Mikko Haataja

Ferrofluids, colloidal dispersions of magnetic nanoparticles, are renowned for pattern formation like few other materials. The Rosensweig instability of a horizontal ferrofluid-air interface in perpendicular magnetic field is especially well known classically, this instability sets the air-ferrofluid interface into an array of spikes that correspond to a new free energy minimum of the system. However, once the pattern is formed, it does not exhibit any notable thermal or non-equilibrium fluctuations, i.e., it is passive. In this work, we present an active version of the Rosensweig patterns. We realize them experimentally by driving a dispersion of magnetic nanoparticles with an electric field into a non-equilibrium gradient state and by inducing the instability using a magnetic field. The coupling of electric and magnetic forcing leads to patterns that can be adjusted from quiescent classic Rosensweig-like behavior (at low activity) to highly dynamic ones displaying peak and defect dynamics, as well as tunability of structure periodicities beyond what is possible in the classic systems (at high activity). We analyze the results using an active agent-based approach as well as a continuum perspective. We construct a simple equilibrium-like effective Rosensweig model to describe the onset of the patterns and propose a minimal Swift-Hohenberg type model capturing the essential active pattern dynamics. Our results suggest that classic continuum systems exhibiting pattern formation can be activated to display life-inspired non-equilibrium phenomena.

Summary Biomolecular condensates are ubiquitous structures found throughout eukaryotic cells, with nuclear condensates playing a key role in the mesoscale organization and functionality of the genome 1,2 . Protein- and RNA-rich liquid-like condensates form through phase separation on and around chromatin, driving diverse condensate morphologies with varying sphericity and intra-condensate chromatin density 3,4 . However, a unifying set of physical principles underlying these varied interactions and their implications for chromatin organization remains elusive. Here, we develop and experimentally validate a mesoscopic model that bridges the physics of phase separation and chromatin mechanics. Specifically, by integrating computational modeling with experiments using two canonical condensate proteins, the heterochromatin protein HP1α, and the euchromatin protein BRD4, we demonstrate that wetting properties and chromatin stiffness shape condensate morphology, while condensates remodel chromatin mechanics and organization. This two-way interplay is governed by elastocapillarity—the deformation of chromatin by condensate interfacial tension — and resolves discrepancies in nuclear condensate behavior, with emergent behaviors that deviate from the simplest liquid-liquid phase separation (LLPS) models 5–8 . Our findings underscore that nuclear condensates and chromatin cannot be studied in isolation, as they are fundamentally interdependent, impacted by biomolecularly-defined wetting properties, with implications for genome organization, transcriptional regulation, and epigenetic control in diverse phenotypes, including cancer 2,9,10 . Beyond the nucleus, the methodologies we present offer a generalizable platform for exploring multiphase, multicomponent soft matter systems across a broad range of biological and synthetic contexts 11 .

Recombinant Silk Proteins Spiders produce silk fibers with exceptional qualities through non-equilibrium pathways. Engineering approaches to mimic fiber pulling include storage and processing of in vitro protein solutions. In article number 2410421, Markus B. Linder and co-workers propose a minimalist phase diagram for an engineered mini-spidroin solution, serving as a guide to various assembly pathways. They observe metastable liquid–liquid phase separation and aging leading to dynamically arrested aggregate or gel states.

Aqueous two-phase systems (ATPSs), phase-separating solutions of water soluble but mutually immiscible molecular species, offer fascinating prospects for selective partitioning, purification, and extraction. Here, we formulate a general Brownian dynamics based coarse-grained simulation model for an ATPS of two water soluble but mutually immiscible polymer species. Including additional solute species into the model is straightforward, which enables capturing the assembly and partitioning response of, e.g., nanoparticles (NPs), additional macromolecular species, or impurities in the ATPS. We demonstrate that the simulation model captures satisfactorily the phase separation, partitioning, and interfacial properties of an actual ATPS using a model ATPS in which a polymer mixture of dextran and polyethylene glycol (PEG) phase separates, and magnetic NPs selectively partition into one of the two polymeric phases. Phase separation and NP partitioning are characterized both via the computational model and experimentally, under different conditions. The simulation model captures the trends observed in the experimental system and quantitatively links the partitioning behavior to the component species interactions. Finally, the simulation model reveals that the ATPS interface fluctuations in systems with magnetic NPs as a partitioned species can be controlled by the magnetic field at length scales much smaller than those probed experimentally to date. • Model for magnetically responsive aqueous two-phase systems. • Surface tension prediction via computational modeling for aqueous two-phase systems. • Computational prediction of partitioning response in aqueous two-phase systems. • Control of interface fluctuations at smaller scales than yet probed experimentally.

In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid-liquid phase separation and a further transition into a gel-like state. In the present work, we formulate a thermodynamically consistent kinetic framework to study the interplay between phase separation, chemical reaction, and aging in spatially inhomogeneous macromolecular mixtures. A numerical algorithm is also proposed to simulate domain growth from collisions of liquid and gel domains via passive Brownian motion in both two and three spatial dimensions. Our results show that the coarsening behavior is significantly influenced by the degree of gelation and Brownian motion. The presence of a gel phase inside condensates strongly limits the diffusive transport processes, and Brownian motion coalescence controls the coarsening process in systems with high area/volume fractions of gel-like condensates, leading to the formation of interconnected domains with atypical domain growth rates controlled by size-dependent translational and rotational diffusivities.

Abstract Recombinant silk proteins provide a route toward sustainable and biocompatible materials. For making such materials, the assembly process from dilute protein into a functional material is central. The assembly mechanism in engineered materials is by necessity different from the natural ones—this poses challenges but also opens opportunities for scaling up and for developing novel properties. The phase behavior of a mini‐spidroin, NT‐2Rep‐CT is studied, which is a widely studied variant of recombinant silk. NT‐2Rep‐CT can be triggered to assemble by lowering the pH, but even at high pH—considered as storage conditions—it can be in various states, such as forming condensates, clusters, gels, and soluble protein. It is shown how its assembly phases evolve through both metastable and dynamically arrested states. The observed behavior of silk protein solutions is highly complex, and elements thereof from phase diagrams associated with polymers, colloidal systems, and globular proteins are found. Based on the characterization of cluster formation and structural intermediates, a minimalist phase diagram is proposed for NT‐2Rep‐CT and argues that the understanding and insight into silk assembly via its phase behavior, and especially the arrested states, is central for designing recombinant silk proteins and their processing for materials applications.

Multicomponent macromolecular mixtures often form higher-order structures, which may display non-ideal mixing and aging behaviors. In this work, we first propose a minimal model of a quaternary system that takes into account the formation of a complex via a chemical reaction involving two macromolecular species; the complex may then phase separate from the buffer and undergo a further transition into a gel-like state. We subsequently investigate how physical parameters such as molecular size, stoichiometric coefficients, equilibrium constants, and interaction parameters affect the phase behavior of the mixture and its propensity to undergo aging via gelation. In addition, we analyze the thermodynamic stability of the system and identify the spinodal regions and their overlap with gelation boundaries. The approach developed in this work can be readily generalized to study systems with an arbitrary number of components. More broadly, it provides a physically based starting point for the investigation of the kinetics of the coupled complex formation, phase separation, and gelation processes in spatially extended systems.

Amyloid fibrils have long been associated with many neurodegenerative diseases. The conventional picture of the formation and proliferation of fibrils from unfolded proteins comprises primary and secondary nucleation of oligomers followed by elongation and fragmentation thereof. In this work, we first employ extensive all-atom molecular dynamics (MD) simulations of short peptides to investigate the governing processes of fibril growth at the molecular scale. We observe that the peptides in the bulk solution can bind onto and subsequently diffuse along the fibril surface, which leads to fibril elongation via either bulk- or surface-mediated docking mechanisms. Then, to guide the quantitative interpretation of these observations and to provide a more comprehensive picture of the growth kinetics of single fibrils, a continuum model which incorporates the key processes observed in the MD simulations is formulated. The model is employed to investigate how relevant physical parameters affect the kinetics of fibril growth and identify distinct growth regimes. In particular, it is shown that fibrils which strongly bind peptides may undergo a transient exponential growth phase in which the entire fibril surface effectively acts as a sink for peptides. We also demonstrate how the relevant model parameters can be estimated from the MD trajectories. Our results provide compelling evidence that the overall fibril growth rates are determined by both bulk and surface peptide fluxes, thereby contributing to a more fundamental understanding of the growth kinetics of amyloid-like fibrils.

Aqueous two-phase systems (ATPSs), that is, phase-separating solutions of water soluble but mutually immiscible molecular species, offer fascinating prospects for selective partitioning, purification, and extraction. Here, we formulate a general Brownian dynamics based coarse-grained simulation model for a polymeric ATPS comprising two water soluble but mutually immiscible polymer species. A third solute species, representing, e.g., nanoparticles (NPs), additional macromolecular species, or impurities can readily be incorporated into the model. We demonstrate that the model captures satisfactorily the phase separation, partitioning, and interfacial properties of a model ATPS composed of a polymer mixture of dextran and polyethylene glycol (PEG) in which magnetic NPs selectively partition into one of the two polymeric phases. The NP partitioning is characterized both via the computational model and experimentally under different conditions. The simulation model captures the trends observed in the experiments and quantitatively links the partitioning behavior to the component species interactions. Finally, the response of the simulation model to external magnetic field, with the magnetic NPs as the additional partitioned component, shows that the ATPS interface fluctuations can be controlled by the magnetic field at length scales much smaller than those probed experimentally to date.

The formation of amyloid fibrils is a complex phenomenon that remains poorly understood at the atomic scale. Herein, we perform extended unbiased all-atom simulations in explicit solvent of a short amphipathic peptide to shed light on the three mechanisms accounting for fibril formation, namely, nucleation via primary and secondary mechanisms, and fibril growth. We find that primary nucleation takes place via the formation of an intermediate state made of two laminated β-sheets oriented perpendicular to each other. The amyloid fibril spine subsequently emerges from the rotation of these β-sheets to account for peptides that are parallel to each other and perpendicular to the main axis of the fibril. Growth of this spine, in turn, takes place via a dock-and-lock mechanism. We find that peptides dock onto the fibril tip either from bulk solution or after diffusing on the fibril surface. The latter docking pathway contributes significantly to populate the fibril tip with peptides. We also find that side chain interactions drive the motion of peptides in the lock phase during growth, enabling them to adopt the structure imposed by the fibril tip with atomic fidelity. Conversely, the docked peptide becomes trapped in a local free energy minimum when docked-conformations are sampled randomly. Our simulations also highlight the role played by nonpolar fibril surface patches in catalyzing and orienting the formation of small cross-β structures. More broadly, our simulations provide important new insights into the pathways and interactions accounting for primary and secondary nucleation as well as the growth of amyloid fibrils.

Polymorphic 2D materials have recently emerged as promising candidates for use in nanoelectronic devices by way of their ability to undergo structural phase transformations induced by external fields. Under cyclic transformations, however, induced interfacial defects may proliferate and compromise the system properties. Herein, we first employ geometric analysis to classify such defects generated during the 2H ↔ 1T and 2H ↔ 1T' transformations in group VI transition-metal dichalcogenide monolayers. Then, simulations of a mesoscale model with atomistic spatial resolution are conducted to assess the proliferation of such defects during cyclic 2H ↔ 1T transformations. It is shown that defect densities reach a steady state, with the 2H phase remaining more pristine than the 1T and 1T' states. We expect that the effects of these defects on the device performance are application-dependent and will require further inquiry.

Complex fibrillar networks mediate liquid-liquid phase separation of biomolecular condensates within the cell. Mechanical interactions between these condensates and the surrounding networks are increasingly implicated in the physiology of the condensates and yet, the physical principles underlying phase separation within intracellular media remain poorly understood. Here, we elucidate the dynamics and mechanics of liquid-liquid phase separation within fibrillar networks by condensing oil droplets within biopolymer gels. We find that condensates constrained within the network pore space grow in abrupt temporal bursts. The subsequent restructuring of condensates and concomitant network deformation is contingent on the fracture of network fibrils, which is determined by a competition between condensate capillarity and network strength. As a synthetic analog to intracellular phase separation, these results further our understanding of the mechanical interactions between biomolecular condensates and fibrillar networks in the cell.

The mission of the DOE Energy Frontier Research Centers CCDM (2014-2018) and CCM (2018-2021) was to theoretically develop, computationally apply, and experimentally validate electronic structure methods for all materials, with a focus on the complex materials, especially layered and two-dimensional materials, strongly-correlated materials, and liquid water. This was achieved by over 200 published journal articles authored by about 17 senior investigators from physics and chemistry and from theory, computation, and experiment, plus their collaborators. In particular, the Centers confirmed the predictive power of the SCAN (strongly constrained and appropriately normed) density functional, which was constructed to satisfy 17 known exact constraints and several appropriate norms. Without being fitted to real bonded systems, and at a modest computational cost, SCAN correctly predicted covalent, ionic, metallic, hydrogen, and van der Waals bonds in many challenging materials. SCAN gave an improved description of defects in semiconductors, surface properties of metals, seven phases of ice, liquid water, liquid and supercooled silicon, subtle structural distortions in ferroelectrics, formation energies and structural predictions for solids, and critical pressures for structural phase transitions. Perhaps most remarkably, SCAN correctly described some strongly-correlated materials that were previously believed to be beyond the reach of density-functional approximations. SCAN is the only density functional that correctly predicts the band gap closing under chemical doping of the cuprate high-temperature superconducting materials. SCAN also predicts a landscape of competing stripe and magnetic phases in the cuprates. For some materials with some codes, SCAN has convergence problems that are greatly reduced by the CCM-developed r2SCAN, without loss of accuracy or rigor. SCAN and r2SCAN still make some self-interaction error, which is greatly reduced by the CCDM/ CCM-developed local orbital scaling correction (LOSC). These Centers further proved that the fundamental energy gaps of a solid from an orbital energy difference and from total energy differences are the same for a large class of generalized Kohn-Sham (GKS) functionals, including SCAN and standard hybrid functionals, and that symmetry breaking arises when a dynamic density fluctuation drops to zero frequency. The Centers identified new mechanisms for catalysis in layered materials with ions intercalated between the layers, investigated charge density waves both in model systems and in real layered materials, studied changes of band gap with the number of layers, and explored topological ultrathin films, bent nanoribbons, and defects.

The physical properties of a semicrystalline polymer thin film are intimately related to the morphology of its crystalline domains. While the mechanisms underlying crystallization of flat-on oriented polymer crystals are well known, similar mechanisms remain elusive for edge-on oriented thin films due to the propensity of substantially thin films to adopt flat-on orientations. Here, we employ an epitaxial polymer-substrate relationship to enforce edge-on crystallization in thin films. Using matrix-assisted pulsed laser evaporation (MAPLE), we deposit films in which crystal nucleation is spatially separated from subsequent epitaxial crystallization. These experiments, together with phase-field simulations, demonstrate a highly anisotropic and localized material depletion during edge-on crystallization. These results provide deeper insight into the physics of polymer crystallization under confinement and introduce a processing motif in the crystallization of ultrathin structured films.