arXiv subjects

William M. Jacobs

Publications and source records attributed to William M. Jacobs.

At least 19 recordsLinked to original sources

arXiv2026

Co-condensation and multivalency enable acetylation-sensitive, concentration-robust assembly of BRD4 condensates

Biomolecular condensates must assemble at specific locations and times inside living cells to perform their biological functions. However, it remains unclear how condensate formation achieves high spatiotemporal precision, responding sensitively to local chemical modifications while remaining robust to fluctuations in protein concentration. Here we study chromatin-associated BRD4 condensates to identify a physical mechanism that enables this combination of sensitivity and robustness. Using an ultra-coarse-grained molecular-dynamics model, we show that co-condensation of BRD4 with chromatin enables rapid assembly below the bulk coexistence concentration, thereby suppressing off-chromatin condensation and enhancing spatial selectivity. Multivalent binding between BRD4 and acetylated histone tails sharpens the dependence of co-condensation on acetylation density through combinatorial effects, increasing contrast between highly acetylated regions and weakly acetylated background chromatin. This mechanism explains how co-condensation and multivalent binding jointly enable sensitive yet robust spatiotemporal targeting by chromatin-associated condensates.

physics.bio-ph↗

arXiv2026

Cooperation and competition of basepairing and electrostatic interactions in mixtures of DNA nanostars and polylysine

Phase separation in biomolecular mixtures can result from multiple physical interactions, which may act either complementarily or antagonistically. In the case of protein-nucleic acid mixtures, charge plays a key role but can have contrasting effects on phase behavior. Attractive electrostatic interactions between oppositely charged macromolecules are screened by added salt, reducing the driving force for coacervation. By contrast, base pairing interactions between nucleic acids are diminished by charge repulsion and thus enhanced by added salt, promoting associative phase separation. To explore this interplay, we combine experiment and theory to map the complex phase behavior of a model solution of poly-L-lysine (PLL) and self-complementary DNA nanostars (NS) as a function of temperature, ionic strength, and macromolecular composition. Despite having opposite salt dependences, we find that electrostatics and base pairing cooperate to stabilize NS-PLL coacervation at high ionic strengths and temperatures, leading to two- or three-phase coexistence under various conditions. We further observe a variety of kinetic pathways to phase separation at different salt concentrations, resulting in the formation of nonequilibrium aggregates or droplets whose compositions evolve on long timescales. Finally, we show that the cooperativity between electrostatics and base pairing can be used to create immiscible coacervates that partition various NS species at intermediate salt concentrations. Our results illustrate how the interplay between distinct interaction modes can greatly increase the complexity of the phase behavior relative to systems with a single type of interaction.

cond-mat.soft↗

arXiv2026

Polydisperse polymer fractionation between phases

Polymer mixtures fractionate between phases depending on their molecular weight. Consequently, by varying solvent conditions, a polydisperse polymer sample can be separated between phases so as to achieve a particular molecular weight distribution in each phase. In principle, predictive physics-based theories can help guide separation design and interpret experimental phase-diagram and fractionation measurements. Even so, applying the standard Flory-Huggins model can require numerical computations that hamper the predictions considering the full molecular weight distribution. Here, we apply a recently-derived exact analytical solution of multi-component Flory-Huggins theory for polydisperse homopolymers to understand the principles of polymer fractionation for common molecular weight distributions. Consistent with previous studies, the method highlights the sensitivity of polymer fractionation to the shape, and in particular the tails, of this distribution. Our results provide a systematic approach to evaluate the full molecular weight distribution in phase coexistence calculations over the possible composition space.

cond-mat.soft↗

arXiv2026

A thermodynamic metric quantitatively predicts disordered protein partitioning and multicomponent phase behavior

Intrinsically disordered regions (IDRs) of proteins mediate sequence-specific interactions underlying diverse cellular processes, including the formation of biomolecular condensates. Although IDRs strongly influence condensate compositions, quantitative frameworks that predict and explain their phase behavior in complex mixtures remain lacking. Here we introduce a thermodynamic model that quantitatively predicts the behavior of arbitrary combinations of IDRs across a wide range of concentrations, with accuracy comparable to state-of-the-art simulations. The model learns low-dimensional, context-independent representations of IDR sequences that combine to form mixture representations, producing context-dependent interactions. These representations define a thermodynamic metric space in which distances between IDRs correspond directly to differences in their thermodynamic properties. We show that the model predicts multicomponent phase diagrams in quantitative agreement with molecular simulations without being trained on free-energy or phase-coexistence data. The metric space provides geometrically intuitive predictions of IDR partitioning, multicomponent condensation, and context-dependent mutational effects, addressing several central problems in IDR biophysics within a single model. Systematic interrogation of the learned representations reveals how amino-acid composition and sequence patterning jointly determine mixture thermodynamics. Together, our results establish a unified and interpretable framework for predicting and understanding the behavior of complex mixtures of IDRs and other sequence-dependent biomolecules.

cond-mat.soft↗

arXiv2026

Roadmap for Condensates in Cell Biology

Biomolecular condensates govern essential cellular processes yet elude description by traditional equilibrium models. This roadmap, distilled from structured discussions at a workshop and reflecting the consensus of its participants, clarifies key concepts for researchers, funding bodies, and journals. After unifying terminology that often separates disciplines, we outline the core physics of condensate formation, review their biological roles, and identify outstanding challenges in nonequilibrium theory, multiscale simulation, and quantitative in-cell measurements. We close with a forward-looking outlook to guide coordinated efforts toward predictive, experimentally anchored understanding and control of biomolecular condensates.

physics.bio-ph↗

arXiv2025

When $B_2$ is Not Enough: Evaluating Simple Metrics for Predicting Phase Separation of Intrinsically Disordered Proteins

Understanding and predicting the phase behavior of intrinsically disordered proteins (IDPs) is of significant interest due to their role in many biological processes. However, effectively characterizing phase behavior and its complex dependence on protein primary sequence remains challenging. In this study, we evaluate the efficacy of several simple computational metrics to quantify the propensity of single-component IDP solutions to phase separate; specific metrics considered include the single-chain radius of gyration, the second virial coefficient, and a newly proposed quantity termed the expenditure density. Each metric is computed using coarse-grained molecular dynamics simulations for 2,034 IDP sequences. Using machine learning, we analyze this data to understand how sequence features correlate with the predictive performance of each metric and to develop insight into their respective strengths and limitations. The expenditure density is determined to be a broadly useful metric that combines simplicity, low computational cost, and accuracy; it also provides a continuous measure that remains informative across both phase-separating and non-phase-separating sequences. Additionally, this metric shows promise in its ability to improve predictions of other properties for IDP systems. This work extends existing literature by advancing beyond binary classification, which can be useful for rapidly screening phase behavior or predicting other properties of IDP-related systems.

cond-mat.soft↗

arXiv2025

Interfacial Effects Determine Nonequilibrium Phase Behaviors in Chemically Driven Fluids

Coupling between chemical fuel consumption and phase separation can lead to condensation at a nonequilibrium steady state, resulting in phase behaviors that are not described by equilibrium thermodynamics. Theoretical models of such "chemically driven fluids" typically invoke near-equilibrium approximations at small length scales. However, because dissipation occurs due to both molecular-scale chemical reactions and mesoscale diffusive transport, it has remained unclear which properties of phase-separated reaction-diffusion systems can be assumed to be at an effective equilibrium. Here we use microscopic simulations to show that mesoscopic fluxes are dependent on nonequilibrium fluctuations at phase-separated interfaces. We further develop a first-principles theory to predict nonequilibrium coexistence curves, localization of mesoscopic fluxes near phase-separated interfaces, and droplet size-scaling relations in good agreement with simulations. Our findings highlight the central role of interfacial properties in governing nonequilibrium condensation and have broad implications for droplet nucleation, coarsening, and size control in chemically driven fluids.

cond-mat.soft↗

arXiv2025

Predicting Heteropolymer Phase Separation Using Two-Chain Contact Maps

Phase separation in polymer solutions often correlates with single-chain and two-chain properties, such as the single-chain radius of gyration, Rg, and the pairwise second virial coefficient, B22. However, recent studies have shown that these metrics can fail to distinguish phase-separating from non-phase-separating heteropolymers, including intrinsically disordered proteins (IDPs). Here we introduce an approach to predict heteropolymer phase separation from two-chain simulations by analyzing contact maps, which capture how often specific monomers from the two chains are in physical proximity. Whereas B22 summarizes the overall attraction between two chains, contact maps preserve spatial information about their interactions. To compare these metrics, we train phase-separation classifiers for both a minimal heteropolymer model and a chemically specific, residue-level IDP model. Remarkably, simple statistical properties of two-chain contact maps predict phase separation with high accuracy, vastly outperforming classifiers based on Rg and B22 alone. Our results thus establish a transferable and computationally efficient method to uncover key driving forces of IDP phase behavior based on their physical interactions in dilute solution.

cond-mat.soft↗

arXiv2025

Dynamical phase transition in the growth of programmable polymorphic materials

The hallmark feature of polymorphic systems is their ability to assemble into many possible structures at the same thermodynamic state. Designer polymorphic materials can in principle be engineered via programmable self-assembly, but the robustness of the assembly process depends on dynamical factors that are poorly understood. Here we predict a new failure mode for the growth of multicomponent polymorphic materials, in which dynamical coexistence occurs between ordered and disordered assembly trajectories. We show that this transition is preceded by the formation of a steady-state disordered wetting layer, suggesting a nonequilibrium analogy to pre-melting phenomena at equilibrium. This dynamical phase transition is likely to occur in a variety of systems and may fundamentally limit the complexity of polymorphic materials that can be designed through programmable self-assembly.

cond-mat.soft↗

arXiv2025

The underappreciated role of nonspecific interactions in the crystallization of DNA-coated colloids

Over the last decade, the field of programmable self-assembly has seen an explosion in the diversity of crystal lattices that can be synthesized from DNA-coated colloidal nanometer- and micrometer-scale particles. The prevailing wisdom has been that a particular crystal structure can be targeted by designing the DNA-mediated interactions, to enforce binding between specific particle pairs, and the particle diameters, to control the packing of the various species. In this article, we show that other ubiquitous nonspecific interactions can play equally important roles in determining the relative stability of different crystal polymorphs and therefore what crystal structure is most likely to form in an experiment. For a binary mixture of same-sized DNA-coated colloidal micrometer-scale particles, we show how changing the magnitudes of nonspecific steric and van der Waals interactions gives rise to a family of binary body-centered tetragonal crystals, including both cesium-chloride and copper-gold crystals. Simulations using pair potentials that account for these interactions reproduce our experimental observations quantitatively, and a theoretical model reveals how a subtle balance between specific and nonspecific forces determines the equilibrium crystal structure. These results highlight the importance of accounting for nonspecific interactions in the crystal-engineering design process.

cond-mat.soft↗

arXiv2025

Multi-objective optimization for targeted self-assembly among competing polymorphs

Most approaches for designing self-assembled materials focus on the thermodynamic stability of a target structure or crystal polymorph. Yet in practice, the outcome of a self-assembly process is often controlled by kinetic pathways. Here we present an efficient machine learning-guided design algorithm to identify globally optimal interaction potentials that maximize both the thermodynamic yield and kinetic accessibility of a target polymorph. We show that optimal potentials exist along a Pareto front, indicating the possibility of a trade-off between the thermodynamic and kinetic objectives. Although the extent of this trade-off depends on the target polymorph and the assembly conditions, we generically find that the trade-off arises from a competition among alternative polymorphs: The most kinetically optimal potentials, which favor the target polymorph on short timescales, tend to stabilize a competing polymorph at longer times. Our work establishes a general-purpose approach for multi-objective self-assembly optimization, reveals fundamental trade-offs between crystallization speed and defect formation in the presence of competing polymorphs, and suggests guiding principles for materials design algorithms that optimize for kinetic accessibility.

cond-mat.soft↗

arXiv2024

Assembly of Complex Colloidal Systems Using DNA

Nearly thirty years after its inception, the field of DNA-programmed colloidal self-assembly has begun to realize its initial promise. In this review, we summarize recent developments in designing effective interactions and understanding the dynamic self-assembly pathways of DNA-coated nanoparticles and microparticles, as well as how these advances have propelled tremendous progress in crystal engineering. We also highlight exciting new directions showing that new classes of subunits combining nanoparticles with DNA origami can be used to engineer novel multicomponent assemblies, including structures with self-limiting, finite sizes. We conclude by providing an outlook on how recent theoretical advances focusing on the kinetics of self-assembly could usher in new materials-design opportunities, like the possibility of retrieving multiple distinct target structures from a single suspension or accessing new classes of materials that are stabilized by energy dissipation, mimicking self-assembly in living systems.

cond-mat.soft↗

arXiv2024

Emergence of multiphase condensates from a limited set of chemical building blocks

Biomolecules composed of a limited set of chemical building blocks can co-localize into distinct, spatially segregated compartments known as biomolecular condensates. While many condensates are known to form spontaneously via phase separation, it has been unclear how immiscible condensates with precisely controlled molecular compositions assemble from a small number of chemical building blocks. We address this question by establishing a connection between the specificity of biomolecular interactions and the thermodynamic stability of coexisting condensates. By computing the minimum interaction specificity required to assemble condensates with target molecular compositions, we show how to design heteropolymer mixtures that produce compositionally complex condensates using only a small number of monomer types. Our results provide insight into how compositional specificity arises in naturally occurring multicomponent condensates and demonstrate a rational algorithm for engineering complex artificial condensates from simple chemical building blocks.

cond-mat.soft↗

arXiv2024

Predicting the morphology of multiphase biomolecular condensates from protein interaction networks

Phase-separated biomolecular condensates containing proteins and RNAs can assemble into higher-order structures by forming thermodynamically stable interfaces between immiscible phases. Using a minimal model of a protein/RNA interaction network, we demonstrate how a "shared" protein species that partitions into both phases of a multiphase condensate can function as a tunable surfactant that modulates the interfacial properties. We use Monte Carlo simulations and free-energy calculations to identify conditions under which a low concentration of this shared species is sufficient to trigger a wetting transition. We also describe a numerical approach based on classical density functional theory to predict concentration profiles and surface tensions directly from the model protein/RNA interaction network. Finally, we show that the wetting phase diagrams that emerge from our calculations can be understood in terms of a simple model of selective adsorption to a fluctuating interface. Our work shows how a low-concentration protein species might function as a biological switch for regulating multiphase condensate morphologies.

cond-mat.soft↗

arXiv2023

Active learning of the thermodynamics-dynamics tradeoff in protein condensates

Phase-separated biomolecular condensates exhibit a wide range of dynamical properties, which depend on the sequences of the constituent proteins and RNAs. However, it is unclear to what extent condensate dynamics can be tuned without also changing the thermodynamic properties that govern phase separation. Using coarse-grained simulations of intrinsically disordered proteins, we show that the dynamics and thermodynamics of homopolymer condensates are strongly correlated, with increased condensate stability being coincident with low mobilities and high viscosities. We then apply an "active learning" strategy to identify heteropolymer sequences that break this correlation. This data-driven approach and accompanying analysis reveal how heterogeneous amino-acid compositions and non-uniform sequence patterning map to a range of independently tunable dynamical and thermodynamic properties of biomolecular condensates. Our results highlight key molecular determinants governing the physical properties of biomolecular condensates and establish design rules for the development of stimuli-responsive biomaterials.

q-bio.BM↗

arXiv2023

Interplay between self-assembly and phase separation in a polymer-complex model

We present a theoretical model for predicting the phase behavior of polymer solutions in which phase separation competes with oligomerization. Specifically, we consider scenarios in which the assembly of polymer chains into stoichiometric complexes prevents the chains from phase-separating via attractive polymer-polymer interactions. Combining statistical associating fluid theory with a two-state description of self-assembly, we find that this model exhibits rich phase behavior, including re-entrance, and we show how system-specific phase diagrams can be derived graphically. Importantly, we discuss why these phase diagrams can resemble -- and yet are qualitatively distinct from -- phase diagrams of polymer solutions with lower critical solution temperatures.

cond-mat.soft↗

arXiv2023

Nonequilibrium interfacial properties of chemically driven fluids

Chemically driven fluids can demix to form condensed droplets that exhibit phase behaviors not observed at equilibrium. In particular, nonequilibrium interfacial properties can emerge when the chemical reactions are driven differentially between the interior and exterior of the phase-separated droplets. Here, we use a minimal model to study changes in the interfacial tension between coexisting phases away from equilibrium. Simulations of both droplet nucleation and interface roughness indicate that the nonequilibrium interfacial tension can either be increased or decreased relative to its equilibrium value, depending on whether the driven chemical reactions are accelerated or decelerated within the droplets. Finally, we show that these observations can be understood using a predictive theory based on an effective thermodynamic equilibrium.

cond-mat.soft↗

arXiv2023

Competition between self-assembly and phase separation governs high-temperature condensation of a DNA liquid

In many biopolymer solutions, attractive interactions that stabilize finite-sized clusters at low concentrations also promote phase separation at high concentrations. Here we study a model biopolymer system that exhibits the opposite behavior: Self-assembly of DNA oligonucleotides into finite-sized, stoichiometric clusters, known as "DNA nanostars", tends to inhibit phase separation of the oligonucleotides at high temperatures. We use microfluidics-based experiments to map the phase behavior of DNA nanostars at high concentrations of divalent cations, revealing a novel phase transition in which the oligonucleotides condense upon increasing temperature. We then show that a theoretical model of competition between self-assembly and phase separation quantitatively predicts changes in experimental phase diagrams arising from DNA sequence perturbations. Our results point to a general mechanism by which self-assembly shapes phase boundaries in complex biopolymer solutions.

cond-mat.soft↗