arXiv subjects

Manuel Reinhardt

Publications and source records attributed to Manuel Reinhardt.

4 recordsLinked to original sources

arXiv2025

Mutual Information Rate -- Linear Noise Approximation and Exact Computation

Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input and output signals, and enables the quantification of information flow in dynamic systems. A common approach for estimating the mutual information rate is the Gaussian approximation which assumes that the input and output trajectories follow Gaussian statistics. However, this method is limited to linear systems, and its accuracy in nonlinear or discrete systems remains unclear. In this work, we assess the accuracy of the Gaussian approximation for non-Gaussian systems by leveraging Path Weight Sampling (PWS), a recent technique for exactly computing the mutual information rate. In two case studies, we examine the limitations of the Gaussian approximation. First, we focus on discrete linear systems and demonstrate that, even when the system's statistics are nearly Gaussian, the Gaussian approximation fails to accurately estimate the mutual information rate. Second, we explore a continuous diffusive system with a nonlinear transfer function, revealing significant deviations between the Gaussian approximation and the exact mutual information rate as nonlinearity increases. Our results provide a quantitative evaluation of the Gaussian approximation's performance across different stochastic models and highlight when more computationally intensive methods, such as PWS, are necessary.

q-bio.MN↗

arXiv2025

ML-PWS: Estimating the Mutual Information Between Experimental Time Series Using Neural Networks

The ability to quantify information transmission is crucial for the analysis and design of both natural and engineered systems. For systems driven by time-varying signals, the fundamental measure is the information transmission rate. However, due to the high dimensionality of signal trajectory space, this rate cannot be obtained directly from time-series data without approximations. Path Weight Sampling (PWS) is a computational technique that enables the exact calculation of the information rate for any stochastic model, raising the question of how this rate can be determined from time-series data in the absence of a prior model. Here, we present a method that combines machine learning (ML) with PWS: a generative model is learned from time-series data, to which PWS is applied to yield a rigorous lower bound on the information rate. We demonstrate the accuracy of this technique, called ML-PWS, by comparing its results on synthetic time-series data generated from several non-linear models against ground-truth results obtained by applying PWS directly to the same models. We illustrate the utility of ML-PWS by applying it to neuronal time-series data.

physics.bio-ph↗

arXiv2025

State- versus Reaction-Based Information Processing in Biochemical Networks

Trajectory mutual information is frequently used to quantify information transfer in biochemical systems. Tractable solutions of the trajectory mutual information can be obtained via the widely used Linear-Noise Approximation (LNA) using Gaussian channel theory. This approach is expected to be accurate for sufficiently large systems. However, recent observations show that there are cases, where the mutual information obtained this way differs qualitatively from results derived using an exact Markov jump process formalism, and that the differences remain even in the large copy number regime. In this letter, we show that these differences can be explained by introducing the notion of reaction- versus state-based descriptions of trajectories. In chemical systems, the information is encoded in the sequence of reaction events, and the reaction-based trajectories of Markov jump processes capture this information. We show that within the Gaussian formalism, trajectories can be defined either based on individual reaction channels, or on a state-based level, where different reaction channels are summarised into a single noise term. While both definitions agree in terms of copy number fluctuations, state-based trajectories contain in general less information than reaction-based trajectories. The commonly used Gaussian mutual information via the Linear-Noise Approximation is consistent with a state-based trajectory notion, which causes a systematic loss of information independent of system size. We show that an alternative, reaction-based variant of the Gaussian mutual information prevents this loss of information. We illustrate the consequences of different trajectory descriptions for two common cellular reaction motifs and discuss their connection with Berg-Purcell and Maximum-Likelihood sensing.

q-bio.MN↗

arXiv2022

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

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.

q-bio.MN↗