Cancer is a significant global health concern, especially for children. Worldwide, it remains one of the leading causes of death, with leukemia being a major contributor to cancer-related fatalities among children and adolescents. Among the various types of leukemia, acute lymphoblastic leukemia (ALL) is the most prevalent in children. Specifically, B-cell acute lymphoblastic leukemia (B-ALL) accounts for approximately 85% of childhood ALL cases.While numerous studies have attempted to unravel the complexities of this disease and propose potential treatments, these approaches have shown limitations and often yielded mixed results. In recent years, mathematical models have emerged as valuable tools in understanding cancer, particularly through the development of logical network models that explore cancer cell behavior and their interactions with the microenvironment.In this work, we construct a discrete logical network model to investigate gene regulation in B lymphocytes, focusing on key genes implicated in the development of pediatric acute lymphoblastic leukemia. The model dynamics are consistent with known activation patterns of these genes in malignant cells, providing a robust framework for studying pediatric B-cell acute lymphoblastic leukemia.

We prove that if $G$ is a graph without 3-cycles and 4-cycles, then the discrete cubical homology of $G$ is trivial in dimension $d$ for all $d\ge 2$. We also construct a sequence $\{G_d\}$ of graphs such that this homology is nontrivial in dimension $d$ for $d\ge 1$. Finally, we show that the discrete cubical homology induced by certain coverings of $G$ equals the ordinary singular homology of a $2$-dimensional cell complex built from $G$, although in general it differs from the discrete cubical homology of the graph as a whole.

BACKGROUND: Macrophages cover a major role in the immune system, being the most plastic cell yielding several key immune functions. METHODS: Here we derived a minimalistic gene regulatory network model for the differentiation of macrophages into the two phenotypes M1 (pro-) and M2 (anti-inflammatory). RESULTS: To test the model, we simulated a large number of such networks as in a statistical ensemble. In other words, to enable the inter-cellular crosstalk required to obtain an immune activation in which the macrophage plays its role, the simulated networks are not taken in isolation but combined with other cellular agents, thus setting up a discrete minimalistic model of the immune system at the microscopic/intracellular (i.e., genetic regulation) and mesoscopic/intercellular scale. CONCLUSIONS: We show that within the mesoscopic level description of cellular interaction and cooperation, the gene regulatory logic is coherent and contributes to the overall dynamics of the ensembles that shows, statistically, the expected behaviour.

Differentiation of CD4+ T cells into effector or regulatory phenotypes is tightly controlled by the cytokine milieu, complex intracellular signaling networks and numerous transcriptional regulators. We combined experimental approaches and computational modeling to investigate the mechanisms controlling differentiation and plasticity of CD4+ T cells in the gut of mice. Our computational model encompasses the major intracellular pathways involved in CD4+ T cell differentiation into T helper 1 (Th1), Th2, Th17 and induced regulatory T cells (iTreg). Our modeling efforts predicted a critical role for peroxisome proliferator-activated receptor gamma (PPARγ) in modulating plasticity between Th17 and iTreg cells. PPARγ regulates differentiation, activation and cytokine production, thereby controlling the induction of effector and regulatory responses, and is a promising therapeutic target for dysregulated immune responses and inflammation. Our modeling efforts predict that following PPARγ activation, Th17 cells undergo phenotype switch and become iTreg cells. This prediction was validated by results of adoptive transfer studies showing an increase of colonic iTreg and a decrease of Th17 cells in the gut mucosa of mice with colitis following pharmacological activation of PPARγ. Deletion of PPARγ in CD4+ T cells impaired mucosal iTreg and enhanced colitogenic Th17 responses in mice with CD4+ T cell-induced colitis. Thus, for the first time we provide novel molecular evidence in vivo demonstrating that PPARγ in addition to regulating CD4+ T cell differentiation also plays a major role controlling Th17 and iTreg plasticity in the gut mucosa.

MOTIVATION: An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. RESULTS: This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Polynomial dynamical systems (PDSs) have been used successfully as a framework for the reconstruction, or reverse engineering of biochemical networks from experimental data. Within this modeling space, a particular PDS is chosen by way of a Gröbner basis, and using different monomial orders may result in different polynomial models. In this paper, we present a systematic method for selecting most likely polynomial models for a given data set, using the Gröbner fan of the ideal of the input data. We apply the method to reverse engineer two biochemical networks, a Boolean model of lactose metabolism in E. coli and a protein signal transduction network in S. cerevisiae and compare our results to those from two published network-reconstruction methods.

MOTIVATION: Epstein-Barr virus (EBV) infects greater than 90% of humans benignly for life but can be associated with tumors. It is a uniquely human pathogen that is amenable to quantitative analysis; however, there is no applicable animal model. Computer models may provide a virtual environment to perform experiments not possible in human volunteers. RESULTS: We report the application of a relatively simple stochastic cellular automaton (C-ImmSim) to the modeling of EBV infection. Infected B-cell dynamics in the acute and chronic phases of infection correspond well to clinical data including the establishment of a long term persistent infection (up to 10 years) that is absolutely dependent on access of latently infected B cells to the peripheral pool where they are not subject to immunosurveillance. In the absence of this compartment the infection is cleared. AVAILABILITY: The latest version 6 of C-ImmSim is available under the GNU General Public License and is downloadable from www.iac.cnr.it/~filippo/cimmsim.html

Let f1,…,fn be homogeneous polynomials generating a generic ideal I in the ring of polynomials in n variables over an infinite field. Moreno-Socias conjectured that for the graded reverse lexicographic term ordering, the initial ideal in(I) is a weakly reverse lexicographic ideal. This paper contains a new proof of Moreno-Socias' conjecture for the case n = 2.