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Building better models of cellular pathways is one of the major challenges of systems biology and functional genomics. There is a need for methods to build on established expert knowledge and reconcile it with results of high-throughput…
In recent years, the field of single-cell data analysis has seen a marked advancement in the development of clustering methods. Despite advancements, most of these algorithms still concentrate on analyzing the provided single-cell matrix…
During development, spatio-temporal patterns ranging from checkerboard to engulfing occur with precise proportions of the respective cell fates. Key developmental regulators are intracellular transcriptional interactions and intercellular…
In molecular phylogeny, relationships among organisms are reconstructed using DNA or protein sequences and are displayed as trees. A linear increase in the number of sequences results in an exponential increase of possible trees. Thus,…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters,…
Identification and counting of cells and mitotic figures is a standard task in diagnostic histopathology. Due to the large overall cell count on histological slides and the potential sparse prevalence of some relevant cell types or mitotic…
Epigenetics plays a key role in cellular differentiation and maintaining cell identity, enabling cells to regulate their genetic activity without altering the DNA sequence. Epigenetic regulation occurs within the context of hierarchically…
Integrating heterogeneous datasets across different measurement platforms is a fundamental challenge in many scientific applications. A common example arises in deconvolution problems, such as cell type deconvolution, where one aims to…
The Tree of Life is the graphical structure that represents the evolutionary process from single-cell organisms at the origin of life to the vast biodiversity we see today. Reconstructing this tree from genomic sequences is challenging due…
In this paper we treat some fractal and statistical features of the DNA sequences. First, a fractal record model of DNA sequence is proposed by mapping DNA sequences to integer sequences, followed by R/S analysis of the model and…
Populations of isogenic embryonic stem cells or clonal bacteria often exhibit extensive phenotypic heterogeneity which arises from stochastic intrinsic dynamics of cells. The internal state of the cell can be transmitted epigenetically in…
A problem of substantial interest is to systematically map variation in chromatin structure to gene expression regulation across conditions, environments, or differentiated cell types. We developed and applied a quantitative framework for…
Modelling the substitution of nucleotides along a phylogenetic tree is usually done by a hidden Markov process. This allows to define a distribution of characters at the leaves of the trees and one might be able to obtain polynomial…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
Single-cell RNA sequencing (scRNA-seq) enables the study of cellular diversity at single cell level. It provides a global view of cell-type specification during the onset of biological mechanisms such as developmental processes and human…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
Cellular phenotypic features derived from histopathology images are the basis of pathologic diagnosis and are thought to be related to underlying molecular profiles. Due to overwhelming cell numbers and population heterogeneity, it remains…
Somatic variants can be used as lineage markers for the phylogenetic reconstruction of cancer evolution. Since somatic phylogenetics is complicated by sample heterogeneity, novel specialized tree-building methods are required for cancer…
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have…