publications

2025

1. Phase Behavior of Cacio e Pepe Sauce

   Giacomo Bartolucci, Daniel Maria Busiello, Matteo Ciarchi, and 5 more authors

   Physics of Fluids, Apr 2025

   Abs DOI

   “Pasta alla Cacio e pepe” is a traditional Italian dish made with pasta, pecorino cheese, and pepper. Despite its simple ingredient list, achieving the perfect texture and creaminess of the sauce can be challenging. In this study, we systematically explore the phase behavior of Cacio e pepe sauce, focusing on its stability at increasing temperatures for various proportions of cheese, water, and starch. We identify starch concentration as the key factor influencing sauce stability, with direct implications for practical cooking. Specifically, we delineate a regime where starch concentrations below 1% (relative to cheese mass) lead to the formation of system-wide clumps, a condition determining what we term the “Mozzarella Phase” and corresponding to an unpleasant and separated sauce. Additionally, we examine the impact of cheese concentration relative to water at a fixed starch level, observing a lower critical solution temperature that we theoretically rationalized by means of a minimal effective free-energy model. We further analyze the effect of a less traditional stabilizer, trisodium citrate, and observe a sharp transition from the Mozzarella Phase to a completely smooth and stable sauce, in contrast to starch-stabilized mixtures, where the transition is more gradual. Finally, we present a scientifically optimized recipe based on our findings, enabling a consistently flawless execution of this classic dish.

2. The Droplet Size Distribution and Its Dynamics in Chemically Active Emulsions

   Jonathan Bauermann, Giacomo Bartolucci, Christoph A. Weber, and 1 more author

   Jan 2025

   Abs DOI

   We present a dynamic theory for the droplet size distribution in chemically active emulsions, considering a simple ternary mixture with a conserved density. We show that the collective behavior of many droplets, such as monodispersity, emerges through a coupling of the conserved density in the far field. Using our theory, we determine the stationary state of such emulsions and characterize the relaxation of the droplet size distributions at late times. A key finding is a universal scaling behavior, leading to the collapse of the rescaled size distributions at late times. Our results suggest that the key features of our dynamic theory are generic and apply to the broader class of multi-component systems with conservation laws and active chemical reactions.

3. Spatiotemporal Organization of Chemical Oscillators via Phase Separation

   Jonathan Bauermann, Giacomo Bartolucci, and Artemy Kolchinsky

   Jul 2025

   Abs DOI

   We study chemical oscillators in the presence of phase separation. By imposing timescale separation between slow reactions and fast diffusion, we define a dynamics at phase equilibrium for the relevant degrees of freedom. We demonstrate that phase separation affects reaction kinetics by localizing reactants within phases, allowing for control of oscillator frequency and amplitude. The analysis is validated with a spatial model. Finally, relaxing the timescale separation between reactions and diffusion leads to waves of phase equilibria at mesoscopic scales.

4. Theory of Non-Dilute Binding and Surface Phase Separation Applied to Membrane-Binding Proteins

   Xueping Zhao, Daxiao Sun, Giacomo Bartolucci, and 3 more authors

   eLife, Jun 2025

   Abs DOI

   Surface binding and surface phase separation of cytosolic scaffold proteins on lipid membranes are involved in many cellular processes, such as cell signaling, cell adhesion, and cortex regulation. However, the interplay between surface binding and surface phase separation is poorly understood. In this work, we study this interplay by deriving a general thermodynamic model and applying it to in vitro reconstitution experiments of membrane-binding proteins involved in tight junction initiation. Our theory extends the classical surface binding isotherm to account for non-dilute and heterogeneous conditions where components can phase separate. We use our theory to demonstrate how surface phase separation is governed by the interaction strength among membrane-bound scaffold proteins and their binding affinity to the membrane surface. Comparing the theory to reconstitution experiments, we show that tuning the oligomerization state of the adhesion receptors in the membrane controls surface phase transition and patterning of the scaffold protein ZO1. These findings suggest a fundamental role of the interplay between non-dilute surface binding and surface phase separation in forming the tight junction. More broadly, our work highlights non-dilute surface binding and surface phase separation as a common organizational principle for membrane-associated structures in living cells.

2024

1. The Interplay between Biomolecular Assembly and Phase Separation

   Giacomo Bartolucci, Ivar S. Haugerud, Thomas C. T. Michaels, and 1 more author

   eLife, May 2024

   Abs DOI

   Many biological functions and dysfunctions rely on two fundamental processes, molecular assembly and the formation of condensed phases such as biomolecular condensates. Condensed phases generally form via phase separation, while molecular assemblies are clusters of molecules of various sizes, shapes, and functionality. We developed a theory that relies on thermodynamic principles to understand the interplay between molecular assembly and phase separation. We propose two prototypical classes of protein interactions and characterize their different equilibrium states and relaxation dynamics. We obtain results consistent with recent in vitro experimental observations of reconstituted proteins, including anomalous size distribution of assemblies, the gelation of condensed phases, and the change in condensate volume during ageing. Our theory provides the framework to unravel the mechanisms underlying physiological assemblies essential for cellular function, and aberrant assemblies that are associated with several neurodegenerative disorders.

2. Critical Transition between Intensive and Extensive Active Droplets

   Jonathan Bauermann, Giacomo Bartolucci, Job Boekhoven, and 2 more authors

   Sep 2024

   Abs DOI

   Emulsions ripen with an average droplet size increasing in time. In chemically active emulsions, coarsening can be absent, leading to a non-equilibrium steady state with mono-disperse droplet sizes. By considering a minimal model for phase separation and chemical reactions maintained away from equilibrium, we show that there is a critical transition in the conserved quantity between two classes of chemically active droplets: intensive and extensive ones. Single intensive active droplets reach a stationary size mainly controlled by the reaction-diffusion length scales. Intensive droplets in an emulsion interact only weakly, and the stationary size of a single droplet approximately sets the size of each droplet. On the contrary, the size of a single extensive active droplet scales with the system size, similar to passive phases. In an emulsion of many extensive droplets, their sizes become stationary only due to interactions among them. We discuss how the critical transition between intensive and extensive active droplets affects shape instabilities, including the division of active droplets, paving the way for the observation of successive division events in chemically active emulsions

3. Theory for Sequence Selection via Phase Separation and Oligomerization

   Ivar S. Haugerud, Giacomo Bartolucci, Dieter Braun, and 1 more author

   Oct 2024

   Abs DOI

   Non-equilibrium selection pressures were proposed for the formation of oligonucleotides with rich functionalities encoded in their sequences, such as catalysis. Since phase separation was shown to direct various chemical processes, we ask whether condensed phases can provide mechanisms for sequence selection. To answer this question, we use non-equilibrium thermodynamics and describe the reversible oligomerization of different monomers to sequences at non-dilute conditions prone to phase separation. We find that when sequences oligomerize, their interactions give rise to phase separation, boosting specific sequences’ enrichment and depletion. Our key result is that phase separation gives rise to a selection pressure for the oligomerization of specific sequence patterns when fragmentation maintains the system away from equilibrium. Specifically, slow fragmentation favors alternating sequences that interact well with their environment (more cooperative), while fast fragmentation selects sequences with extended motifs capable of specific sequence interactions (less cooperative). Our results highlight that out-of-equilibrium condensed phases could provide versatile hubs for Darwinian-like evolution toward functional sequences, both relevant for the molecular origin of life and de novo life.

2023

1. Sequence Self-Selection by Cyclic Phase Separation

   Giacomo Bartolucci, Adriana Calaça Serrão, Philipp Schwintek, and 7 more authors

   Proceedings of the National Academy of Sciences, Oct 2023

   Abs DOI

   The emergence of functional oligonucleotides on early Earth required a molecular selection mechanism to screen for specific sequences with prebiotic functions. Cyclic processes such as daily temperature oscillations were ubiquitous in this environment and could trigger oligonucleotide phase separation. Here, we propose sequence selection based on phase separation cycles realized through sedimentation in a system subjected to the feeding of oligonucleotides. Using theory and experiments with DNA, we show sequence-specific enrichment in the sedimented dense phase, in particular of short 22-mer DNA sequences. The underlying mechanism selects for complementarity, as it enriches sequences that tightly interact in the dense phase through base-pairing. Our mechanism also enables initially weakly biased pools to enhance their sequence bias or to replace the previously most abundant sequences as the cycles progress. Our findings provide an example of a selection mechanism that may have eased screening for auto-catalytic self-replicating oligonucleotides.

2. Formation of Liquid Shells in Active Droplet Systems

   Jonathan Bauermann, Giacomo Bartolucci, Job Boekhoven, and 2 more authors

   Physical Review Research, Dec 2023

   Abs DOI

   We study a chemically active binary mixture undergoing phase separation and show that under nonequilibrium conditions, stable liquid spherical shells can form via a spinodal instability in the droplet center. A single liquid shell tends to grow until it undergoes a shape instability beyond a critical size. In an active emulsion, many stable and stationary liquid shells can coexist. We discuss conditions under which liquid shells are stable and dominant as compared to regimes where droplets undergo shape instabilities and divide.

3. Liquid Spherical Shells Are a Non-Equilibrium Steady State of Active Droplets

   Alexander M. Bergmann, Jonathan Bauermann, Giacomo Bartolucci, and 6 more authors

   Nature Communications, Oct 2023

   Abs DOI

   Liquid-liquid phase separation yields spherical droplets that eventually coarsen to one large, stable droplet governed by the principle of minimal free energy. In chemically fueled phase separation, the formation of phase-separating molecules is coupled to a fuel-driven, non-equilibrium reaction cycle. It thus yields dissipative structures sustained by a continuous fuel conversion. Such dissipative structures are ubiquitous in biology but are poorly understood as they are governed by non-equilibrium thermodynamics. Here, we bridge the gap between passive, close-to-equilibrium, and active, dissipative structures with chemically fueled phase separation. We observe that spherical, active droplets can undergo a morphological transition into a liquid, spherical shell. We demonstrate that the mechanism is related to gradients of short-lived droplet material. We characterize how far out of equilibrium the spherical shell state is and the chemical power necessary to sustain it. Our work suggests alternative avenues for assembling complex stable morphologies, which might already be exploited to form membraneless organelles by cells.

2021

1. Controlling Composition of Coexisting Phases via Molecular Transitions

   Giacomo Bartolucci, Omar Adame-Arana, Xueping Zhao, and 1 more author

   Biophysical Journal, Nov 2021

   Abs DOI

   Phase separation and transitions among different molecular states are ubiquitous in living cells. Such transitions can be governed by local equilibrium thermodynamics or by active processes controlled by biological fuel. It remains largely unexplored how the behavior of phase-separating systems with molecular transitions differs between thermodynamic equilibrium and cases in which the detailed balance of the molecular transition rates is broken because of the presence of fuel. Here, we present a model of a phase-separating ternary mixture in which two components can convert into each other. At thermodynamic equilibrium, we find that molecular transitions can give rise to a lower dissolution temperature and thus reentrant phase behavior. Moreover, we find a discontinuous thermodynamic phase transition in the composition of the droplet phase if both converting molecules attract themselves with similar interaction strength. Breaking the detailed balance of the molecular transition leads to quasi-discontinuous changes in droplet composition by varying the fuel amount for a larger range of intermolecular interactions. Our findings showcase that phase separation with molecular transitions provides a versatile mechanism to control properties of intracellular and synthetic condensates via discontinuous switches in droplet composition.

2. Thermodynamics of Wetting, Prewetting and Surface Phase Transitions with Surface Binding

   Xueping Zhao, Giacomo Bartolucci, Alf Honigmann, and 2 more authors

   New Journal of Physics, Dec 2021

   Abs DOI

   In living cells, protein-rich condensates can wet the cell membrane and surfaces of membrane-bound organelles. Interestingly, many phase-separating proteins also bind to membranes leading to a molecular layer of bound molecules. Here we investigate how binding to membranes affects wetting, prewetting and surface phase transitions. We derive a thermodynamic theory for a three-dimensional bulk in the presence of a two-dimensional, flat membrane. At phase coexistence, we find that membrane binding facilitates complete wetting and thus lowers the wetting angle. Moreover, below the saturation concentration, binding facilitates the formation of a thick layer at the membrane and thereby shifts the prewetting phase transition far below the saturation concentration. The distinction between bound and unbound molecules near the surface leads to a large variety of surface states and complex surface phase diagrams with a rich topology of phase transitions. Our work suggests that surface phase transitions combined with molecular binding represent a versatile mechanism to control the formation of protein-rich domains at intra-cellular surfaces.

2018

1. Transition Path Theory from Biased Simulations

   Giacomo Bartolucci, Simone Orioli, and Pietro Faccioli

   The Journal of Chemical Physics, Aug 2018

   DOI