Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0802.4279

Molecular Systems with Infinite and Finite Degrees of Freedom. Part II: Deterministic Dynamics and Examples

L. Sbano·M. Kirkilionis
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper we consider deterministic limits of molecular stochastic systems with finite and infinite degrees of freedom. The method to obtain the deterministic vector field is based on the continuum limit of such microscopic systems which has been derived in [11]. With the aid of the theory we finally develop a new approach for molecular systems that describe typical enzyme kinetics or other interactions between molecular machines like genetic elements and smaller communicating molecules. In contrast to the literature on enzyme kinetics the resulting deterministic functional responses are not derived by time-scale arguments on the macroscopic level, but are a result of time scaling transition rates on the discrete microscopic level. We present several examples of common functional responses found in the literature, like Michaelis-Menten and Hill equation. We finally give examples of more complex but typical macro-molecular machinery.

Explore related subjects

q-bio.MN

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

L. Sbano, M. Kirkilionis. 2008-02-28. Molecular Systems with Infinite and Finite Degrees of Freedom. Part II: Deterministic Dynamics and Examples. https://arxiv.org/abs/0802.4279

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

Obstruction of Absolute Concentration Robustness by Conservation Laws in Non-Redundant Zero-One Networks

Absolute concentration robustness (ACR) is a structural property of biochemical reaction networks in which a species attains the same steady-state concentration at every positive steady state, independently of initial conditions and rate constants. Existing detection methods rely on algebraic elimination and typically scale exponentially with network size. We develop a topology-based alternative for non-redundant zero-one networks of stoichiometric dimension at most two, a class that already captures enzyme catalysis, carbon-nanotube transitions, and other elementary biochemical mechanisms. Organizing our analysis around a structural index $s^*$, the number of distinct rows in the stoichiometric matrix, we obtain a complete classification of all such networks admitting non-vacuous ACR for generic rate constants. In dimension one, ACR occurs only for the elementary inflow and outflow module. In dimension two, ACR is possible if and only if $s^*\leq 3$; for $s^*=3$, the admissible networks are precisely those obtained as species refinements of consistent subnetworks of five canonical biochemical prototypes. For $s^*\geq 4$, non-vacuous ACR is impossible for any generic rate assignment.

q-bio.MN↗