arXiv subjects

Erez Braun

Publications and source records attributed to Erez Braun.

10 recordsLinked to original sources

arXiv2026

Dynamical noisy canalization in morphogenesis: lessons from Hydra regeneration

Developmental robustness is framed as progress through a fixed Waddington-type landscape. We argue that in morphogenesis this landscape evolves through coupled bio-signaling, mechanical, and physiological processes, while fluctuations aid exploration. In Hydra regeneration, stochastic Ca activity plays a major role in reshaping the landscape of accessible morphologies as regeneration unfolds, including the early progressive confinement of tissue fluctuations. We propose testing this framework of dynamical noisy canalization in developmental systems.

physics.bio-ph↗

arXiv2026

Rupture-Repair Cycles in Regenerating Hydra Tissues

Destructive mechanical breakdowns and fractures are ubiquitous events in driven physical matter; living tissues, by contrast, can rupture repeatedly while restoring integrity. Here we study rupture repair interplay in regenerating Hydra tissues, which cycle through osmotic inflation, pressure release by rupture, and resealing. We utilize bright field imaging of the tissue projected area as a readout of the rupture magnitude before it is arrested. Analyzing these event statistics, we find that the tail of the area-drop distribution is controlled by Ca2+-dependent repair efficiency. When the Ca2+ response is weakened, either by partially blocking gap-junctions mediating the intercellular communication, or by inhibiting stretch-activated Ca2+ channels, the actomyosin force that arrests the rupture process is delayed or reduced. Under these conditions, rare large pressure releases become more likely, and the tail of the distribution crosses over from an exponential behavior, exhibiting a characteristic scale, to a power-law one consistent with a critical-like regime reflecting intermittent rupture propagation. These results identify mechanically evoked Ca2+ activity as a control axis linking repair to rupture statistics in a living tissue. It supports a picture of rupture front advancing by stick-slip-like dynamics as it encounters a heterogeneous mechanical landscape, akin to failure-front propagation in disordered materials.

physics.bio-ph↗

arXiv2025

The Dual Nature of Body-Axis Formation in Hydra Regeneration: Polarity-Morphology Concurrency

The formation of a body-axis is central to animal development and involves both polarity and morphology. While polarity is traditionally associated with biochemical patterning, the morphological aspect of axis formation remains elusive. In regenerating Hydra tissues, we find that morphological evolution in all tissue samples depends on inherited positional information from the donor axis, and a foot precursor emerges early in the process. From the onset of regeneration, the Ca2+ excitations that drive actomyosin forces for tissue reshaping follow a gradient aligned with the head-foot polarity direction. We conclude that polarity and morphological axis progression occur concurrently through interlinked processes, and that the foot plays a dominant role in this process, a role usually attributed to the head organizer. A simple toy model accounts for the observed regeneration dynamics and illustrates the mechanochemical integration of polarity and morphogenesis. We expect the insights from Hydra to be relevant to broader developmental systems.

physics.bio-ph↗

arXiv2024

Fluctuation-Driven Morphological Patterning: A Novel Approach to Morphogenesis

Recent experimental investigations into Hydra regeneration revealed a remarkable phenomenon: the morphological transformation of a tissue fragment from the incipient spherical configuration to a tube-like structure - the hallmark of a mature Hydra - has the dynamical characteristics of a first-order phase-transition, with calcium field fluctuations within the tissue playing an essential role. This morphological transition was shown to be generated by activation over an energy barrier within an effective potential that underlies morphogenesis. Inspired by this intriguing insight, we propose a novel mechanism where stochastic fluctuations drive the emergence of morphological patterns. Thus, the inherent fluctuations determine the nature of the dynamics and are not incidental noise in the background of the otherwise deterministic dynamics. Instead, they play an important role as a driving force that defines the attributes of the pattern formation dynamics and the nature of the transition itself. Here, we present a simple model that captures the essence of this novel mechanism for morphological pattern formation. Specifically, we consider a one-dimensional tissue arranged as a closed contour embedded in a two-dimensional space, where the local curvature of the contour is coupled to a non-negative scalar field. An effective temperature parameter regulates the strength of the fluctuations in the system. The tissue exhibits fluctuations near a circular shape at sufficiently low coupling strengths, but as the coupling strength exceeds some critical value, the circular state becomes unstable. The nature of the transition, namely whether it is a first or a second-order-like transition, depends on the temperature and the effective cutoff on the wavelength of the spatial variations in the system. It is also found that entropic barriers separate the various metastable states of the system.

physics.bio-ph↗

arXiv2023

Universal Calcium fluctuations in Hydra morphogenesis

Understanding how the collective physical processes drive robust morphological transitions in animal development requires the characterization of the relevant fields underlying morphogenesis. Calcium (Ca2+) is known to be such a field. Here we show that the Ca2+ spatial fluctuations, in whole-body Hydra regeneration, exhibit universal properties captured by a field-theoretic model describing fluctuations in a tilted double-well potential. We utilize an external electric field and Heptanol, a drug blocking gap junctions, as two separate controls affecting the Ca2+ activity and pausing the regeneration process in a reversible way. Subjecting the Hydra tissue to an electric field increases the calcium activity and its spatial correlations, while applying Heptanol inhibits the activity and weakens the spatial correlations. The statistical characteristics of the Ca2+ spatial fluctuations, i.e., the coefficient of variation and the skewness - exhibit universal shape distributions across tissue samples and conditions, demonstrating the existence of global constraints over this field. Our analysis shows that the Hydra's tissue resides near the onset of bistability; the local Ca2+ activity in different regions fluctuates between low and high excited states. The controls modulate the dynamics near that onset, preserving the universal characteristics of the Ca2+ fluctuations and, by that, maintaining the tissue's ability to regenerate.

physics.bio-ph↗

arXiv2023

Hydra morphogenesis as phase-transition dynamics

We utilize whole-body Hydra regeneration from a small tissue segment to develop a physics framework for animal morphogenesis. Introducing experimental controls over this process, an external electric field and a drug that blocks gap junctions, allows us to characterize the essential step in the morphological transition - from a spherical shape to an elongated spheroid. We find that spatial fluctuations of the Ca2+ distribution in the Hydra's tissue drive this transition and construct a field-theoretic model that explains the morphological transition as a first-order-like phase transition resulting from the coupling of the Ca2+ field and the tissue's local curvature. Various predictions of this model are verified experimentally.

physics.bio-ph↗

arXiv2021

Calcium fluctuations drive morphological patterning at the onset of Hydra morphogenesis

Morphogenesis in animal development involves significant morphological transitions leading to the emerging body plan of a mature animal. Understanding how the collective physical processes drive robust morphological patterning requires a coarse-grained description of the dynamics and the characterization of the underlying fields. Here I show that calcium spatial fluctuations serve as an integrator field of the electrical-mechanical processes of morphogenesis in whole-body Hydra regeneration and drive the morphological dynamics. We utilize external electric fields to control the developmental process and study a critical transition in morphogenesis, from the initial spheroidal shape of the tissue to an elongated cylindrical shape defining the body plan of a mature animal. Morphogenesis paused under external voltage is associated with a significant increase of the calcium activity compared with the activity supporting normal development. The enhanced calcium activity is characterized by intensified spatial fluctuations, extended spatial correlations across the tissue and faster temporal fluctuations. In contrast, the normal morphogenesis process is characterized by relatively moderate calcium fluctuation activity and restrained spatial correlations. Our methodology of controlling morphogenesis by a physical electric field allows us to gain a global statistical view of the dynamics. It shows that the normalized calcium spatial fluctuations exhibit a universal shape distribution, across tissue samples and conditions, suggesting the existence of a global constrain over these fluctuations. Studying the correlations in space and time of the calcium fluctuation field at the onset of morphogenesis opens a new vista on this process and paints a picture of development analogous to a dynamical phase transition.

physics.bio-ph↗

arXiv2019

Electric-induced reversal of morphogenesis in Hydra

Morphogenesis involves the dynamic interplay of biochemical, mechanical and electrical processes. Here we ask: to what extent can the course of morphogenesis be modulated and controlled by an external electric field? We show that above a critical amplitude, an external electric field can halt morphogenesis in Hydra regeneration. Moreover, above this critical amplitude, the electric field can even lead to reversal dynamics: a fully developed Hydra folds back into its incipient spheroid morphology. The potential to renew morphogenesis is re-exposed when the field is reduced back to amplitudes below criticality. These dynamics are accompanied by modulations of the Wnt3 activity, a central component of the head organizer in Hydra. Reversal of morphogenesis is shown to be triggered by enhanced epithelial electrical excitations, accompanied by intensified calcium activity, indicating that electrical processes play an instructive role to a level that can direct developmental trajectories. Reversal of morphogenesis by external fields, calls for extending its framework beyond programmatic, forward-driven, hierarchical processes.

physics.bio-ph↗

arXiv2015

Single-cell protein dynamics reproduce universal fluctuations in cell populations

Protein variability in single cells has been studied extensively in populations, but little is known about temporal protein fluctuations in a single cell over extended times. We present here traces of protein copy number measured in individual bacteria over multiple generations and investigate their statistical properties, comparing them to previously measured population snapshots. We find that temporal fluctuations in individual traces exhibit the same universal features as those previously observed in populations. Scaled fluctuations around the mean of each trace exhibit the same universal distribution shape as found in populations measured under a wide range of conditions and in two distinct microorganisms. Additionally, the mean and variance of the traces over time obey the same quadratic relation. Analyzing the temporal features of the protein traces in individual cells, reveals that within a cell cycle protein content increases as an exponential function with a rate that varies from cycle to cycle. This leads to a compact description of the protein trace as a 3-variable stochastic process - the exponential rate, the cell-cycle duration and the value at the cycle start - sampled once each cell cycle. This compact description is sufficient to preserve the universal statistical properties of the protein fluctuations, namely, the protein distribution shape and the quadratic relationship between variance and mean. Our results show that the protein distribution shape is insensitive to sub-cycle intracellular microscopic details and reflects global cellular properties that fluctuate between generations.

physics.bio-ph↗

arXiv2012

Universal protein fluctuations in populations of microorganisms

The copy number of any protein fluctuates among cells in a population; characterizing and understanding these fluctuations is a fundamental problem in biophysics. We show here that protein distributions measured under a broad range of biological realizations collapse to a single non-Gaussian curve under scaling by the first two moments. Moreover in all experiments the variance is found to depend quadratically on the mean, showing that a single degree of freedom determines the entire distribution. Our results imply that protein fluctuations do not reflect any specific molecular or cellular mechanism, and suggest that some buffering process masks these details and induces universality.

physics.bio-ph↗