Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1206.2311

Quasi-potential landscape in complex multi-stable systems

Joseph Xu Zhou·M. D. S. Aliyu·Erik Aurell·Sui Huang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Developmental dynamics of multicellular organism is a process that takes place in a multi-stable system in which each attractor state represents a cell type and attractor transitions correspond to cell differentiation paths. This new understanding has revived the idea of a quasi-potential landscape, first proposed by Waddington as a metaphor. To describe development one is interested in the "relative stabilities" of N attractors (N>2). Existing theories of state transition between local minima on some potential landscape deal with the exit in the transition between a pair attractor but do not offer the notion of a global potential function that relate more than two attractors to each other. Several ad hoc methods have been used in systems biology to compute a landscape in non-gradient systems, such as gene regulatory networks. Here we present an overview of the currently available methods, discuss their limitations and propose a new decomposition of vector fields that permit the computation of a quasi-potential function that is equivalent to the Freidlin-Wentzell potential but is not limited to two attractors. Several examples of decomposition are given and the significance of such a quasi-potential function is discussed.

Explore related subjects

q-bio.MNcond-mat.other

Keep this discovery

BibTeXRIS

Joseph Xu Zhou, M. D. S. Aliyu, Erik Aurell, Sui Huang. 2012-06-11. Quasi-potential landscape in complex multi-stable systems. https://arxiv.org/abs/1206.2311

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Thermodynamic and Statistical Signatures of Modality Changes in Concentration Distributions Driven by Stochastic Switching Between Two Activity States

Stochastic switching between gene expression states, coupled with production and degradation dynamics, governs the accumulation of mRNA and proteins in cells. The concentrations of these accumulated entities dictate the phenotypic distribution of genetically identical cells. The underlying accumulation dynamics are well-captured by a two-state promoter switching model, with statistical and thermodynamic properties quantified via the Fano factor and entropy production rates. However, how these measures correlate with concentration distributions and their shifts under varying kinetic parameters remains largely unexplored. To this end, we use chemical master equations to study a generalized model of mRNA accumulation dynamics in the presence of stochastic switching between two activity states and state-dependent production and degradation rates. We derive exact expressions for the steady-state probability distribution and analytically compute the mean concentration, Fano factor, and entropy production rate (EPR). Simplifying these expressions, we identify contributions arising from stochastic switching rates and relaxation dynamics toward equilibrium in each activity state. Next, using our theoretical results, we characterize the variation in the Fano factor and EPR as a function of mean expression during modality changes of the distributions mediated by the variation of switching rates. We also identify the conditions in kinetic parameters that achieve the highest Fano factor and entropy production rates. Our findings establish a generalized framework for examining stochastic accumulation dynamics, clarifying how kinetic parameters dictate molecular distributions, noise, and dissipation. These insights extend readily to broader contexts coupling stochastic switching with accumulation, including protein burst dynamics, phenotype-switching-mediated drug intake, and queuing theory.

q-bio.MN↗
arXiv2026

Are You Learning Biological Signal or Shortcuts? Auditing and Mitigating Bias in Protein-Protein Interaction Datasets

Protein-protein interaction (PPI) databases do not faithfully reflect biological realities. Instead, they are influenced by study and technical biases that distort certain protein and interaction attributes. Machine learning models can exploit these as learning shortcuts if the negative dataset is not constructed with care. So far, the shortcuts introduced during PPI dataset construction have only been examined in isolation. Here, we systematically characterize both reported and, to our knowledge, previously unreported biases in PPI datasets that lead machine learning models to learn shortcuts instead of biological signal. We analyze HIPPIE, IntAct, and STRING, dedicated PPI databases, as well as two datasets derived from 3D-structural information in the Protein Data Bank (PDB). We show that random data splitting introduces strong topological shortcuts. When train-test protein overlap is removed, the resulting datasets still retain usable shortcuts stemming from self-interactions, taxonomic identity, and functional relatedness, whose prevalence interestingly depends on the data source. We further show that sampling negatives from a set of high-confidence non-interactors, an intuitively appealing choice, can amplify the shortcut stemming from functional relatedness. To detect and mitigate these biases, we provide an open Nextflow pipeline that combines similarity-aware, data-loss-minimizing dataset splitting with bias-minimizing negative sampling, both formulated as integer linear programs. Its key concept of quantifying biases to minimize them through optimization-based negative sampling can, in principle, be extended to any machine learning problem where the pool of negative candidates is much larger than the positives and is thus of interest also beyond PPI prediction.

q-bio.MN↗
arXiv2026

Orchestra: Corroboration-Based Regulatory Candidate Discovery via Composed Bioinformatics MCP Agents

Orchestra composes two independently built bioinformatics MCP servers -- RegNetAgents, which infers gene regulatory network topology from ARACNe networks, and CASCADE, which supplies four independent evidence sources (LINCS knockdown, DepMap essentiality, super-enhancer status, DoRothEA transcription-factor confidence) -- into one multi-agent workflow exposed via the Model Context Protocol. Its central architectural claim is that requiring RegNetAgents' topology evidence and CASCADE's experimental evidence to agree on a candidate regulator yields a more trustworthy candidate than either alone -- not previously tested directly, since RegNetAgents' own validation asked only whether its candidate lists beat chance. We test this on the TCGA tumor-acquired regulator tier (regulators in a gene's tumor ARACNe network but absent from the GREmLN population-averaged baseline), selecting candidates by ARACNe mutual-information (MI) edge weight. On RegNetAgents' published BRCA/COAD focal-gene panel plus matched negative controls, agreement among at least 2 of the 4 CASCADE sources predicts OncoKB cancer-gene status among focal genes (odds ratio 2.89, Benjamini-Hochberg-adjusted p=0.0166) but not among negative controls (p=0.0721); a single source is not diagnostic for either group. The pattern replicates and strengthens in a third cancer type, STAD, on a separately constructed panel (odds ratio 5.82), and against an independently curated ground truth (the Sanger COSMIC Cancer Gene Census). MI edge weight is the strongest single predictor overall (p=0.0003); a logistic-regression likelihood-ratio test confirms corroboration adds value beyond it in both panels (p=0.0234; p=0.0001). Every experiment invokes Orchestra's real agentic entry point.

q-bio.MN↗