arXiv subjects

Age Tjalma

Publications and source records attributed to Age Tjalma.

3 recordsLinked to original sources

arXiv2026

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↗

arXiv2025

Intuitive dissection of the Gaussian information bottleneck method with an application to optimal prediction

Efficient signal representation is essential for the functioning of living and artificial systems operating under resource constraints. A widely recognized framework for deriving such representations is the information bottleneck method, which yields the optimal strategy for encoding a random variable, such as the signal, in a way that preserves maximal information about a functionally relevant variable, subject to an explicit constraint on the amount of information encoded. While in its general formulation the method is numerical, it admits an analytical solution in an important special case where the variables involved are jointly Gaussian. In this setting, the solution predicts discrete transitions in the dimensionality of the optimal representation as the encoding capacity is increased. Although these signature transitions, along with other features of the optimal strategy, can be derived from a constrained optimization problem, a clear and intuitive understanding of their emergence is still lacking. In our work, we advance our understanding of the Gaussian information bottleneck method through multiple mutually enriching perspectives, including geometric and information-theoretic ones. These perspectives offer novel intuition about the set of optimal encoding directions, the nature of the critical points where the optimal number of encoding components changes, and about the way the optimal strategy navigates between these critical points. We then apply our treatment of the method to a previously studied signal prediction problem, obtaining new insights on how different features of the signal are encoded across multiple components to enable optimal prediction of future signals. Altogether, our work deepens the foundational understanding of the information bottleneck method in the Gaussian setting, motivating the exploration of analogous perspectives in broader, non-Gaussian contexts.

q-bio.MN↗

arXiv2023

Predicting a noisy signal: the costs and benefits of time averaging as a noise mitigation strategy

One major challenge for living cells is the measurement and prediction of signals corrupted by noise. In general, cells need to make decisions based on their compressed representation of noisy, time-varying signals. Strategies for signal noise mitigation are often tackled using Wiener filtering theory, but this theory cannot account for systems that have limited resources and hence must compress the signal. To study how accurately linear systems can predict noisy, time-varying signals in the presence of a compression constraint, we extend the information bottleneck method. We show that the optimal integration kernel reduces to the Wiener filter in the absence of a compression constraint. This kernel combines a delta function at short times and an exponential function that decays on a timescale that sets the integration time. Moreover, there exists an optimal integration time, which arises from a trade-off between time averaging signal noise and dynamical error. As the level of compression is increased, time averaging becomes harder, and as a result the optimal integration time decreases and the delta peak increases. We compare the behaviour of the optimal system with that of a canonical motif in cell signalling, the push-pull network, finding that the system reacts to signal noise and compression in a similar way.

q-bio.QM↗