Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2203.03461

Path Weight Sampling: Exact Monte Carlo Computation of the Mutual Information between Stochastic Trajectories

Manuel Reinhardt·Gašper Tkačik·Pieter Rein ten Wolde
View original source ↗Read source document ↗Export metadata ↓

Abstract

Most natural and engineered information-processing systems transmit information via signals that vary in time. Computing the information transmission rate or the information encoded in the temporal characteristics of these signals, requires the mutual information between the input and output signals as a function of time, i.e. between the input and output trajectories. Yet, this is notoriously difficult because of the high-dimensional nature of the trajectory space, and all existing techniques require approximations. We present an exact Monte Carlo technique called Path Weight Sampling (PWS) that, for the first time, makes it possible to compute the mutual information between input and output trajectories for any stochastic system that is described by a master equation. The principal idea is to use the master equation to evaluate the exact conditional probability of an individual output trajectory for a given input trajectory, and average this via Monte Carlo sampling in trajectory space to obtain the mutual information. We present three variants of PWS, which all generate the trajectories using the standard stochastic simulation algorithm. While Direct PWS is a brute-force method, Rosenbluth-Rosenbluth PWS exploits the analogy between signal trajectory sampling and polymer sampling, and Thermodynamic Integration PWS is based on a reversible work calculation in trajectory space. PWS also makes it possible to compute the mutual information between input and output trajectories for systems with hidden internal states as well as systems with feedback from output to input. Applying PWS to the bacterial chemotaxis system, consisting of 182 coupled chemical reactions, demonstrates not only that the scheme is highly efficient, but also that the number of receptor clusters is much smaller than hitherto believed, while their size is much larger.

Explore related subjects

q-bio.MNcond-mat.softcs.ITmath.ITphysics.bio-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Manuel Reinhardt, Gašper Tkačik, Pieter Rein ten Wolde. 2023-10-04. Path Weight Sampling: Exact Monte Carlo Computation of the Mutual Information between Stochastic Trajectories. https://doi.org/10.1103/physrevx.13.041017

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

KEEP EXPLORING

Related papers

arXiv2026

Mapping disease-regulatory flux through eQTL-based causal gene networks: a complex-trait framework applied to coronary artery disease

A substantial proportion of inherited susceptibility to common diseases is mediated through tissue-specific regulatory variation. The omnigenic model hypothesizes that much of this risk arises from distant (trans) regulatory effects that are propagated via gene-regulatory networks (GRNs) from numerous regulatory genes onto a relatively small set of core genes. Two major challenges have hindered an empirical assessment of this model. First, transcriptome-wide association studies primarily assess gene expression that is regulated locally (in cis), and thus miss trans-acting effects. Second, trans regulation has so far been examined only in aggregate, without identifying which regulatory genes transmit disease-associated signals to which target genes. Here, we present a framework that decomposes each gene's disease association into a local cis component and a set of trans components attributable to its upstream regulators, propagated along a directed causal GRN. For each gene, we estimate sparse Bayesian expression models and we assess model performance using out-of-sample prediction. Propagating trans signals through the inferred network yields a disease-regulatory flux map: a directed, signed representation that quantifies the contribution of each regulator to the disease association of each target gene. Applying this framework to seven tissues relevant to coronary artery disease, we demonstrate how genetic variation flows through the GRN to affect disease risk. Outgoing regulatory influences from individual genes are directionally heterogeneous, whereas disease-associated genes tend to integrate convergent input from multiple regulators; these convergent targets are enriched for cardiovascular-related biological processes. Consequently, each gene's disease association can be reinterpreted as a detailed allocation of the disease signal among its contributing regulators.

q-bio.MN↗
arXiv2026

Local energetic coupling enhances the expressivity of chemical computation

Living systems compute with chemistry by mapping environmental signals onto specific internal chemical states. Despite recent advances in molecular programming, it remains unclear which physicochemical features control the computational expressivity of chemical systems. Here we inverse-design thermodynamically consistent chemical reaction networks whose steady-state response to an environmental input computes a target nonlinear function. Using implicit differentiation we train the free-energy landscape directly: standard chemical potentials, transition-state energies and thermodynamic drives. Increasingly large networks generated by elementary ligation and cleavage steps fit increasingly complex nonmonotonic polynomial functions, with expressivity scaling logarithmically with network size, predicted primarily by the number of reactions. Training individual energetic parameter classes reveals that internal thermodynamic drives, capable of breaking detailed balance, dominate trainability, with comparable performances achieved only by pairs of parameter classes. These results identify nonequilibrium drive as the most effective single resource for steady-state computational expressivity in chemical reaction networks.

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↗