Enhancers are key regulators of mammalian gene expression, yet how they interact with promoters in space (contact vs. action-at-a-distance) and in time (transient vs. stable) remains poorly understood. Recent studies suggest that enhancers can activate promoters across distances exceeding 200 nanometers, challenging classical contact models, but limited spatiotemporal resolution has obscured the mechanistic details of enhancer-promoter (E-P) interactions and their link to transcription. Here, we engineered a synthetic biology platform optimized for the simultaneous visualization of E-P 3D distance and nascent transcription using super-resolution live-cell imaging. By applying five complementary approaches integrating imaging, 3D genomics, and gene expression data across cell lines, we estimate that transcriptional activation is mediated by ~25-42 nanometer contacts on the seconds timescale. Our results support a transient contact mechanism for E-P-mediated gene activation.

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 summarized 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.

Three-dimensional genomics methods such as Hi-C and Micro-C have uncovered chromatin loops across the genome and linked these loops to gene regulation. However, these methods only measure three-dimensional interaction probabilities on a relative scale. Here we overcome this limitation by using live-imaging data to calibrate Micro-C in mouse embryonic stem cells, thus obtaining absolute looping probabilities for 65,929 Micro-C-identified chromatin loops. We find that the looped state is generally rare, with a mean pairwise looping probability of 1.2% and a maximum of 25% across the quantified loops. On average, CTCF-CTCF loops are stronger than cis-regulatory loops (2.2% versus <1%). Our findings can be extended to human cells with available Micro-C data under certain assumptions. Overall, we establish an approach for genome-wide absolute loop quantification and report that loops occur with low probabilities, generalizing recent live-imaging results to the whole genome.

During development, groups of cells generate shape by coordinating their mechanical properties through an interplay of self-organization and prepatterning. Hydra displays a striking planar pattern of actin fibers at the organism scale, and mechanics influence the morphogenesis of biological structures during its prepatterned regeneration. However, how mechanics participate in the formation of an ordered pattern from a totally disordered state remains unknown. To study this, we used cellular aggregates formed from dissociated Hydra cells, which initially lose all actin polarity yet regenerate a long-range actin pattern. We showed quantitatively that the actin meshwork evolves from a disordered symmetric state to an ordered state in which rotational symmetry is broken, and translation symmetry is partially broken, with the nematic and smectic order parameters increasing over days. During the first hours, the actin meshwork displayed spatial heterogeneity in the nematic order parameter, and ordered domains separated by line defects progressively grew and fused. This suggests that local cell-cell interactions drive the transition from disorder to order. To understand the mechanism of ordering, we perturbed the tissue's physical constraints. We showed that while topology and geometry do not have a direct effect, anisotropic stretch biases the emerging orientation of the actin meshwork within hours. Surprisingly, although a Wnt head organizer is expected to play a role in the actin ordering, the stretch-associated alignment happened without the prior formation of a head organizer. This demonstrates the role of tissue mechanics in the alignment of the actin fibers during the disorder-to-order transition.

3D genomics methods such as Hi-C and Micro-C have uncovered chromatin loops across the genome and linked these loops to gene regulation. However, these methods only measure 3D interaction probabilities on a relative scale. Here, we overcome this limitation by using live imaging data to calibrate Micro-C in mouse embryonic stem cells, thus obtaining absolute looping probabilities for 36,804 chromatin loops across the genome. We find that the looped state is generally rare, with a mean probability of 2.3% and a maximum of 26% across the quantified loops. On average, CTCF-CTCF loops are stronger than loops between cis-regulatory elements (3.2% vs. 1.1%). Our findings can be extended to human stem cells and differentiated cells under certain assumptions. Overall, we establish an approach for genome-wide absolute loop quantification and report that loops generally occur with low probabilities, generalizing recent live imaging results to the whole genome.

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.

Biomolecular condensates have been proposed to buffer intracellular concentrations and reduce noise. However, concentrations need not be buffered in multicomponent systems, leading to a non-constant saturation concentration (csat) when individual components are varied. Simplified equilibrium considerations suggest that noise reduction might be closely related to concentration buffering and that a fixed saturation concentration is required for noise reduction to be effective. Here, we present a theoretical analysis to demonstrate that these suggestions do not apply to mesoscopic fluctuating systems. We show that concentration buffering and noise reduction are distinct concepts, which cannot be used interchangeably. We further demonstrate that concentration buffering and a constant csat are neither necessary nor sufficient for noise reduction to be effective. Clarity about these concepts is important for studying the role of condensates in controlling cellular noise and for the interpretation of concentration relationships in cells. A record of this paper’s transparent peer review process is included in the supplemental information.

Studying the role of molecularly distinct lipid species in cell signaling remains challenging due to a scarcity of methods for performing quantitative lipid biochemistry in living cells. We have recently used lipid uncaging to quantify lipid-protein affinities and rates of lipid trans-bilayer movement and turnover in the diacylglycerol signaling pathway. This approach is based on acquiring live-cell dose-response curves requiring light dose titrations and experimental determination of uncaging photoreaction efficiency. We here aimed to develop a methodological approach that allows us to retrieve quantitative kinetic data from uncaging experiments that 1) require only typically available datasets without the need for specialized additional constraints and 2) should in principle be applicable to other types of photoactivation experiments. Our new analysis framework allows us to identify model parameters such as diacylglycerol-protein affinities and trans-bilayer movement rates, together with initial uncaged diacylglycerol levels, using noisy single-cell data for a broad variety of structurally different diacylglycerol species. We find that lipid unsaturation degree and side-chain length generally correlate with faster lipid trans-bilayer movement and turnover and also affect lipid-protein affinities. In summary, our work demonstrates how rate parameters and lipid-protein affinities can be quantified from single-cell signaling trajectories with sufficient sensitivity to resolve the subtle kinetic differences caused by the chemical diversity of cellular signaling lipid pools.

Biomolecular condensates have been proposed to buffer intracellular concentrations and reduce noise. Recent results demonstrate that concentrations need not be buffered in multicomponent systems, leading to a non-constant saturation concentration ( c sat ) when individual components are varied. Simplified equilibrium considerations suggest that noise reduction might be closely related to concentration buffering and that a fixed saturation concentration is required for noise reduction to be effective. Here we present a theoretical analysis to demonstrate that these suggestions do not apply to mesoscopic fluctuating systems. We show that concentration buffering and noise reduction are distinct concepts, which cannot be used interchangeably. We further demonstrate that concentration buffering – and a constant c sat – are neither necessary nor sufficient for noise reduction to be effective. Clarity about these concepts is important for studying the role of condensates in controlling cellular noise and for the interpretation of concentration relationships in cells. ### Competing Interest Statement The authors have declared no competing interest.

Basic helix-loop-helix genes, particularly proneural genes, are well-described triggers of cell differentiation, yet information on their dynamics is limited, notably in human development. Here, we focus on Neurogenin 3 (NEUROG3), which is crucial for pancreatic endocrine lineage initiation. By monitoring both NEUROG3 gene expression and protein in single cells using a knockin dual reporter in 2D and 3D models of human pancreas development, we show an approximately 2-fold slower expression of human NEUROG3 than that of the mouse. We observe heterogeneous peak levels of NEUROG3 expression and reveal through long-term live imaging that both low and high NEUROG3 peak levels can trigger differentiation into hormone-expressing cells. Based on fluorescence intensity, we statistically integrate single-cell transcriptome with dynamic behaviors of live cells and propose a data-mapping methodology applicable to other contexts. Using this methodology, we identify a role for KLK12 in motility at the onset of NEUROG3 expression.

The front cover artwork is provided by David T. Gonzales of the Max Planck Institute of Molecular Cell Biology and Genetics. The image shows a collection of aqueous water‐in‐oil droplets with lipid bilayer interfaces. Inside each droplet is a cell‐free expression system that is capable of gene expression or intercellular communication. Read the full text of the Research Article at 10.1002/syst.202300029.

Compartmentalized biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyze mathematically - especially in the presence of stochasticity. We have recently proposed an effective moment equation approach to study the statistical properties of compartmentalized biochemical systems. So far, however, this approach is limited to polynomial rate laws and moreover, it relies on suitable moment closure approximations, which can be difficult to find in practice. In this work we propose a systematic method to derive closed moment dynamics for compartmentalized biochemical systems. We show that for the considered class of systems, the moment equations involve expectations over functions that factorize into two parts, one depending on the molecular content of the compartments and one depending on the compartment number distribution. Our method exploits this structure and approximates each function with suitable polynomial expansions, leading to a closed system of moment equations. We demonstrate the method using three systems inspired by cell populations and organelle networks and study its accuracy across different dynamical regimes.

Building synthetic multicellular systems using non-living molecular components is a grand challenge in the field of bottom-up synthetic biology. Towards this goal, a diverse range of chemistries have been developed to provide mechanisms of intercellular communication and methods to assemble multicellular compartments. However, building bottom-up synthetic multicellular systems is still challenging because it requires the integration of intercellular reaction networks with compatible cellular compartment properties. In this study, we encapsulated cell-free expression systems (CFES) expressing two quorum sensing genetic circuits into droplet interface bilayer (DIB) synthetic cells to demonstrate intercellular communication and feedback. We further develop a method of generating custom DIB multicellular structures by acoustic liquid handling to automatically dispense the CFES droplets and show the potential for multiplexing compartmentalized gene circuits for generating heterogeneous populations of cells. Our work provides a step towards building more complex multicellular systems with feedback mechanisms from the bottom-up to study and experimentally model biological multiscalar processes.

Studying the role of molecularly distinct lipid species in cell signaling remains challenging due to a scarcity of methods for performing quantitative lipid biochemistry in living cells. We have recently used lipid uncaging to quantify lipid-protein affinities and rates of lipid transbilayer movement and turnover in the diacylglycerol signaling pathway using population average time series data. So far, this approach does not allow to account for the cell-to-cell variability of cellular signaling responses. We here report a framework that allows to uniquely identify model parameters such diacylglycerol-protein affinities and transbilayer movement rates at the single cell level for a broad variety of structurally different diacylglycerol species. We find that lipid unsaturation degree and longer side chains generally correlate with faster lipid transbilayer movement and turnover and higher lipid-protein affinities. In summary, our work demonstrates how rate parameters and lipid-protein affinities can be quantified from single cell signaling trajectories with sufficient sensitivity to resolve the subtle kinetic differences caused by the chemical diversity of cellular signaling lipid pools.

The Front Cover shows collections of communicating synthetic cells composed of water-in-oil droplets separated and stabilized by lipid bilayer interfaces and containing cell-free expression system with quorum sensing gene circuits. Cover design by David T. Gonzales. More information can be found in the Research Article by T.-Y. Dora Tang and co-worker.

Correct nervous system development depends on the timely differentiation of progenitor cells into neurons. While the output of progenitor differentiation is well investigated at the population and clonal level, how stereotypic or variable fate decisions are during development is still more elusive. To fill this gap, we here follow the fate outcome of single neurogenic progenitors in the zebrafish retina over time using live imaging. We find that neurogenic progenitor divisions produce two daughter cells, one of deterministic and one of probabilistic fate. Interference with the deterministic branch of the lineage affects lineage progression. In contrast, interference with fate probabilities of the probabilistic branch results in a broader range of fate possibilities than in wild‐type and involves the production of any neuronal cell type even at non‐canonical developmental stages. Combining the interference data with stochastic modelling of fate probabilities revealed that a simple gene regulatory network is able to predict the observed fate decision probabilities during wild‐type development. These findings unveil unexpected lineage flexibility that could ensure robust development of the retina and other tissues.

We develop numerical and analytical approaches to calculate mutual information between complete paths of two molecular components embedded into a larger reaction network. In particular, we focus on a continuous-time Markov chain formalism, frequently used to describe intracellular processes involving lowly abundant molecular species. Previously, we have shown how the path mutual information can be calculated for such systems when two molecular components interact directly with one another with no intermediate molecular components being present. In this work, we generalize this approach to biochemical networks involving an arbitrary number of molecular components. We present an efficient Monte Carlo method as well as an analytical approximation to calculate the path mutual information and show how it can be decomposed into a pair of transfer entropies that capture the causal flow of information between two network components. We apply our methodology to study information transfer in a simple three-node feedforward network, as well as a more complex positive feedback system that switches stochastically between two metastable modes.

The ability to build synthetic cellular populations from the bottom-up provides the groundwork to realize minimal living tissues comprising single cells which can communicate and bridge scales into multicellular systems. Engineered systems made of synthetic micron-sized compartments and integrated reaction networks coupled with mathematical modeling can facilitate the design and construction of complex and multiscale chemical systems from the bottom-up. Toward this goal, we generated populations of monodisperse liposomes encapsulating cell-free expression systems (CFESs) using double-emulsion microfluidics and quantified transcription and translation dynamics within individual synthetic cells of the population using a fluorescent Broccoli RNA aptamer and mCherry protein reporter. CFE dynamics in bulk reactions were used to test different coarse-grained resource-limited gene expression models using model selection to obtain transcription and translation rate parameters by likelihood-based parameter estimation. The selected model was then applied to quantify cell-free gene expression dynamics in populations of synthetic cells. In combination, our experimental and theoretical approaches provide a statistically robust analysis of CFE dynamics in bulk and monodisperse synthetic cell populations. We demonstrate that compartmentalization of CFESs leads to different transcription and translation rates compared to bulk CFE and show that this is due to the semipermeable lipid membrane that allows the exchange of materials between the synthetic cells and the external environment.

Animal genomes are folded into loops and topologically associating domains (TADs) by CTCF and loop-extruding cohesins, but the live dynamics of loop formation and stability remain unknown. Here, we directly visualized chromatin looping at the Fbn2 TAD in mouse embryonic stem cells using super-resolution live-cell imaging and quantified looping dynamics by Bayesian inference. Unexpectedly, the Fbn2 loop was both rare and dynamic, with a looped fraction of approximately 3 to 6.5% and a median loop lifetime of approximately 10 to 30 minutes. Our results establish that the Fbn2 TAD is highly dynamic, and about 92% of the time, cohesin-extruded loops exist within the TAD without bridging both CTCF boundaries. This suggests that single CTCF boundaries, rather than the fully CTCF-CTCF looped state, may be the primary regulators of functional interactions.

The dynamics of biochemical reaction networks require a stochastic description when copy number fluctuations become significant. Such description is provided by moment equations that capture the statistical properties of the involved molecular components such as their average abundance and variability. Certain applications require a special form of moment equations, where the statistics of some components are described conditionally on complete trajectories of other components. Typical examples include information theoretical analyses of biochemical networks, model reduction and subnetwork simulation, or statistical inference where time-varying molecular signals are inferred from counting observations. These conditional moment equations have so far been limited to relatively simple reaction systems as their manual derivation becomes difficult for systems involving many components and interactions. Here, we present a Python tool for the automated derivation of moment equations conditional on complete time trajectories for arbitrary user-defined reaction systems and showcase its utility in the context of subnetwork simulation. With this automated tool, conditional moment equations become applicable to a broad class of biochemical systems.