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Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways.

ABSTRACT: We study the nonequilibrium phase transitions from the absorbing phase to the active phase for the model of diseases spreading (Susceptible-Infected-Refractory-Susceptible (SIRS)) on a regular one-dimensional lattice. In this model, particles of three species (S, I, and R) on a lattice react as follows: [Formula: see text] with probability [Formula: see text], [Formula: see text] after infection time [Formula: see text] and [Formula: see text] after recovery time [Formula: see text]. In the case of [Formula: see text], this model has been found to have two critical thresholds separating the active phase from absorbing phases. The first critical threshold [Formula: see text] corresponds to a low infection probability and the second critical threshold [Formula: see text] corresponds to a high infection probability. At the first critical threshold [Formula: see text], our Monte Carlo simulations of this model suggest the phase transition to be of directed percolation class (DP). However, at the second critical threshold [Formula: see text] we observe that the system becomes so sensitive to initial values conditions which suggest the phase transition to be a discontinuous transition. We confirm this result using order parameter quasistationary probability distribution and finite-size analysis for this model at [Formula: see text].

SUBMITTER: Saif MA

PROVIDER: S-EPMC10700335 | biostudies-literature | 2023 Dec

REPOSITORIES: biostudies-literature

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Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways.

Saif M Ali MA

Scientific reports 20231206 1

We study the nonequilibrium phase transitions from the absorbing phase to the active phase for the model of diseases spreading (Susceptible-Infected-Refractory-Susceptible (SIRS)) on a regular one-dimensional lattice. In this model, particles of three species (S, I, and R) on a lattice react as follows: [Formula: see text] with probability [Formula: see text], [Formula: see text] after infection time [Formula: see text] and [Formula: see text] after recovery time [Formula: see text]. In the case ...[more]

PMID: 38057341

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Project description:During commitment of a multipotent stem or progenitor cell to a particular lineage, a large number of genes alter their expression in a coordinated manner orchestrated by the gene regulatory network (GRN). The constraints imposed by the GRN govern how cells move in the high-dimensional gene expression state space and can be understood as a dynamical system in which phenotypic cell states (cell types) are attractors that stabilize the cell-type characteristic gene expression pattern against molecular noise. Despite insights from various theoretical models, it remains elusive how multipotent cells, when committing to a specific lineage, exit their attractor and enter a new distinct attractor. Here we show, using single-cell resolution monitoring of transcript patterns by qPCR that commitment of multipotent blood progenitor cells to either the erythroid or the myeloid lineage is preceded by a destabilization of the progenitorsâ?? attractor state and a slowing-down of relaxation of cells from outlier states, indicating a critical state transition (â??tipping pointâ??). The high-dimensionality of the system (many genes) and availability of individual trajectories of a large ensemble of systems (many cells) affords a novel signature for critical transition which can be predicted from theory: Decrease of correlation between cells and concomitant increase of correlation between genes as the cell population approaches the tipping point. Consistent with a destabilizing bifurcation that simultaneously opens access to the erythroid and myeloid attractors, differentiation signal for either lineage caused some cells to commit to the â??wrongâ?? fate; moreover providing conflicting signals resulted in a delayed decision at the bifurcation point that however was ultimately resolved by commitment to one fate. These results suggest that the theoretical framework of â??early-warning signsâ?? and critical transitions can be applied to ensembles of high-dimensional systems, offering a formal tool for analyzing single-cell omics data beyond current descriptive computational pattern recognition. Mouse blood progenitor cells (EML cell line) was exposed to EPO, IL-3/GM-CSF or a mixture of both cytokines and gene expression change was measured in sorted subpopulations wrt Sca1 progenitor surface marker expression. In total, there was 4 conditions (including control), three time points (including d0) and 20 samples (10 samples in duplicates) were analyzed. Two independent experiments were performed for each condition. The untreated progenitor cell population was used as control.

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Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways.

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Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways.

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