Research Overview
I investigate how complex structures and dynamic behaviors emerge in living and physical systems (usually) far from equilibrium, with a primary focus on problems in biophysics. Many central phenomena in biology, such as morphogenesis, stress responses, and collective migration, arise not from precise molecular blueprints, but from the interplay of fluctuations, mechanical constraints, and biochemical interactions. My research develops theoretical frameworks grounded in statistical mechanics, nonlinear dynamics, and field theory, aimed at revealing the physical principles that govern such processes. A key feature of my work is close collaboration with experimental groups, enabling the direct testing and refinement of theoretical predictions in well-controlled biological systems such as Hydra, bacterial colonies, and single-cell models, as well as in quantum fluids and superconductors. This theory-experiment synergy allows us to explore how order, variability, and robustness coexist in complex living matter.
- Morphogenesis: Beyond Turing—A Field-Theoretic Approach to Shape Formation
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Despite decades of research, there is still no broadly accepted theoretical framework for morphogenesis—the process by which biological tissues acquire their shape. The most influential idea to date, Turing’s reaction-diffusion mechanism, proposes that patterns arise from the interaction of chemical species that diffuse and react at different rates. While elegant and fruitful in some contexts, this framework suffers from fundamental limitations: it applies only to a narrow class of instabilities, often requires fine-tuned parameters, and most critically, it fails to capture the intimate coupling between chemical patterning and tissue mechanics - a core aspect of real biological morphogenesis.
My study is focused on Hydra regeneration, an ideal model system due to its simple anatomy, well-characterized cellular compo
sition, and the clear morphological transformation from a spherical aggregate to a tubular body plan during regeneration. This transition occurs spontaneously, without centralized control, and is robust despite being driven by highly dynamic and fluctuating tissue rearrangements.
My approach uses field-theoretic and dynamical systems tools to model morphogenesis not as a deterministic unfolding of pre-patterns, but as the evolution of a morphological potential landscape shaped by mechanical and biochemical interactions. In this framework, stochastic fluctuations are not merely noise, but act as essential drivers that can induce transitions between metastable morphological states.
A key prediction of this approach is the occurrence of stochastic morphological swings—transient transitions between spherical and tubular shapes that occur as the tissue explores its morphological landscape. This prediction was experimentally verified in regenerating Hydra tissues subjected to periodic electric fields, revealing the dynamical interplay between noise, mechanics, and morphology. This result exemplifies a new paradigm for morphogenesis, one that moves beyond reaction-diffusion and treats shape formation as a fluctuation-driven, mechanically coupled process in an evolving field.
Stochastic morphological swings during Hydra regeneration
- Cells in Disrupted States and Emergent Cellular Behavior
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Biological systems, even at the scale of a single E. coli bacterium, are astonishingly complex. Each cell contains many thousands
of molecular species involved in metabolism, signaling, transport, gene expression, and stress response, all finely tuned to ensure that the cell fulfills its functional roles with remarkable efficiency. However, the strong coupling between many of these components makes it essentially impossible to isolate subsystems or apply a straightforward reductionist approach. As a result, faithfully modelling the full dynamics of a living cell remains far beyond reach.
picture drawn by the geneticist Jérôme Lejeune
Yet, when a cell is exposed to conditions it was not evolutionarily "designed" to handle - such as sudden antibiotic exposure or extreme stress - it may enter what we call a “disrupted state”.In this regime, the internal regulation becomes transiently compromised, and the biological system begins to exhibit many characteristic features of systems governed by statistical physics. It may exhibit chaotic dynamics, loss of regulatory control, and glassy features such as aging, where recovery timescales grow with the duration of exposure and memory of the past is retained over long times. These are signatures not of evolved robustness, but of high-dimensional dynamics operating without reliable internal feedback.
My approach to understanding this regime is to analyze the disrupted state as a physical system, and then trace the emergence of regulated cellular behavior by perturbing slightly away from disruption. To do so, I use a range of tools, including random network models, random matrix theory, and a Petri net–based formalism to describe transitions between regulatory configurations and functional states.
This framework led to key insights presented in our Nature paper, where we showed that bacterial recovery after antibiotic-induced stress exhibits universal, long-tailed distributions of return times, consistent with dynamics near a critical point in a disordered system. Importantly, the distribution of recovery times depends strongly on the duration of the stress - a hallmark of aging dynamics. These features emerged naturally from random network models without requiring detailed molecular mechanisms, suggesting that persistence and resilience are emergent, collective phenomena, not just outcomes of specific genetic circuits.
Kymograph of microfluidic observations of the growth arrest of single E. coli bacteria subjected to SHX and their recovery.
Link to an article in "haaretz"
- Chemotaxis: Collective Dynamics and Pattern Formation in Active Biological Matter
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As mentioned above, the internal dynamics of a single cell, such as E. Coli, is extraordinarily complex. Yet when observed under regular, non-stressful conditions, individual bacterial behavior tends to be robust and predictable. Nevertheless, when many such cells interact, even in seemingly simple environments, they can give rise to rich and non-trivial collective behaviors that are often not easily inferred from single-cell dynamics.
From a physical perspective, E. coli can be viewed as a form of self-propelled active matter with intrinsic polarity. Even at this coarse level of description, such systems can exhibit emergent phenomena including phase transitions, turbulent-like flows, chemotactic instabilities, and complex spatiotemporal patterns. In my research I develop and apply tools from statistical physics and nonlinear dynamics to understand the physics of these collective behaviors, and to explore how biological function and adaptability emerge in dense, interacting systems of active agents.
One example of this approach is our study of E. coli colonies under unfavorable, acidic conditions. In these environments, the bacteria consume protons and thereby create self-generated chemical gradients. This triggers negative chemotaxis, where cells move away from areas they have acidified. We showed that this feedback leads to a chemotactic instability, producing dense, localized condensates of bacteria. Over longer timescales, these condensates merge through long-range interactions, resulting in coarsening dynamics and spatial structures that evolve via screened aggregation.
Pattern formation in the density of E. Coli due to negative chemotaxis
- Vortex Physics: Weak Solutions, Core Reconstruction, and Competing Orders
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The traditional description of vortex dynamics in superfluids is based on the Gross–Pitaevskii equation (GPE), which models the condensate wavefunction as a smooth field everywhere except at isolated vortex cores. While the GPE has been enormously successful, it implicitly assumes that the solution is valid at all points in space. This approach overlooks the possibility of "weak solutions"—configurations that minimize the action but fail to satisfy the GPE on a set of measure zero. These weak solutions are not mathematical artifacts; they capture essential physics at the vortex core, where the standard mean-field description breaks down.
To address this, we developed the Popov formalism, a hydrodynamic field theory in which weak solutions are treated as strong solutions. This framework reveals a striking phenomenon: the vortex core undergoes a non-analytic reconstruction, where the order parameter vanishes not just at a point but along a finite cut. This reconstruction endows each vortex with internal degrees of freedom—akin to a hidden "dipole moment"—that can influence the dynamics and, in principle, be revealed through carefully designed measurements.
One major consequence of this internal structure is the instability of the Abrikosov lattice. The Abrikosov lattice, a triangular array of vortices, is the stable ground state of a rotating superfluid or a type-II superconductor under a magnetic field, as first described by Abrikosov in the 1950s. However, once vortex cores are allowed to deform, the simple triangular lattice can no longer minimize the energy. Instead, the vortices develop orientational order of their internal degrees of freedom, leading to superlattice-like structures. For finite numbers of vortices, this gives rise to “magic numbers” that determine preferred, symmetric configurations of the vortex array.
Cuts orientations in clusters of vortices undergoing a core reconstruction
While these ideas have been developed primarily for neutral superfluids, the same principles apply, in principle, to superconductors, though the situation is more complex. At finite temperature, the vortex core in a superconductor contains a normal (non-superconducting) region, complicating the interplay between superflow and core reconstruction. Moreover, many superconductors—especially low-dimensional or strongly spin–orbit coupled systems—can exhibit multiple competing order parameters, which further enrich and complicate vortex behavior.
In recent work, we explored vortex physics in the presence of competing superconducting orders, focusing on layered materials such as NbSe₂. In thin superconducting films, magnetic field lines penetrate in the form of vortices, and their magnetic field decays over a characteristic length scale known as the Pearl length. This length, which governs the strength of vortex–vortex interactions and magnetic screening, is expected to depend inversely on the film thickness, reflecting the reduced screening ability of thinner films. However, we showed that in materials where surface and bulk superconducting states coexist, this scaling behavior can break down. In ultrathin samples, the surface superconductivity can dominate, leading to an anomalous saturation of the Pearl length that deviates sharply from the conventional 1/thickness prediction. These findings reveal a novel form of competition between superconducting orders, manifested directly in the Peral length of the vortex.
Pearl length as a function of the film thickness
