arXiv subjects

Pieter Rein ten Wolde

Publications and source records attributed to Pieter Rein ten Wolde.

At least 19 recordsLinked to original sources

arXiv2026

Navigation driven by bidirectional information transmission between sensing and actuation

A wide variety of biological functions are driven by feedback between sensing and actuation. A paradigmatic example is cellular navigation. During navigation, the sensory system maps the environmental input signal onto a sensory output, which then drives an actuation response, thereby changing the future sensory input. How the accuracy of this bidirectional information transmission controls navigation is not currently understood. Here, we study how information controls navigation by analytically solving two generic models that describe two major classes of biological navigators: spatial- and temporal-sensing cells. We find that, in the linear-response regime of shallow gradients, navigation performance is fully determined by bidirectional information transmission alone, as quantified by feedforward and feedback transfer entropies. Elementary system parameters affect navigation performance only through their effect on these information flows. We call these relations Behavioral Equations of State (BESTs): equalities that map information to function in a system-independent way. BESTs predict an experimentally testable data collapse for the performance of navigators with different sensing and actuation parameters. We test the validity of our theory by performing stochastic simulations of chemotaxis of the bacterium Escherichia coli, computing the relevant transfer entropies exactly with the TE-PWS algorithm. The observed performance obeys the BEST without any fitting or scaling parameters. Thus, our theory identifies bidirectional information transmission between sensing and actuation as an organizing principle for navigation.

physics.bio-ph↗

arXiv2026

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↗

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

Bit reset protocols that obey activity-constrained speed limits do not minimize work for a given speed

The goal of thermodynamic optimal control theory is to find protocols to change the state of a system from an initial to a desired final distribution, within a finite time, with the least possible expenditure of work. The optimal protocol is closely linked to the intrinsic dynamics of the system at hand. The fact that these dynamics can vary widely has made a general solution elusive. Recent years have seen great progress by recasting the question in terms of a quantity called total activity, i.e. the average number of jumps between states of the system, rather than the time that the operation is allowed to take. This perspective has allowed for general expressions for the minimal work as a function of the total activity, and the minimal total activity required for a given work. The expression for minimal total activity can be recast as an apparent minimal operation time or speed limit. However, it is unclear whether protocols optimized under a constrained activity actually require the lowest work input for a given operation time. In the context of bit reset, we show that directly minimizing work for a given operation time leads to protocols that require significantly less work to perform the operation than the activity-constrained protocol of the same duration. We show how the resulting protocols differ. One reason for the difference is the fact that the activity rate is not constant over the course of the protocol: it depends on both the transition rates and the distribution of the bit, both of which change during the copy operation. In the limit of long protocol duration, we find an expression for the difference between the resulting minimal work for both optimization schemes, for a general class of dynamics. The time-constrained approach always outperforms the activity-constrained approach for a given constrained duration, and the difference in work can be arbitrarily large.

cond-mat.stat-mech↗

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

Exact computation of Transfer Entropy with Path Weight Sampling

The ability to quantify the directional flow of information is vital to understanding natural systems and designing engineered information-processing systems. A widely used measure to quantify this information flow is the transfer entropy. However, until now, this quantity could only be obtained in dynamical models using approximations that are typically uncontrolled. Here we introduce a computational algorithm called Transfer Entropy-Path Weight Sampling (TE-PWS), which makes it possible, for the first time, to quantify the transfer entropy and its variants exactly for any stochastic model, including those with multiple hidden variables, nonlinearity, transient conditions, and feedback. By leveraging techniques from polymer and path sampling, TE-PWS efficiently computes the transfer entropy as a Monte-Carlo average over signal trajectory space. We use our exact technique to demonstrate that commonly used approximate methods to compute transfer entropies incur large systematic errors and high computational costs. As an application, we use TE-PWS in linear and nonlinear systems to reveal how transfer entropy can overcome naive applications of the data processing inequality in the presence of feedback.

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↗

arXiv2025

Exploiting bias in optimal finite-time copying protocols

We study a finite-time cyclic copy protocol that creates persisting correlations between a memory and a data bit. The average work to copy the two states of the data bit consists of the mutual information created between the memory and data bit after copying, a cost due to the difference between the initial and final states of the memory bit, and a finite-time cost. At low copy speeds, the optimal initial distribution of the memory bit matches the bias in the expected outcome, set by the bias in the data bit and the copying accuracies. However, if both states of the data are copied with the same accuracy, then in the high-speed regime copying the unlikely data bit state becomes prohibitively costly with a biased memory; the optimal initial distribution is then pushed towards 50:50. Copying with unequal accuracies, at fixed copy-generated mutual information, yields an opposite yet more effective strategy. Here, the initial memory distribution becomes increasingly biased as the copy speed increases, drastically lowering the work and raising the maximum speed. This strategy is so effective that it induces a symmetry breaking transition for an unbiased data bit.

cond-mat.stat-mech↗

arXiv2024

Stable developmental patterns of gene expression without morphogen gradients

Gene expression patterns (GEPs) are established by cross-regulating target genes that interpret morphogen gradients. However, as development progresses, morphogen activity is reduced, leaving the emergent GEP without stabilizing positional cues. The GEP then can be deteriorated by the intrinsically noisy biochemical processes acting at the cellular level. However, the established GEPs remain spatio-temporally stable in many biological systems. Here we combine spatial-stochastic simulations with an enhanced sampling method (Non-Stationary Forward Flux Sampling) and a recently developed stability theory to address how spatiotemporal integrity of a GEP is maintained without morphogen gradients. Using a minimal embryo model consisting of spatially coupled biochemical reactor volumes, we study a stripe pattern in which weak cross-repression between nearest neighbor domians alternates with strong repression between next-nearest neighbor domains, inspired by the gap gene system in the Drosophila embryo. We find that fine-tuning of the weak repressive interactions to an optimal level increases temporal stability of GEPs by orders of magnitude, providing stability over developmentally relevant times, without morphogen gradients. The numerically determined optimal parameter regime closely agrees with the predictions of the stability theory. By analizing the dynamics of GEP asymmetry factors, we trace back the pattern stability enhancement to the emergence of a metastable basin and restoring forces that counteract pattern perturbations. The origin of these forces is further explained by the effective model, describing the emergent deterministic dynamics of the system. Altogether, we show that metastable attractors can emerge as a property of stochastic GEPs even without system-wide positional cues, provided that the gene regulatory interactions shaping the pattern are optimally tuned.

physics.bio-ph↗

arXiv2024

Predicting concentration changes via discrete sampling

To successfully navigate chemical gradients, microorganisms need to predict how the ligand concentration changes in space. Due to their limited size, they do not take a spatial derivative over their body length but rather a temporal derivative, comparing the current signal with that in the recent past, over the so-called adaptation time. This strategy is pervasive in biology, but it remains unclear what determines the accuracy of such measurements. Using a generalized version of the previously established sampling framework, we investigate how resource limitations and the statistics of the input signal set the optimal design of a well-characterized network that measures temporal concentration changes: the Escherichia coli chemotaxis network. Our results show how an optimal adaptation time arises from the trade-off between the sampling error, caused by the stochastic nature of the network, and the dynamical error, caused by uninformative fluctuations in the input. A larger resource availability reduces the sampling error, which allows for a smaller adaptation time, thereby simultaneously decreasing the dynamical error. Similarly, we find that the optimal adaptation time scales inversely with the gradient steepness, because steeper gradients lift the signal above the noise and reduce the sampling error. These findings shed light on the principles that govern the optimal design of the E. coli chemotaxis network specifically, and any system measuring temporal changes more broadly.

q-bio.MN↗

arXiv2023

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↗

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↗

arXiv2023

Synchronous replication initiation of multiple origins

Initiating replication synchronously at multiple origins of replication allows the bacterium Escherichia coli to divide even faster than the time it takes to replicate the entire chromosome in nutrient-rich environments. What mechanisms give rise to synchronous replication initiation remains however poorly understood. Via mathematical modelling, we identify four distinct synchronization regimes depending on two quantities: the duration of the so-called licensing period during which the initiation potential in the cell remains high after the first origin has fired and the duration of the blocking period during which already initiated origins remain blocked. For synchronous replication initiation, the licensing period must be long enough such that all origins can be initiated, but shorter than the blocking period to prevent reinitiation of origins that have already fired. We find an analytical expression for the degree of synchrony as a function of the duration of the licensing period, which we confirm by simulations. Our model reveals that the delay between the firing of the first and the last origin scales with the coefficient of variation (CV) of the initiation volume. Matching these to the values measured experimentally shows that the firing rate must rise with the cell volume with an effective Hill coefficient that is at least 20; the probability that all origins fire before the blocking period is over is then at least 92%. Our analysis thus reveals that the low CV of the initiation volume is a consequence of synchronous replication initiation. Finally, we show that the previously presented molecular model for the regulation of replication initiation in E. coli can give rise to synchronous replication initiation for biologically realistic parameters.

physics.bio-ph↗

arXiv2023

Constriction of actin rings by passive crosslinkers

In many organisms, cell division is driven by the constriction of a cytokinetic ring, which consists of actin filaments and crosslinking proteins. While it has long been believed that the constriction is driven by motor proteins, it has recently been discovered that passive crosslinkers that do not turn over fuel are able to generate enough force to constrict actin filament rings. To study the ring constriction dynamics, we develop a model that includes the driving force of crosslinker condensation and the opposing forces of friction and filament bending. We analyze the constriction force as a function of ring topology and crosslinker concentration, and predict forces that are sufficient to constrict an unadorned plasma membrane. Our model also predicts that actin-filament sliding arises from an interplay between filament rotation and crosslinker hopping, producing frictional forces that are low compared to those of crosslinker-mediated microtubule sliding.

physics.bio-ph↗

arXiv2023

Trade-offs between cost and information in cellular prediction

Living cells can leverage correlations in environmental fluctuations to predict the future environment and mount a response ahead of time. To this end, cells need to encode the past signal into the output of the intracellular network from which the future input is predicted. Yet, storing information is costly while not all features of the past signal are equally informative on the future input signal. Here, we show, for two classes of input signals, that cellular networks can reach the fundamental bound on the predictive information as set by the information extracted from the past signal: push-pull networks can reach this information bound for Markovian signals, while networks that take a temporal derivative can reach the bound for predicting the future derivative of non-Markovian signals. However, the bits of past information that are most informative about the future signal are also prohibitively costly. As a result, the optimal system that maximizes the predictive information for a given resource cost is, in general, not at the information bound. Applying our theory to the chemotaxis network of Escherichia coli reveals that its adaptive kernel is optimal for predicting future concentration changes over a broad range of background concentrations, and that the system has been tailored to predicting these changes in shallow gradients.

physics.bio-ph↗

arXiv2022

Robust replication initiation from coupled homeostatic mechanisms

The bacterium Escherichia coli initiates replication once per cell cycle at a precise volume per origin and adds an on average constant volume between successive initiation events, independent of the initiation size. Yet, a molecular model that can explain these observations has been lacking. Experiments indicate that E. coli controls replication initiation via titration and activation of the initiator protein DnaA. Here, we study by mathematical modelling how these two mechanisms interact to generate robust replication-initiation cycles. We first show that a mechanism solely based on titration generates stable replication cycles at low growth rates, but inevitably causes premature reinitiation events at higher growth rates. In this regime, the DnaA activation switch becomes essential for stable replication initiation. Conversely, while the activation switch alone yields robust rhythms at high growth rates, titration can strongly enhance the stability of the switch at low growth rates. Our analysis thus predicts that both mechanisms together drive robust replication cycles at all growth rates. In addition, it reveals how an origin-density sensor yields adder correlations.

physics.bio-ph↗

arXiv2021

Energetic constraints on filament mediated cell polarization

Cell polarization underlies many cellular processes, such as differentiation, migration, and budding. Many living cells, such as budding yeast and fission yeast, use cytoskeletal structures to actively transport proteins to one location on the membrane and create a high density spot of membrane-bound proteins. Yet, the thermodynamic constraints on filament-based cell polarization remain unknown. We show by mathematical modeling that cell polarization requires detailed balance to be broken, and we quantify the free-energy cost of maintaining a polarized state of the cell. Our study reveals that detailed balance cannot only be broken via the active transport of proteins along filaments, but also via a chemical modification cycle, allowing detailed balance to be broken by the shuttling of proteins between the filament, membrane, and cytosol. Our model thus shows that cell polarization can be established via two distinct driving mechanisms, one based on active transport and one based on non-equilibrium binding. Furthermore, the model predicts that the driven binding process dissipates orders of magnitude less free-energy than the transport-based process to create the same membrane spot. Active transport along filaments may be sufficient to create a polarized distribution of membrane-bound proteins, but an additional chemical modification cycle of the proteins themselves is more efficient and less sensitive to the physical exclusion of proteins on the transporting filaments, providing insight in the design principles of the Pom1/Tea1/Tea4 system in fission yeast and the Cdc42 system in budding yeast.

physics.bio-ph↗

arXiv2019

Shape Transformations of Vesicles induced by Swim Pressure

While the behavior of vesicles in thermodynamic equilibrium has been studied extensively, how active forces control vesicle shape transformations is not understood. Here, we combine theory and simulations to study the shape behavior of vesicles containing active Brownian particles. We show that the combination of active forces, dimensionality and membrane bending free energy creates a plethora of novel phase transitions. At low swim pressure, the vesicle exhibits a discontinuous transition from a spherical to a prolate shape, which has no counterpart in two dimensions. At high swim pressure it exhibits stochastic spatio-temporal oscillations. Our work helps to understand and control the shape dynamics of membranes in active-matter systems.

cond-mat.soft↗