arXiv subjects

Breschine Cummins

Publications and source records attributed to Breschine Cummins.

3 recordsLinked to original sources

arXiv2026

Boolean models coarsely sample continuous dynamics of regulatory networks

Boolean models are widely used to characterize the dynamics of gene regulatory networks. However, their coarse state discretization limits their ability to capture complex continuous dynamics and continuous parameter dependencies. In this paper, we present a rigorous mathematical framework that embeds monotone Boolean models into a broader class of multilevel combinatorial models, which in turn embed into the Dynamic Signatures Generated by Regulatory Networks (DSGRN) methodology. We define the DSGRN parameter graph, which encodes the notion of parameter adjacency and is used to map Boolean functions to specific nodes within the DSGRN parameter space. We prove that these multilevel discrete update functions act as a multilevel refinement of monotone Boolean models. We demonstrate that purely Boolean models systematically underestimate network dynamics by missing crucial intermediate behaviors such as higher-order multistability and stable periodic orbits. We show that the DSGRN framework efficiently captures a strictly richer set of dynamics consistent with ordinary differential equations (ODEs), providing a mathematically rigorous and computationally viable bridge between discrete and continuous network modeling.

q-bio.MN↗

arXiv2024

Generalized Measures of Population Synchrony

Synchronized behavior among individuals is a ubiquitous feature of populations. Understanding mechanisms of (de)synchronization demands meaningful, interpretable, computable quantifications of synchrony, relevant to measurements that can be made of dynamic populations. Despite the importance to analyzing and modeling populations, existing notions of synchrony often lack rigorous definitions, may be specialized to a particular experimental system and/or measurement, or may have undesirable properties that limit their utility. We introduce a notion of synchrony for populations of individuals occupying a compact metric space that depends on the Fréchet variance of the distribution of individuals. We establish several fundamental and desirable mathematical properties of this synchrony measure, including continuity and invariance to metric scaling. We establish a general approximation result that controls the disparity between synchrony in the true space and the synchrony observed through a discretization of state space, as may occur when observable states are limited by measurement constraints. We develop efficient algorithms to compute synchrony in a variety of state spaces, including all finite state spaces and empirical distributions on the circle, and provide accessible implementations in an open-source Python module. To demonstrate the usefulness of the synchrony measure in biological applications, we investigate several biologically relevant models of mechanisms that can alter the dynamics of synchrony over time, and reanalyze published data concerning the dynamics of the intraerythrocytic developmental cycles of $\textit{Plasmodium}$ parasites. We anticipate that the rigorous definition of population synchrony and the mathematical and biological results presented here will be broadly useful in analyzing and modeling populations in a variety of contexts.

q-bio.PE↗

arXiv2023

A yeast cell cycle pulse generator model shows consistency with multiple oscillatory and checkpoint mutant datasets

The regulatory mechanisms driving progression of the yeast cell cycle appears to be comprised of an interacting network of transcription factors (TFs), cyclin-dependent kinases (CDK) and ubiquitin ligases. From a systems perspective the controlling regulatory network must produce robust periodic behavior during proliferative phases, but have the capability to halt the cycle when unfavorable conditions trigger a checkpoint arrest. How the individual components of the network contribute to these dynamical phenotypes remains an open question. Here we evaluate the capability of a simplified network model hypothesized to contain key elements of the regulation of cell-cycle progression to reproduce observed transcriptomic behaviors. We match time-series data from both cycling and checkpoint arrested cells to the predictions of a relatively simple cell-cycle network model using an asynchronous multi-level Boolean approach. We show that this single network model, despite its simplicity, is capable of exhibiting dynamical behavior similar to the datasets in most cases, and where it does not, we identified hypotheses that suggest missing components of the network.

math.DS↗