A programmable reaction-diffusion system for spatiotemporal cell signaling circuit design.

Cells self-organize molecules in space and time to generate complex behaviors, but we lack synthetic strategies for engineering spatiotemporal signaling. We present a programmable reaction-diffusion platform for designing protein oscillations, patterns, and circuits in mammalian cells using two bacterial proteins, MinD and MinE (MinDE). MinDE circuits act like "single-cell radios," emitting frequency-barcoded fluorescence signals that can be spectrally isolated and analyzed using digital signal processing tools. We define how to genetically program these signals and connect their spatiotemporal dynamics to cell biology using engineerable protein-protein interactions. This enabled us to construct sensitive reporter circuits that broadcast endogenous cell signaling dynamics on a frequency-barcoded imaging channel and to build control signal circuits that synthetically pattern activities in the cell, such as protein condensate assembly and actin filamentation. Our work establishes a paradigm for visualizing, probing, and engineering cellular activities at length and timescales critical for biological function.

Receptor-associated independent cAMP nanodomains mediate spatiotemporal specificity of GPCR signaling.

G protein-coupled receptors (GPCRs) relay extracellular stimuli into specific cellular functions. Cells express many different GPCRs, but all these GPCRs signal to only a few second messengers such as cAMP. It is largely unknown how cells distinguish between signals triggered by different GPCRs to orchestrate their complex functions. Here, we demonstrate that individual GPCRs signal via receptor-associated independent cAMP nanodomains (RAINs) that constitute self-sufficient, independent cell signaling units. Low concentrations of glucagon-like peptide 1 (GLP-1) and isoproterenol exclusively generate highly localized cAMP pools around GLP-1- and ß2-adrenergic receptors, respectively, which are protected from cAMP originating from other receptors and cell compartments. Mapping local cAMP concentrations with engineered GPCR nanorulers reveals gradients over only tens of nanometers that define the size of individual RAINs. The coexistence of many such RAINs allows a single cell to operate thousands of independent cellular signals simultaneously, rather than function as a simple "on/off" switch.

Control of Tissue Development by Morphogens.

Intercellular signaling molecules, known as morphogens, act at a long range in developing tissues to provide spatial information and control properties such as cell fate and tissue growth. The production, transport, and removal of morphogens shape their concentration profiles in time and space. Downstream signaling cascades and gene regulatory networks within cells then convert the spatiotemporal morphogen profiles into distinct cellular responses. Current challenges are to understand the diverse molecular and cellular mechanisms underlying morphogen gradient formation, as well as the logic of downstream regulatory circuits involved in morphogen interpretation. This knowledge, combining experimental and theoretical results, is essential to understand emerging properties of morphogen-controlled systems, such as robustness and scaling.

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning.

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

Cellular Control of Viscosity Counters Changes in Temperature and Energy Availability.

Cellular functioning requires the orchestration of thousands of molecular interactions in time and space. Yet most molecules in a cell move by diffusion, which is sensitive to external factors like temperature. How cells sustain complex, diffusion-based systems across wide temperature ranges is unknown. Here, we uncover a mechanism by which budding yeast modulate viscosity in response to temperature and energy availability. This "viscoadaptation" uses regulated synthesis of glycogen and trehalose to vary the viscosity of the cytosol. Viscoadaptation functions as a stress response and a homeostatic mechanism, allowing cells to maintain invariant diffusion across a 20°C temperature range. Perturbations to viscoadaptation affect solubility and phase separation, suggesting that viscoadaptation may have implications for multiple biophysical processes in the cell. Conditions that lower ATP trigger viscoadaptation, linking energy availability to rate regulation of diffusion-controlled processes. Viscoadaptation reveals viscosity to be a tunable property for regulating diffusion-controlled processes in a changing environment.

Optical Mapping of cAMP Signaling at the Nanometer Scale.

Cells relay a plethora of extracellular signals to specific cellular responses by using only a few second messengers, such as cAMP. To explain signaling specificity, cAMP-degrading phosphodiesterases (PDEs) have been suggested to confine cAMP to distinct cellular compartments. However, measured rates of fast cAMP diffusion and slow PDE activity render cAMP compartmentalization essentially impossible. Using fluorescence spectroscopy, we show that, contrary to earlier data, cAMP at physiological concentrations is predominantly bound to cAMP binding sites and, thus, immobile. Binding and unbinding results in largely reduced cAMP dynamics, which we term "buffered diffusion." With a large fraction of cAMP being buffered, PDEs can create nanometer-size domains of low cAMP concentrations. Using FRET-cAMP nanorulers, we directly map cAMP gradients at the nanoscale around PDE molecules and the areas of resulting downstream activation of cAMP-dependent protein kinase (PKA). Our study reveals that spatiotemporal cAMP signaling is under precise control of nanometer-size domains shaped by PDEs that gate activation of downstream effectors.

The Root Cap Cuticle: A Cell Wall Structure for Seedling Establishment and Lateral Root Formation.

The root cap surrounding the tip of plant roots is thought to protect the delicate stem cells in the root meristem. We discovered that the first layer of root cap cells is covered by an electron-opaque cell wall modification resembling a plant cuticle. Cuticles are polyester-based protective structures considered exclusive to aerial plant organs. Mutations in cutin biosynthesis genes affect the composition and ultrastructure of this cuticular structure, confirming its cutin-like characteristics. Strikingly, targeted degradation of the root cap cuticle causes a hypersensitivity to abiotic stresses during seedling establishment. Furthermore, lateral root primordia also display a cuticle that, when defective, causes delayed outgrowth and organ deformations, suggesting that it facilitates lateral root emergence. Our results show that the previously unrecognized root cap cuticle protects the root meristem during the critical phase of seedling establishment and promotes the efficient formation of lateral roots.

Transmembrane Pickets Connect Cyto- and Pericellular Skeletons Forming Barriers to Receptor Engagement.

Phagocytic receptors must diffuse laterally to become activated upon clustering by multivalent targets. Receptor diffusion, however, can be obstructed by transmembrane proteins ("pickets") that are immobilized by interacting with the cortical cytoskeleton. The molecular identity of these pickets and their role in phagocytosis have not been defined. We used single-molecule tracking to study the interaction between Fcγ receptors and CD44, an abundant transmembrane protein capable of indirect association with F-actin, hence likely to serve as a picket. CD44 tethers reversibly to formin-induced actin filaments, curtailing receptor diffusion. Such linear filaments predominate in the trailing end of polarized macrophages, where receptor mobility was minimal. Conversely, receptors were most mobile at the leading edge, where Arp2/3-driven actin branching predominates. CD44 binds hyaluronan, anchoring a pericellular coat that also limits receptor displacement and obstructs access to phagocytic targets. Force must be applied to traverse the pericellular barrier, enabling receptors to engage their targets.

Dendritic Integration of Sensory Evidence in Perceptual Decision-Making.

Perceptual decisions require the accumulation of sensory information to a response criterion. Most accounts of how the brain performs this process of temporal integration have focused on evolving patterns of spiking activity. We report that subthreshold changes in membrane voltage can represent accumulating evidence before a choice. αß core Kenyon cells (αßc KCs) in the mushroom bodies of fruit flies integrate odor-evoked synaptic inputs to action potential threshold at timescales matching the speed of olfactory discrimination. The forkhead box P transcription factor (FoxP) sets neuronal integration and behavioral decision times by controlling the abundance of the voltage-gated potassium channel Shal (KV4) in αßc KC dendrites. αßc KCs thus tailor, through a particular constellation of biophysical properties, the generic process of synaptic integration to the demands of sequential sampling.

Friction Mediates Scission of Tubular Membranes Scaffolded by BAR Proteins.

Membrane scission is essential for intracellular trafficking. While BAR domain proteins such as endophilin have been reported in dynamin-independent scission of tubular membrane necks, the cutting mechanism has yet to be deciphered. Here, we combine a theoretical model, in vitro, and in vivo experiments revealing how protein scaffolds may cut tubular membranes. We demonstrate that the protein scaffold bound to the underlying tube creates a frictional barrier for lipid diffusion; tube elongation thus builds local membrane tension until the membrane undergoes scission through lysis. We call this mechanism friction-driven scission (FDS). In cells, motors pull tubes, particularly during endocytosis. Through reconstitution, we show that motors not only can pull out and extend protein-scaffolded tubes but also can cut them by FDS. FDS is generic, operating even in the absence of amphipathic helices in the BAR domain, and could in principle apply to any high-friction protein and membrane assembly.

Live Cell Imaging Reveals the Dynamics of Telomerase Recruitment to Telomeres.

Telomerase maintains genome integrity by adding repetitive DNA sequences to the chromosome ends in actively dividing cells, including 90% of all cancer cells. Recruitment of human telomerase to telomeres occurs during S-phase of the cell cycle, but the molecular mechanism of the process is only partially understood. Here, we use CRISPR genome editing and single-molecule imaging to track telomerase trafficking in nuclei of living human cells. We demonstrate that telomerase uses three-dimensional diffusion to search for telomeres, probing each telomere thousands of times each S-phase but only rarely forming a stable association. Both the transient and stable association events depend on the direct interaction of the telomerase protein TERT with the telomeric protein TPP1. Our results reveal that telomerase recruitment to telomeres is driven by dynamic interactions between the rapidly diffusing telomerase and the chromosome end.

Stress-dependent macromolecular crowding in the mitochondrial matrix.

Macromolecules of various sizes induce crowding of the cellular environment. This crowding impacts on biochemical reactions by increasing solvent viscosity, decreasing the water-accessible volume and altering protein shape, function, and interactions. Although mitochondria represent highly protein-rich organelles, most of these proteins are somehow immobilized. Therefore, whether the mitochondrial matrix solvent exhibits macromolecular crowding is still unclear. Here, we demonstrate that fluorescent protein fusion peptides (AcGFP1 concatemers) in the mitochondrial matrix of HeLa cells display an elongated molecular structure and that their diffusion constant decreases with increasing molecular weight in a manner typical of macromolecular crowding. Chloramphenicol (CAP) treatment impaired mitochondrial function and reduced the number of cristae without triggering mitochondrial orthodox-to-condensed transition or a mitochondrial unfolded protein response. CAP-treated cells displayed progressive concatemer immobilization with increasing molecular weight and an eightfold matrix viscosity increase, compatible with increased macromolecular crowding. These results establish that the matrix solvent exhibits macromolecular crowding in functional and dysfunctional mitochondria. Therefore, changes in matrix crowding likely affect matrix biochemical reactions in a manner depending on the molecular weight of the involved crowders and reactants.

Long-range formation of the Bicoid gradient requires multiple dynamic modes that spatially vary across the embryo.

Morphogen gradients provide essential positional information to gene networks through their spatially heterogeneous distribution, yet how they form is still hotly contested, with multiple models proposed for different systems. Here, we focus on the transcription factor Bicoid (Bcd), a morphogen that forms an exponential gradient across the anterior-posterior (AP) axis of the early Drosophila embryo. Using fluorescence correlation spectroscopy we find there are spatial differences in Bcd diffusivity along the AP axis, with Bcd diffusing more rapidly in the posterior. We establish that such spatially varying differences in Bcd dynamics are sufficient to explain how Bcd can have a steep exponential gradient in the anterior half of the embryo and yet still have an observable fraction of Bcd near the posterior pole. In the nucleus, we demonstrate that Bcd dynamics are impacted by binding to DNA. Addition of the Bcd homeodomain to eGFP::NLS qualitatively replicates the Bcd concentration profile, suggesting this domain regulates Bcd dynamics. Our results reveal how a long-range gradient can form while retaining a steep profile through much of its range.

The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro.

During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in vitro.

Collective chemomechanical oscillations in active hydrogels.

We report on the collective response of an assembly of chemomechanical Belousov-Zhabotinsky (BZ) hydrogel beads. We first demonstrate that a single isolated spherical BZ hydrogel bead with a radius below a critical value does not oscillate, whereas an assembly of the same BZ hydrogel beads presents chemical oscillation. A BZ chemical model with an additional flux of chemicals out of the BZ hydrogel captures the experimentally observed transition from oxidized nonoscillating to oscillating BZ hydrogels and shows this transition is due to a flux of inhibitors out of the BZ hydrogel. The model also captures the role of neighboring BZ hydrogel beads in decreasing the critical size for an assembly of BZ hydrogel beads to oscillate. We finally leverage the quorum sensing behavior of the collective to trigger their chemomechanical oscillation and discuss how this collective effect can be used to enhance the oscillatory strain of these active BZ hydrogels. These findings could help guide the eventual fabrication of a swarm of autonomous, communicating, and motile hydrogels.

Modeling of brain efflux: Constraints of brain surfaces.

Fluid efflux from the brain plays an important role in solute waste clearance. Current experimental approaches provide little spatial information, and data collection is limited due to short duration or low frequency of sampling. One approach shows tracer efflux to be independent of molecular size, indicating bulk flow, yet also decelerating like simple membrane diffusion. In an apparent contradiction to this report, other studies point to tracer efflux acceleration. We here develop a one-dimensional advection-diffusion model to gain insight into brain efflux principles. The model is characterized by nine physiological constants and three efflux parameters for which we quantify prior uncertainty. Using Bayes' rule and the two efflux studies, we validate the model and calculate data-informed parameter distributions. The apparent contradictions in the efflux studies are resolved by brain surface boundaries being bottlenecks for efflux. To critically test the model, a custom MRI efflux assay measuring solute dispersion in tissue and release to cerebrospinal fluid was employed. The model passed the test with tissue bulk flow velocities in the range 60 to 190 [Formula: see text]m/h. Dimensional analysis identified three principal determinants of efflux, highlighting brain surfaces as a restricting factor for metabolite solute clearance.

4Pi MINFLUX arrangement maximizes spatio-temporal localization precision of fluorescence emitter.

We introduce MINFLUX localization with interferometric illumination through opposing objective lenses for maximizing the attainable precision in 3D-localization of single inelastic scatterers, such as fluorophores. Our 4Pi optical configuration employs three sequentially tilted counter-propagating beam pairs for illumination, each providing a narrow interference minimum of illumination intensity at the focal point. The localization precision is additionally improved by adding the inelastically scattered or fluorescence photons collected through both objective lenses. Our 4Pi configuration yields the currently highest precision per detected photon among all localization schemes. Tracking gold nanoparticles as non-blinking inelastic scatterers rendered a position uncertainty <0.4 nm3 in volume at a localization frequency of 2.9 kHz. We harnessed the record spatio-temporal precision of our 4Pi MINFLUX approach to examine the diffusion of single fluorophores and fluorescent nanobeads in solutions of sucrose in water, revealing local heterogeneities at the nanoscale. Our results show the applicability of 4Pi MINFLUX to study molecular nano-environments of diffusion and its potential for quantifying rapid movements of molecules in cells and other material composites.

Differences in enantiomeric diffusion can lead to selective chiral amplification.

A fundamental question associated with chirality is how mixtures containing equal amounts of interconverting enantiomers can spontaneously convert to systems enriched in only one of them. Enantiomers typically have similar chemical properties, but can exhibit distinct reactivity under specific conditions, and these differences can be used to bias the system's composition in favor of one enantiomer. Transport properties are also expected to differ for enantiomers in chiral solvents, but the role of such differences in chiral symmetry breaking has not been clarified yet. In this work, we develop a theoretical framework to show that asymmetry in diffusion properties can trigger a spontaneous and selective symmetry breaking in mixtures of enantiomers. We derive a generic evolution equation for the enantiomeric excess in a chiral solvent. This equation shows that the relative stability of homochiral domains is dictated by the difference of diffusion coefficients of the two enantiomers. Consequently, deracemization toward a specific enantiomeric excess can be achieved when this difference is large enough. These results hold significant implications for our understanding of chiral symmetry breaking.

Spiking at the edge: Excitability at interfaces in reaction-diffusion systems.

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator-prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction-diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media.

Quantum acoustics unravels Planckian resistivity.

Strange metals exhibit universal linear-in-temperature resistivity described by a Planckian scattering rate, the origin of which remains elusive. By employing an approach inspired by quantum optics, we arrive at the coherent state representation of lattice vibrations: quantum acoustics. Utilizing this nonperturbative framework, we demonstrate that lattice vibrations could serve as active drivers in the Planckian resistivity phenomenon, challenging prevailing theories. By treating charge carriers as quantum wave packets negotiating the dynamic acoustic field, we find that a competition ensues between localization and delocalization giving rise to the previously conjectured universal quantum bound of diffusion, [Formula: see text], independent of temperature or any other material parameters. This leads to the enigmatic T-linear resistivity over hundreds of degrees, except at very low temperatures. Quantum diffusion also explains why strange metals have much higher electrical resistivity than typical metals. Our work elucidates the critical role of phonons in Planckian resistivity from a unique perspective and reconsiders their significance in the transport properties of strange metals.