arXiv subjects

Kyu Hyong Park

Publications and source records attributed to Kyu Hyong Park.

3 recordsLinked to original sources

arXiv2026

Relating biomarkers and phenotypes using dynamical trap spaces

Connecting the dynamics of biomolecular networks to experimentally measurable cell phenotypes remains a central challenge in systems biology. Here we introduce a model-based definition of phenotype as a partial steady state that is committed to a certain dynamical outcome while otherwise being minimally constrained. We focus on Boolean models and define \emph{dynamical phenotypes} as complete trap spaces that maximally specify a chosen set of phenotype-determining nodes that correspond to biomarkers while keeping external inputs unconstrained. We show that dynamical phenotypes can be efficiently identified without full attractor enumeration. Using four published models, including a 70-node Boolean model of T cell differentiation, we show that dynamical phenotypes recover known cell types and activation states, and indicate the environmental conditions ensuring their existence. We also propose a method to identify informative phenotype-determining nodes based on the canalization of the Boolean functions. This method reveals biologically relevant cell state information that is complementary to the phenotypes manually defined by model creators and is validated by two attractor-based approaches. Our results demonstrate that dynamical phenotypes provide a scalable framework for linking model structure, external inputs, and phenotypic outcomes, and offer a principled tool for model-guided biomarker selection.

q-bio.MN↗

arXiv2025

On the number of asynchronous attractors in AND-NOT Boolean networks

Boolean Networks (BNs) describe the time evolution of binary states using logic functions on the nodes of a network. They are fundamental models for complex discrete dynamical systems, with applications in various areas of science and engineering, and especially in systems biology. A key aspect of the dynamical behavior of BNs is the number of attractors, which determines the diversity of long-term system trajectories. Due to the noisy nature and incomplete characterization of biological systems, a stochastic asynchronous update scheme is often more appropriate than the deterministic synchronous one. AND-NOT BNs, whose logic functions are the conjunction of literals, are an important subclass of BNs because of their structural simplicity and their usefulness in analyzing biological systems for which the only information available is a collection of interactions among components. In this paper, we establish new theoretical results regarding asynchronous attractors in AND-NOT BNs. We derive two new upper bounds for the number of asynchronous attractors in an AND-NOT BN based on structural properties (strong even cycles and dominating sets, respectively) of the AND-NOT BN. These findings contribute to a more comprehensive understanding of asynchronous dynamics in AND-NOT BNs, with implications for attractor enumeration and counting, as well as for network design and control.

cs.DM↗

arXiv2024

An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks?

Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular in systems biology due to their ability to model long-term biological phenotypes within a qualitative, predictive framework. Boolean networks model phenotypes as attractors, which are closely linked to minimal trap spaces (inescapable hypercubes in the system's state space). In biological applications, attractors and minimal trap spaces are typically in one-to-one correspondence. However, this correspondence is not guaranteed: motif-avoidant attractors (MAAs) that lie outside minimal trap spaces are possible. MAAs are rare and (despite recent efforts) poorly understood. Here we summarize the current state of knowledge regarding MAAs and present several novel observations regarding their response to node deletion reductions and linear extensions of edges. We conduct large-scale computational studies on an ensemble of 14,000 models derived from published Boolean models of biological systems, and more than 100 million Random Boolean Networks. Our findings quantify the rarity of MAAs (in particular, we found no MAAs in the biological models), but highlight the role of network reduction in introducing MAAs into the dynamics. We also show that MAAs are fragile to linear extensions: in sparse networks, even a single linear node can disrupt virtually all MAAs. Motivated by this observation, we improve the upper bound on the number of delays needed to disrupt a motif-avoidant attractor.

q-bio.MN↗