arXiv subjects

Gašper Tkačik

Publications and source records attributed to Gašper Tkačik.

At least 19 recordsLinked to original sources

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

Long-term evolution of regulatory DNA sequences. Part 2: Theory and future challenges

Promoters and enhancers are cis-regulatory elements (CREs), DNA sequences that bind transcription factor (TF) proteins to up- or down-regulate target genes. Decades-long efforts yielded TF-DNA interaction models that predict how strongly an individual TF binds arbitrary DNA sequences and how individual binding events on the CRE combine to affect gene expression. These insights can be synthesized into a global, biophysically-realistic, and quantitative genotype-phenotype (GP) map for gene regulation, a "holy grail" for the application of evolutionary theory. A global map provides a rare opportunity to simulate long-term evolution of regulatory sequences and pose several fundamental questions: How long does it take to evolve CREs de novo? How many non-trivial regulatory functions exist in sequence space? How connected are they? For which regulatory architecture is CRE evolution most rapid and evolvable? In this article, the second of a two-part series, we review the application of evolutionary concepts - epistasis, robustness, evolvability, tunability, plasticity, and bet-hedging - to the evolution of gene regulatory sequences. We then evaluate the potential for a unifying theory for the evolution of regulatory sequences, and identify key open challenges.

q-bio.PE↗

arXiv2026

Long-term evolution of regulatory DNA sequences. Part 1: Simulations on global, biophysically-realistic genotype-phenotype maps

Promoters and enhancers are cis-regulatory elements (CREs), DNA sequences that bind transcription factor (TF) proteins to up- or down-regulate target genes. Decades-long efforts yielded TF-DNA interaction models that predict how strongly an individual TF binds arbitrary DNA sequences and how individual binding events on the CRE combine to affect gene expression. These insights can be synthesized into a global, biophysically-realistic, and quantitative genotype-phenotype (GP) map for gene regulation, a "holy grail" for the application of evolutionary theory. A global map provides a rare opportunity to simulate long-term evolution of regulatory sequences and pose several fundamental questions: How long does it take to evolve CREs de novo? How many non-trivial regulatory functions exist in sequence space? How connected are they? For which regulatory architecture is CRE evolution most rapid and evolvable? In this article, the first of a two-part series, we briefly review the pertinent modeling and simulation efforts for a unique system that enables close, quantitative, and mechanistic links between biophysics, as well as systems, synthetic, and evolutionary biology.

q-bio.PE↗

arXiv2025

Nonlocal decoding of positional and correlational information during development

In many developmental systems, cells differentiate into a tissue by reading out morphogen concentration fields, a process fundamentally limited by noise. How much can the precision of this process be improved by nonlocal information, e.g., via cell-cell communication? Using a Bayes-optimal framework, we show that positional inference depends crucially on morphogen spatial correlations and on the ``structural prior'' that encodes the geometry of the cellular lattice performing the readout. We derive upper bounds on positional information gain due to nonlocal readout and identify signal processing algorithms that approximate optimal positional inference, as well as simple chemical reaction schemes which implement such algorithms. Our theory suggests that correlational information can be exploited to significantly enhance developmental precision.

physics.bio-ph↗

arXiv2025

Marr's three levels for embryonic development: information, dynamical systems, gene networks

Developmental patterning comprises processes that range from purely instructed, where external signals specify cell fates, to fully self-organized, where spatial patterns emerge autonomously through cellular interactions. We propose that both extremes -- as well as the continuum of intermediate cases -- can be conceptualized as information processing systems, whose operation can be described using ``Marr's three levels of analysis'': the computational problem being solved, the algorithms employed, and their molecular implementation. At the first level, we argue that normative theories, such as information-theoretic optimization principles, provide a formalization of the computational problem. At the second level, we show how simplified information processing architectures provide a framework for developmental algorithms, which are formalized mathematically using dynamical systems theory. At the third level, the implementation of developmental algorithms is described by mechanistic biophysical and gene regulatory network models.

physics.bio-ph↗

arXiv2025

Meta-Learning Theory-Informed Inductive Biases using Deep Kernel Gaussian Processes

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of real biological datasets are prohibitively laborious, and often impossible. To this end, we introduce a Bayesian meta-learning framework designed to automatically convert raw functional predictions from normative theories into tractable probabilistic models. We employ adaptive deep kernel Gaussian processes, meta-learning a kernel on synthetic data generated from a normative theory. This Theory-Informed Kernel specifies a probabilistic model representing the theory predictions -- usable for both fitting data and rigorously validating the theory. As a demonstration, we apply our framework to the early visual system, using efficient coding as our normative theory. We show improved response prediction accuracy in ex vivo recordings of mouse retinal ganglion cells stimulated by natural scenes compared to conventional data-driven baselines, while providing well-calibrated uncertainty estimates and interpretable representations. Using exact Bayesian model selection, we also show that our informed kernel can accurately infer the degree of theory-match from data, confirming faithful encapsulation of theory structure. This work provides a more general, scalable, and automated approach for integrating theoretical knowledge into data-driven scientific inquiry in neuroscience and beyond.

cs.AI↗

arXiv2025

Invariant non-equilibrium dynamics of transcriptional regulation optimize information flow

Eukaryotic gene regulation is based on stochastic yet controlled promoter switching, during which genes transition between transcriptionally active and inactive states. Despite the molecular complexity of this process, recent studies reveal a surprising invariance of the "switching correlation time" ($T_C$), which characterizes promoter activity fluctuations, across gene expression levels in diverse genes and organisms. A biophysically plausible explanation for this invariance remains missing. Here, we show that this invariance imposes stringent constraints on minimal yet plausible models of transcriptional regulation, requiring at least four system states and non-equilibrium dynamics that break detailed balance. Using Bayesian inference on Drosophila gap gene expression data, we demonstrate that such models (i) accurately reproduce the observed $T_C$-invariance; (ii) remain robust to parameter perturbations; and (iii) maximize information transmission from transcription factor concentration to gene expression. These findings suggest that eukaryotic gene regulation has evolved to balance precision with reaction rate and energy dissipation constraints, favoring non-equilibrium architectures for optimal information transmission.

q-bio.MN↗

arXiv2025

Token-driven totally asymmetric simple exclusion process

We consider a family of totally asymmetric simple exclusion processes (TASEPs), consisting of particles on a lattice that require binding by a "token" in various physical configurations to advance over the lattice. Using a combination of theory and simulations, we address the following questions: (i) How token binding kinetics affects the current-density relation on the lattice; (ii) How this current-density relation depends on the scarcity of tokens; (iii) How tokens propagate the effects of the locally-imposed disorder (such as a slow site) over the entire lattice; (iv) How a shared pool of tokens couples concurrent TASEPs running on multiple lattices; (v) How our results translate to TASEPs with open boundaries that exchange particles with the reservoir. Since real particle motion (including in biological systems that inspired the standard TASEP model, e.g., protein synthesis or movement of molecular motors) is often catalyzed, regulated, actuated, or otherwise mediated, the token-driven TASEP dynamics analyzed in this paper should allow for a better understanding of real systems and enable a closer match between TASEP theory and experimental observations.

cond-mat.stat-mech↗

arXiv2023

Information content and optimization of self-organized developmental systems

A key feature of many developmental systems is their ability to self-organize spatial patterns of functionally distinct cell fates. To ensure proper biological function, such patterns must be established reproducibly, by controlling and even harnessing intrinsic and extrinsic fluctuations. While the relevant molecular processes are increasingly well understood, we lack a principled framework to quantify the performance of such stochastic self-organizing systems. To that end, we introduce a new information-theoretic measure for self-organized fate specification during embryonic development. We show that the proposed measure assesses the total information content of fate patterns, and decomposes it into interpretable contributions corresponding to the positional and correlational information. By optimizing the proposed measure, our framework provides a normative theory for developmental circuits, which we demonstrate on lateral inhibition, cell type proportioning, and reaction-diffusion models of self-organization. This paves a way towards a classification of developmental systems based on a common information-theoretic language, thereby organizing the zoo of implicated chemical and mechanical signaling processes.

physics.bio-ph↗

arXiv2023

Deriving a genetic regulatory network from an optimization principle

Many biological systems approach physical limits to their performance, motivating the idea that their behavior and underlying mechanisms could be determined by such optimality. Nevertheless, optimization as a predictive principle has only been applied in very simplified setups. Here, in contrast, we explore a mechanistically-detailed class of models for the gap gene network of the Drosophila embryo, and determine its 50+ parameters by optimizing the information that gene expression levels convey about nuclear positions, subject to physical constraints on the number of available molecules. Optimal networks recapitulate the architecture and spatial gene expression profiles of the real organism. Our framework makes precise the many tradeoffs involved in maximizing functional performance, and allows us to explore alternative networks to address the questions of necessity vs contingency. Multiple solutions to the optimization problem may be realized in closely related organisms.

physics.bio-ph↗

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↗

arXiv2022

Statistical modeling of adaptive neural networks explains coexistence of avalanches and oscillations in resting human brain

Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equilibrium feedback-driven Ising like class of neural networks that simultaneously and quantitatively captures scale-free avalanches and scale-specific oscillations. In the most simple yet fully microscopic model version we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations and collective behaviors of nearly-synchronous extreme events on multiple sensors, to neuronal avalanches unfolding over multiple sensors across multiple time bins. Importantly, the inferred parameters correlate with model-independent signatures of "closeness to criticality", indicating that the coexistence of scale-specific (neural oscillations) and scale-free (neuronal avalanches) dynamics in brain activity occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations.

q-bio.NC↗

arXiv2021

Eukaryotic gene regulation at equilibrium, or non?

Models of transcriptional regulation that assume equilibrium binding of transcription factors have been very successful at predicting gene expression from sequence in bacteria. However, analogous equilibrium models do not perform as well in eukaryotes, most likely due to the largely out-of-equilibrium nature of eukaryotic regulatory processes. These processes come with unavoidable energy expenditure at the molecular level to support precise, reliable, or fast gene expression responses that could correspond to evolutionarily optimized regulatory strategies. Unfortunately, the space of possible non-equilibrium mechanisms is vast and predominantly uninteresting. The key question is therefore how this space can be navigated efficiently, to focus on mechanisms and models that are biologically relevant. In this review, we advocate for the normative role of theory - theory that prescribes rather than just describes - in providing such a focus. Theory should expand its remit beyond inferring models from data (by fitting), towards identifying non-equilibrium gene regulatory schemes (by optimizing) that may have been evolutionarily selected due to their favorable functional characteristics which outperform regulation at equilibrium. This approach can help us navigate the expanding complexity of regulatory architectures, and refocus the questions about the observed biological mechanisms from how they work towards why they have evolved in the first place. We illustrate our reasoning by toy examples for which we provide simulation code.

q-bio.MN↗

arXiv2019

Action at a distance in transcriptional regulation

There is increasing evidence that protein binding to specific sites along DNA can activate the reading out of genetic information without coming into direct physical contact with the gene. There also is evidence that these distant but interacting sites are embedded in a liquid droplet of proteins which condenses out of the surrounding solution. We argue that droplet-mediated interactions can account for crucial features of gene regulation only if the droplet is poised at a non-generic point in its phase diagram. We explore a minimal model that embodies this idea, show that this model has a natural mechanism for self-tuning, and suggest direct experimental tests.

q-bio.SC↗

arXiv2019

A Tight Upper Bound on Mutual Information

We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and maximum a posteriori decodes (most probable signals given channel output). As part of our derivation, we describe the key properties of the distribution of signals, channel outputs and decodes, that minimizes equivocation and maximizes mutual information. This work addresses a problem in data analysis, where mutual information between signals and decodes is sometimes used to lower bound the mutual information between signals and channel outputs. Our result provides a corresponding upper bound.

cs.IT↗

arXiv2018

Estimating information in time-varying signals

Across diverse biological systems -- ranging from neural networks to intracellular signaling and genetic regulatory networks -- the information about changes in the environment is frequently encoded in the full temporal dynamics of the network nodes. A pressing data-analysis challenge has thus been to efficiently estimate the amount of information that these dynamics convey from experimental data. Here we develop and evaluate decoding-based estimation methods to lower bound the mutual information about a finite set of inputs, encoded in single-cell high-dimensional time series data. For biological reaction networks governed by the chemical Master equation, we derive model-based information approximations and analytical upper bounds, against which we benchmark our proposed model-free decoding estimators. In contrast to the frequently-used k-nearest-neighbor estimator, decoding-based estimators robustly extract a large fraction of the available information from high-dimensional trajectories with a realistic number of data samples. We apply these estimators to previously published data on Erk and Ca signaling in mammalian cells and to yeast stress-response, and find that substantial amount of information about environmental state can be encoded by non-trivial response statistics even in stationary signals. We argue that these single-cell, decoding-based information estimates, rather than the commonly-used tests for significant differences between selected population response statistics, provide a proper and unbiased measure for the performance of biological signaling networks.

q-bio.QM↗

arXiv2017

Discrete modes of social information processing predict individual behavior of fish in a group

Individual computations and social interactions underlying collective behavior in groups of animals are of great ethological, behavioral, and theoretical interest. While complex individual behaviors have successfully been parsed into small dictionaries of stereotyped behavioral modes, studies of collective behavior largely ignored these findings; instead, their focus was on inferring single, mode-independent social interaction rules that reproduced macroscopic and often qualitative features of group behavior. Here we bring these two approaches together to predict individual swimming patterns of adult zebrafish in a group. We show that fish alternate between an active mode in which they are sensitive to the swimming patterns of conspecifics, and a passive mode where they ignore them. Using a model that accounts for these two modes explicitly, we predict behaviors of individual fish with high accuracy, outperforming previous approaches that assumed a single continuous computation by individuals and simple metric or topological weighing of neighbors behavior. At the group level, switching between active and passive modes is uncorrelated among fish, yet correlated directional swimming behavior still emerges. Our quantitative approach for studying complex, multi-modal individual behavior jointly with emergent group behavior is readily extensible to additional behavioral modes and their neural correlates, as well as to other species.

q-bio.NC↗

arXiv2017

Statistical mechanics for metabolic networks during steady-state growth

Which properties of metabolic networks can be derived solely from stoichiometric information about the network's constituent reactions? Predictive results have been obtained by Flux Balance Analysis (FBA), by postulating that cells set metabolic fluxes within the allowed stoichiometry so as to maximize their growth. Here, we generalize this framework to single cell level using maximum entropy models from statistical physics. We define and compute, for the core metabolism of Escherichia coli, a joint distribution over all fluxes that yields the experimentally observed growth rate. This solution, containing FBA as a limiting case, provides a better match to the measured fluxes in the wild type and several mutants. We find that E. coli metabolism is close to, but not at, the optimality assumed by FBA. Moreover, our model makes a wide range of predictions: (i) on flux variability, its regulation, and flux correlations across individual cells; (ii) on the relative importance of stoichiometric constraints vs. growth rate optimization; (iii) on quantitative scaling relations for singe-cell growth rate distributions. We validate these scaling predictions using data from individual bacterial cells grown in a microfluidic device at different sub-inhibitory antibiotic concentrations. Under mild dynamical assumptions, fluctuation-response relations further predict the autocorrelation timescale in growth data and growth rate adaptation times following an environmental perturbation.

q-bio.MN↗