Multidisciplinary insight into clonal expansion of HTLV-1-infected cells in adult T-cell leukemia via modeling by deterministic finite automata coupled with high-throughput sequencing

Abstract

Background: Clonal expansion of leukemic cells leads to onset of adult T-cell leukemia (ATL), an aggressive lymphoid malignancy with a very poor prognosis. Infection with human T-cell leukemia virus type-1 (HTLV-1) is the direct cause of ATL onset, and integration of HTLV-1 into the human genome is essential for clonal expansion of leukemic cells. Therefore, monitoring clonal expansion of HTLV-1-infected cells via isolation of integration sites assists in analyzing infected individuals from early infection to the final stage of ATL development. However, because of the complex nature of clonal expansion, the underlying mechanisms have yet to be clarified. Combining computational/mathematical modeling with experimental and clinical data of integration site-based clonality analysis derived from next generation sequencing technologies provides an appropriate strategy to achieve a better understanding of ATL development.

Methods: As a comprehensively interdisciplinary project, this study combined three main aspects: wet laboratory experiments, in silico analysis and empirical modeling.

Results: We analyzed clinical samples from HTLV-1-infected individuals with a broad range of proviral loads using a high-throughput methodology that enables isolation of HTLV-1 integration sites and accurate measurement of the size of infected clones. We categorized clones into four size groups, "very small", "small", "big", and "very big", based on the patterns of clonal growth and observed clone sizes. We propose an empirical formal model based on deterministic finite state automata (DFA) analysis of real clinical samples to illustrate patterns of clonal expansion.

Conclusions: Through the developed model, we have translated biological data of clonal expansion into the formal language of mathematics and represented the observed clonality data with DFA. Our data suggest that combining experimental data (absolute size of clones) with DFA can describe the clonality status of patients. This kind of modeling provides a basic understanding as well as a unique perspective for clarifying the mechanisms of clonal expansion in ATL.

Keywords: Adult T-cell leukemia; Clonal expansion; Deterministic finite state automata (DFA); Human T-cell leukemia virus ype-1; Integration site; Mathematical computational modeling; Next-generation sequencing; State-transition diagram.

Fig. 1

Clonality of samples with various PVLs. The clonal distribution in genomic DNA samples of the analyzed individuals. Each colored segment of a bar represents one unique integration site; the width of the segment is the clone size. Bars with segments of relatively similar sizes are considered to have relatively uniform distribution. The samples are displayed in ascending order based on the size of their largest clones

Fig. 2

Distribution of clone sizes among the analyzed samples. Observed clone sizes were scatter plotted for each sample. The clone sizes are shown on a logarithmic scale. The red lines indicate the three thresholds of 128, 512 and 2048 cells distinguishing the four size groups, VS, S, B and VB

Fig. 3

DFA machines for each sample. State diagrams and transition tables of the samples are represented by seven DFA machines (M1–M7). Asterisks indicate final states

Fig. 4

The main DFA machine representing clonality across all samples. Both the state diagram and transition table for all samples for machine M are shown. q0 is the start state; c1, c2, c3, and c4 correspond to VS, S, B, and VB, respectively. Asterisks indicate final states