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A novel construction of genome space with biological geometry.

ABSTRACT: A genome space is a moduli space of genomes. In this space, each point corresponds to a genome. The natural distance between two points in the genome space reflects the biological distance between these two genomes. Currently, there is no method to represent genomes by a point in a space without losing biological information. Here, we propose a new graphical representation for DNA sequences. The breakthrough of the subject is that we can construct the moment vectors from DNA sequences using this new graphical method and prove that the correspondence between moment vectors and DNA sequences is one-to-one. Using these moment vectors, we have constructed a novel genome space as a subspace in R(N). It allows us to show that the SARS-CoV is most closely related to a coronavirus from the palm civet not from a bird as initially suspected, and the newly discovered human coronavirus HCoV-HKU1 is more closely related to SARS than to any other known member of group 2 coronavirus. Furthermore, we reconstructed the phylogenetic tree for 34 lentiviruses (including human immunodeficiency virus) based on their whole genome sequences. Our genome space will provide a new powerful tool for analyzing the classification of genomes and their phylogenetic relationships.

SUBMITTER: Yu C

PROVIDER: S-EPMC2885272 | biostudies-literature | 2010 Jun

REPOSITORIES: biostudies-literature

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A novel construction of genome space with biological geometry.

Yu Chenglong C Liang Qian Q Yin Changchuan C He Rong L RL Yau Stephen S-T SS

DNA research : an international journal for rapid publication of reports on genes and genomes 20100401 3

A genome space is a moduli space of genomes. In this space, each point corresponds to a genome. The natural distance between two points in the genome space reflects the biological distance between these two genomes. Currently, there is no method to represent genomes by a point in a space without losing biological information. Here, we propose a new graphical representation for DNA sequences. The breakthrough of the subject is that we can construct the moment vectors from DNA sequences using this ...[more]

PMID: 20360268

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Project description:There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks.

Project description:PurposeRobust and reliable reconstruction of images from noisy and incomplete projection data holds significant potential for proliferation of cost-effective medical imaging technologies. Since conventional reconstruction techniques can generate severe artifacts in the recovered images, a notable line of research constitutes development of appropriate algorithms to compensate for missing data and to reduce noise. In the present work, we investigate the effectiveness of state-of-the-art methodologies developed for image inpainting and noise reduction to preserve the quality of reconstructed images from undersampled PET data. We aimed to assess and ascertain whether missing data recovery is best performed in the projection space prior to reconstruction or adjoined with the reconstruction step in image space.MethodsDifferent strategies for data recovery were investigated using realistic patient derived phantoms (brain and abdomen) in PET scanners with partial geometry (small and large gap structures). Specifically, gap filling strategies in projection space were compared with reconstruction based compensation in image space. The methods used for filling the gap structure in sinogram PET data include partial differential equation based techniques (PDE), total variation (TV) regularization, discrete cosine transform(DCT)-based penalized regression, and dictionary learning based inpainting (DLI). For compensation in image space, compressed sensing based image reconstruction methods were applied. These include the preconditioned alternating projection (PAPA) algorithm with first and higher order total variation (HOTV) regularization as well as dictionary learning based compressed sensing (DLCS). We additionally investigated the performance of the methods for recovery of missing data in the presence of simulated lesion. The impact of different noise levels in the undersampled sinograms on performance of the approaches were also evaluated.ResultsIn our first study (brain imaging), DLI was shown to outperform other methods for small gap structure in terms of root mean square error (RMSE) and structural similarity (SSIM), though having relatively high computational cost. For large gap structure, HOTV-PAPA produces better results. In the second study (abdomen imaging), again the best performance belonged to DLI for small gap, and HOTV-PAPA for large gap. In our experiments for lesion simulation on patient brain phantom data, the best performance in term of contrast recovery coefficient (CRC) for small gap simulation belonged to DLI, while in the case of large gap simulation, HOTV-PAPA outperformed others. Our evaluation of the impact of noise on performance of approaches indicated that in case of low and medium noise levels, DLI still produces favorable results among inpainting approaches. However, for high noise levels, the performance of PDE4 (variant of PDE) and DLI are very competitive.ConclusionsOur results showed that estimation of missing data in projection space as a preprocessing step before reconstruction can improve the quality of recovered images especially for small gap structures. However, when large portions of data are missing, compressed sensing techniques adjoined with the reconstruction step in image space were the best strategy.

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A novel construction of genome space with biological geometry.

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A novel construction of genome space with biological geometry.

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