Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0704.0036

A remark on the number of steady states in a multiple futile cycle

Liming Wang·Eduardo D. Sontag
View original source ↗Read source document ↗Export metadata ↓

Abstract

The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In this paper, we study the number of positive steady states of a general multisite phosphorylation-dephosphorylation cycle, and how the number of positive steady states varies by changing the biological parameters. We show analytically that (1) for some parameter ranges, there are at least n+1 (if n is even) or n (if n is odd) steady states; (2) there never are more than 2n-1 steady states (in particular, this implies that for n=2, including single levels of MAPK cascades, there are at most three steady states); (3) for parameters near the standard Michaelis-Menten quasi-steady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard Michaelis-Menten quasi-steady state conditions, there is at most one steady state.

Explore related subjects

q-bio.QMq-bio.MN

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Liming Wang, Eduardo D. Sontag. 2007-07-20. A remark on the number of steady states in a multiple futile cycle. https://arxiv.org/abs/0704.0036

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

KEEP EXPLORING

Related papers

arXiv2026

Learning Epidemic Threshold Equations from Simulation: REEBLRA, an Interpretable Bayesian Classification Framework for Reproduction Numbers

The basic reproduction number, $R_0$, is central to infectious-disease modelling, yet analytic expressions can be difficult to derive for high-dimensional, nonlinear, or structurally complex models. We introduce REEBLRA ($R_0$ Equation Estimation using Bayesian Logistic Regression Algorithm), an interpretable framework that learns explicit surrogate equations for epidemic thresholds from parameter--response data. Rather than directly regressing $R_0$, REEBLRA estimates $\Pr\{R_0(\boldsymbolθ)>c\}$ for parameter vector $\boldsymbolθ$ and threshold $c$. It provides a binary equation for classifying epidemic invasion ($R_0>1$) and successive threshold equations defining ordered brackets that approximate $R_0$, the expected number of secondary infections caused by a typical case in a fully susceptible population. The resulting equations support parameter screening, sensitivity interpretation, threshold classification, and exploratory analysis when analytic derivation is cumbersome. Bayesian logistic regression using standardized polynomial-like features and proper weakly informative priors yields regularized estimates, posterior uncertainty, and finite coefficients under complete or quasi-complete separation. We establish a mechanistic--surrogate concordance principle linking the full fitted-score gradient to the local gradient of $\log R_0$ under explicit regularity and tangency assumptions, allowing conditional interpretation of threshold directions. Across seven analytic-label benchmarks associated with ODE models, including a 15-compartment five-group SIR system, five-fold binary AUC was 0.999--1.000 and ordered-bracket accuracy was 0.951--0.998. REEBLRA complements rather than replaces mechanistic derivations, bridging simulation, machine learning, and reproduction-number analysis. An accompanying Shiny app supports implementation.

q-bio.QM↗
arXiv2026

Can synthetic data reproduce real-world findings in epidemiology? A replication study using adversarial random forests

Synthetic data hold substantial potential to address practical challenges in epidemiology due to restricted data access and privacy concerns. However, many current methods suffer from limited quality, high computational demands, and complexity for non-experts. Furthermore, common evaluation strategies for synthetic data often fail to directly reflect statistical utility and measure privacy risks sufficiently. Against this background, a critical underexplored question is whether synthetic data can reliably reproduce key findings from epidemiological research while preserving privacy. We propose adversarial random forests (ARF) as an efficient and convenient method for synthesizing tabular epidemiological data. To evaluate its performance, we replicated statistical analyses from six epidemiological publications covering blood pressure, anthropometry, myocardial infarction, accelerometry, loneliness, and diabetes, from the German National Cohort (NAKO Gesundheitsstudie), the Bremen STEMI Registry U45 Study, and the Guelph Family Health Study. We further assessed how dataset dimensionality and variable complexity affect the quality of synthetic data, and contextualized ARF's performance by comparison with commonly used tabular data synthesizers in terms of utility, privacy, generalization, and runtime. Across all replicated studies, results on ARF-generated synthetic data consistently aligned with original findings. Even for datasets with relatively low sample size-to-dimensionality ratios, replication outcomes closely matched the original results across descriptive and inferential analyses. Reduced dimensionality and variable complexity further enhanced synthesis quality. ARF demonstrated favourable performance regarding utility, privacy preservation, and generalization relative to other synthesizers and superior computational efficiency.

q-bio.QM↗
arXiv2026

An Open Reliability Atlas of Sensitivity and Failure Modes in the Pulse Physiology Engine

Pulse is an actively maintained open-source adult-physiology simulator, yet its maintainers report no formal sensitivity analysis of its operational inputs. We present the first open reliability atlas across its critical-care envelope: Morris elementary-effects sampling of seven inputs, four severity scenarios, male and female bodies (1,280 simulations). Sensitivity is skewed: three inputs carry a median 93% of each output's total. A four-flag classifier reveals failure modes: two operator-actionable, one sex-stratified. Tidal-volume oscillation (20.6% of runs) is consistent with patient-ventilator dyssynchrony; locking the VC-AC trigger to -2 cmH2O collapses that variability. At FiO2 = 1.0, transient hyperoxia makes 120-second runs underestimate plateau PaO2; 300-second healthy-lung reruns give a median 643 mmHg. Solver divergence was all-male in an input-extreme regime (20/1,280); reducing the male blood-volume baseline to the 4,082 mL floor eliminated it. Runs and flags are released openly, showing users which regions need checking before training on Pulse output.

q-bio.QM↗