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Multistep cell fate transitions with stepwise changes of transcriptional profiles are common to many developmental, regenerative and pathological processes. The multiple intermediate cell lineage states can serve as differentiation checkpoints or branching points for channeling cells to more than one lineages. However, mechanisms underlying these transitions remain elusive. Here, we explored gene regulatory circuits that can generate multiple intermediate cellular states with stepwise modulations of transcription factors. With unbiased searching in the network topology space, we found a motif family containing a large set of networks can give rise to four attractors with the stepwise regulations of transcription factors, which limit the reversibility of three consecutive steps of the lineage transition. We found that there is an enrichment of these motifs in a transcriptional network controlling the early T cell development, and a mathematical model based on this network recapitulates multistep transitions in the early T cell lineage commitment. By calculating the energy landscape and minimum action paths for the T cell model, we quantified the stochastic dynamics of the critical factors in response to the differentiation signal with fluctuations. These results are in good agreement with experimental observations and they suggest the stable characteristics of the intermediate states in the T cell differentiation. These dynamical features may help to direct the cells to correct lineages during development. Our findings provide general design principles for multistep cell linage transitions and new insights into the early T cell development. The network motifs containing a large family of topologies can be useful for analyzing diverse biological systems with multistep transitions.

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HIV-1 is the most common and pathogenic strain of human immunodeficiency virus consisting of many subtypes. To study the difference among HIV-1 subtypes in infection, diagnosis and drug design, it is important to identify HIV-1 subtypes from clinical HIV-1 samples. In this work, we propose an effective numeric representation called Subsequence Natural Vector (SNV) to encode HIV-1 sequences. Using the representation, we introduce an improved linear discriminant analysis method to classify HIV-1 viruses correctly. SNV is based on distribution of nucleotides in HIV-1 viral sequences. It not only computes the number of nucleotides, but also describes the position and variance of nucleotides in viruses. To validate our alignment-free method, 6902 complete genomes and 11,668 pol gene sequences of HIV-1 subtypes were collected from the up-to-date Los Alamos HIV database. SNV outperforms the three popular methods, Kameris, Comet and REGA, with almost 100% Sensitivity and Specificity, also with much less time. Our subtyping algorithm especially works better for circulating recombinant forms (CRFs) consisting of a few sequences. Our approach is also powerful to separate unique recombinant forms (URFs) from other subtypes with 100% Sensitivity and Specificity. Moreover, phylogenetic trees based on SNV representation are constructed using full-length HIV-1 genomes and pol genes respectively, where viruses from the same subtype are clustered together correctly.