A heuristic processing is applied here for finding all quasi-cliques with density in various levels.

The core of the algorithm is deciding whether or not to add a vertex to a community. For a vertex v not in C, we define the contribution of v to C by

$$\mathrm{c}(\mathrm{v},\mathrm{C})=\frac{\sum _{\mathrm{u}\in \mathrm{V}(\mathrm{C})}\mathrm{w}(\mathrm{u}\mathrm{v})}{|\mathrm{V}(\mathrm{C})|}$$

A vertex v is added into C if c(v,C)>α d(C) where α is a user specified parameter.

Algorithm Grow(C,G)

(grow a community C in G)

• while V(G)\V(C)≠Ø;

  • begin
  • pick v∈V(G)\V(C) such that c(v,C) is a
• maximum

  • if c(v,C) > α d(C) then add v to C
  • else return
  • end

Algorithm Decompose(G,w₀)

(decompose a graph G into communities using edges with weights at least w₀)

• compute E₀ = {e∈E(G): w(e)≥w₀}

• for each e=uv∈E₀ in decreasing order of w(e)

  • begin
  • if either u or v is not in any community
• then

  •   begin
  •   create a new empty community
  • C and add u, v into C
  •   Grow(C,G)
  •   end
  • end
• repeatedly

  • if for any two communities C₁ and C₂, |C₁∩C₂| >β min(|C₁|, |C₂|) then merge C₁ and C₂ into a new community C=C₁ ∪ C₂ (where β is a user specified parameter).

Algorithm Contraction(G)

Each community becomes a vertex. The weight of an edge is defined by

$$\mathrm{W}({\mathrm{C}}_1,{\mathrm{C}}_2)=\frac{\sum _{\mathrm{e}\in E_{\mathrm{c}}}\mathrm{w}(\mathrm{e})}{|{\mathrm{E}}_{\mathrm{c}}|}$$

where E_c is the set of crossing edges which is defined by E_c = {v₁v₂: v₁∈C₁,v₂∈C₂, v₁≠v₂}

2-2. The main algorithm

Algorithm Main-Algorithm

(produce hierarchic clustering tree for a graph G)

• while E(G)≠Ø

  • begin
  • Choose w₀ according to some criterion
  • Decompose(G,w₀)
  • Contraction(G)
  • store the resulted graph to G
  • end

• trace the movement of each vertex and produce the hierarchic tree

Note: the choice of w₀ depends on the weights of the edges in E(G). Usually e₀=γ max w(e).

3. Data pretreatment

The quasi-clique merger algorithm produces much less clusters. This is one of the important features of the new method. However, if the weights of most edges are distributed in a very small interval, then the above algorithm may not be able to recognize the small difference and therefore, produces only a very small number of clusters. In order to output an appropriate number of clusters, we introduce the following data pretreatment in our processing.

3-1. Input

One of the most common formats of inputs is an m×n-matrix A = [a_ij]. Microarray data are usually in this format. Clustering processing is to separate the set of rows into several clusters.

3-2. "Minority rules"

Find the average b_j of the j-th column, for every j.

$$a_{ij}\leftarrow a_{ij}-b_j.$$

This processing sets zeros for all those average values and therefore, highlights the difference for those above average and bellow average.

3-3. Similarity – angles between vectors

Each row is considered as a vector v_i and the angle between two vectors is used to measure their difference. Hence, the similarity between two vectors v_i and v_j is Cos θ where θ is the angle between the vectors (Cos θ is determined by inner product).

3-4. Difference amplifier

$$a_{ij}\leftarrow f(a_{ij})$$

The function f that we used in our application for proteomic profiling for cancer cell lines is a composite function of a rational function (of order (−3)) and an anti-trigonometry function.

4. Application -- proteomic profiling for cancer cell lines

Assessment of an individual’s predisposition to drugs is essential to achieve the goal of personalized medicine. This approach is needed to allow clinicians to choose a treatment option that includes the most effective therapeutic agents for a given patient while avoiding ineffective agents and unnecessary side effects. In a previous study, we explored proteomic contributions to drug sensitivity and predicted the drug responses of 60 human cancer cell lines (NCI-60 panel) to 118 anti-cancer agents by proteomic profiling (7). The protein expression levels were measured in untreated cells. As the focus was on predicting the response to therapy and not analyzing the molecular consequences of therapy, this study provides a basis for predicting drug responses based on protein markers in the tumors of untreated patients.

It is especially challenging to predict chemosensitivity in a clinical context because drug responses reflect the properties intrinsic to both the target cells and host metabolism (8). Our analysis was limited to the intrinsic properties of cells in culture by modeling the response of the NCI-60 panel of 60 human cancer cell lines, which includes lines derived from leukemias, melanomas, and carcinomas of ovarian, renal, breast, prostate, colon, lung, and central nervous system (CNS) origin. These cell lines have been screened previously for the activity of 118 anti-cancer drugs whose mechanisms of action are putatively known (9). Some of these drugs are currently in routine clinical use for cancer treatment; others are in clinical trials or the late stages of drug development.

We investigated the feasibility of predicting drug responses using protein expression levels. Both the proteomic profiles (10) and drug activity database (9) were generated by the National Cancer Institute (NCI) and are available at the NCI website (http://discover.nci.nih.gov/datasets.jsp). The protein expression database was generated by proteomic assays with 52-antibody, reverse-phase, protein lysate microarrays in each individual cell line (10). We sought to identify important protein markers for predicting responses to the 118 anti-cancer agents in each cell line. Classifiers of the complete range of drug responses (sensitive, intermediate, and resistant) were developed, one for each drug evaluated. The chemosensitivity classifiers were designed to be independent of the cells’ tissue origin.

This study identified the protein markers for predicting chemosensitivity of the 118 agents in 60 cancer cell lines. The markers can, in principle, provide a basis to devise the optimal combination of therapies directed specifically to eliminate the cancer cells, while minimizing toxicity to the normal cells (11). In addition, the markers can theoretically portrait a unique molecular signature for detection and diagnosis of a cancer (10)–(12). Among the studied drugs, 5-Fluorouracil (5-FU) (NSC 19893) has been included in the treatment combinations for patients with stage III colon cancer (13). Using Random forests in software package R (http://www.r-project.org/), eight protein markers were identified for the prediction of drug response to 5-FU, including CDH1, CDH2, KRT8, ERBB2, MSN, MVP, MAP2K1, and MGMT. All of these proteins, except for KRT8, are involved in the pathogenesis of colon cancer. In order to investigate the feasibility of using these markers to diagnose colon cancer, we performed unsupervised hierarchical clustering on the 60 cancer cell lines by using the expression levels of these eight proteins. There were a total of seven colon cancer cell lines in the NCI-60 panel, including KM-12, HCT-15, HT29, COLO-205, HCC-2998, HCT-116 and SW-620. All of them were aggregated together using the new clustering method, indicating that the identified protein markers provided a basis not only for detection and diagnosis of colon cancer, but also for devising the optimal therapeutic combination targeted specifically to eliminate the cancer cells.

Fig. 1 is the output of the program, in which all colon cancer cell line are clustered in one cluster. It is noteworthy that our previous research (7) was not able to produce such cluster by using the CIMminer (Fig. 2) (http://discover.nci.nih.gov/cimminer/) developed by the National Cancer Institute (14).

Fig. 1.

Fig. 2.

5. Conclusion

The new clustering method (quasi-clique merger and its associated pre-treatment) introduced in this paper is based on a graph theoretical model. This method is designed for searching and merging cliques or clique-like subgraphs in an input dataset. This method is capable to produce more meaningful clusters than many other methods. The application to 60 human cancer cell lines has clearly indicates that the results produced by this method have surpassed those based on previous methods on the same datasets.