Dynamic control of DNA condensation.

Artificial biomolecular condensates are emerging as a versatile approach to organize molecular targets and reactions without the need for lipid membranes. Here we ask whether the temporal response of artificial condensates can be controlled via designed chemical reactions. We address this general question by considering a model problem in which a phase separating component participates in reactions that dynamically activate or deactivate its ability to self-attract. Through a theoretical model we illustrate the transient and equilibrium effects of reactions, linking condensate response and reaction parameters. We experimentally realize our model problem using star-shaped DNA motifs known as nanostars to generate condensates, and we take advantage of strand invasion and displacement reactions to kinetically control the capacity of nanostars to interact. We demonstrate reversible dissolution and growth of DNA condensates in the presence of specific DNA inputs, and we characterize the role of toehold domains, nanostar size, and nanostar valency. Our results will support the development of artificial biomolecular condensates that can adapt to environmental changes with prescribed temporal dynamics.

Design principles of 3D epigenetic memory systems.

Cells remember their identities, in part, by using epigenetic marks-chemical modifications placed along the genome. How can mark patterns remain stable over cell generations despite their constant erosion by replication and other processes? We developed a theoretical model that reveals that three-dimensional (3D) genome organization can stabilize epigenetic memory as long as (i) there is a large density difference between chromatin compartments, (ii) modifying "reader-writer" enzymes spread marks in three dimensions, and (iii) the enzymes are limited in abundance relative to their histone substrates. Analogous to an associative memory that encodes memory in neuronal connectivity, mark patterns are encoded in a 3D network of chromosomal contacts. Our model provides a unified account of diverse observations and reveals a key role of 3D genome organization in epigenetic memory.

Chemical reaction motifs driving non-equilibrium behaviours in phase separating materials.

Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the behaviours of a phase separating system is difficult to fully predict theoretically. In this paper, we analyse a mean field theory coupling CRNs to a combined system of phase separating and non-phase separating materials and analyse how the properties of the CRNs affect different classes of non-equilibrium behaviour: microphase separation or temporally oscillating patterns. We examine the problem of achieving microphase separated condensates by statistical analysis of the Jacobians, of which the most important motifs are negative feedback of the phase separating component and combined inhibition/activation by the non-phase separating components. We then identify CRN motifs that are likely to yield microphase by examining randomly generated networks and parameters. Molecular sequestration of the phase separating motif is shown to be the most robust towards yielding microphase separation. Subsequently, we find that dynamics of the phase separating species is promoted most easily by inducing oscillations in the diffusive components coupled to the phase separating species. Our results provide guidance towards the design of CRNs that manage the formation, dissolution and organization of compartments.

Light-controlled growth of DNA organelles in synthetic cells.

Living cells regulate many of their vital functions through dynamic, membraneless compartments that phase separate (condense) in response to different types of stimuli. In synthetic cells, responsive condensates could similarly play a crucial role in sustaining their operations. Here we use DNA nanotechnology to design and characterize artificial condensates that respond to light. These condensates form via the programmable interactions of star-shaped DNA subunits (nanostars), which are engineered to include photo-responsive protection domains. In the absence of UV irradiation, the nanostar interactions are not conducive to the formation of condensates. UV irradiation cleaves the protection domains, increases the nanostar valency and enables condensation. We demonstrate that this approach makes it possible to tune precisely the kinetics of condensate formation by dosing UV exposure time. Our experimental observations are complemented by a computational model that characterizes phase transitions of mixtures of particles of different valency, under changes in the mixture composition and bond interaction energy. In addition, we illustrate how UV activation is a useful tool to control the formation and size of DNA condensates in emulsion droplets, as a prototype organelle in a synthetic cell. This research expands our capacity to remotely control the dynamics of DNA-based components via physical stimuli and is particularly relevant to the development of minimal artificial cells and responsive biomaterials.

Fueling DNA Self-Assembly via Gel-Released Regulators.

The development of responsive, multicomponent molecular materials requires means to physically separate yet easily couple distinct processes. Here we demonstrate methods to use molecules and reactions loaded into microliter-sized polyacrylamide hydrogels (mini-gels) to control the dynamic self-assembly of DNA nanotubes. We first characterize the UV-mediated release of DNA molecules from mini-gels, changing diffusion rates and minimizing spontaneous leakage of DNA. We then demonstrate that mini-gels can be used as compartments for storage and release of DNA that mediates the assembly or disassembly of DNA nanotubes in a one-pot process and that the speed of DNA release is controlled by the mini-gel porosity. With this approach, we achieve control of assembly and disassembly of nanotubes with distinct kinetics, including a finite delay that is obtained by loading distinct DNA regulators into distinct mini-gels. We finally show that mini-gels can also host and localize enzymatic reactions, by transcribing RNA regulators from synthetic genes loaded in the mini-gels, with diffusion of RNA to the aqueous phase resulting in the activation of self-assembly. Our experimental data are recapitulated by a mathematical model that describes the diffusion of DNA molecules from the gel phase to the aqueous phase in which they control self-assembly of nanotubes. Looking forward, DNA-loaded mini-gels may be further miniaturized and patterned to build more sophisticated storage compartments for use within multicomponent, complex biomolecular materials relevant for biomedical applications and artificial life.

Ray Optics for Gliders.

Control of self-propelled particles is central to the development of many microrobotic technologies, from dynamically reconfigurable materials to advanced lab-on-a-chip systems. However, there are few physical principles by which particle trajectories can be specified and can be used to generate a wide range of behaviors. Within the field of ray optics, a single principle for controlling the trajectory of light─Snell's law─yields an intuitive framework for engineering a broad range of devices, from microscopes to cameras and telescopes. Here we show that the motion of self-propelled particles gliding across a resistance discontinuity is governed by a variant of Snell's law, and develop a corresponding ray optics for gliders. Just as the ratio of refractive indexes sets the path of a light ray, the ratio of resistance coefficients is shown to determine the trajectories of gliders. The magnitude of refraction depends on the glider's shape, in particular its aspect ratio, which serves as an analogue to the wavelength of light. This enables the demixing of a polymorphic, many-shaped, beam of gliders into distinct monomorphic, single-shaped, beams through a friction prism. In turn, beams of monomorphic gliders can be focused by spherical and gradient friction lenses. Alternatively, the critical angle for total internal reflection can be used to create shape-selective glider traps. Overall our work suggests that furthering the analogy between light and microscopic gliders may be used for sorting, concentrating, and analyzing self-propelled particles.

The Growth Rate of DNA Condensate Droplets Increases with the Size of Participating Subunits.

Liquid-liquid phase separation (LLPS) is a common phenomenon underlying the formation of dynamic membraneless organelles in biological cells, which are emerging as major players in controlling cellular functions and health. The bottom-up synthesis of biomolecular liquid systems with simple constituents, like nucleic acids and peptides, is useful to understand LLPS in nature as well as to develop programmable means to build new amorphous materials with properties matching or surpassing those observed in natural condensates. In particular, understanding which parameters determine condensate growth kinetics is essential for the synthesis of condensates with the capacity for active, dynamic behaviors. Here we use DNA nanotechnology to study artificial liquid condensates through programmable star-shaped subunits, focusing on the effects of changing subunit size. First, we show that LLPS is achieved in a 6-fold range of subunit size. Second, we demonstrate that the rate of growth of condensate droplets scales with subunit size. Our investigation is supported by a general model that describes how coarsening and coalescence are expected to scale with subunit size under ideal assumptions. Beyond suggesting a route toward achieving control of LLPS kinetics via design of subunit size in synthetic liquids, our work suggests that particle size may be a key parameter in biological condensation processes.

Spatial distributions of nonconservatively interacting particles.

Certain types of active systems can be treated as an equilibrium system with excess nonconservative forces driving some of the microscopic degrees of freedom. We derive results for how many particles having both conservative and nonconservative forces will behave. Treating nonconservative forces perturbatively, we show how the probability distribution of the microscopic degrees of freedom is modified from the Boltzmann distribution. We then derive approximate forms of this distribution through analyzing the nature of our perturbations. We compare the perturbative expansion for the microscopic probability distribution to an exactly solvable active system. Finally, we consider how the approximate forms for the microscopic distributions we have derived lead to different macroscopic states when coarse grained for two different kinds of systems, a collection of motile particles, and a system where nonconservative forces are applied in space. In the former, we are able to show that nonconservative forces lead to an effective attractive interaction between motile particles, and in the latter we note that by introducing nonconservative interactions between particles we modify densities through extra terms which couple to surfaces. In this way, we are able to recast certain active problems as the statistical mechanics of nonconservative forces.

Chemically active nanodroplets in a multi-component fluid.

We introduce a model of chemically active particles of a multi-component fluid that can change their interactions with other particles depending on their state. Since such switching of interactions can only be maintained by the input of chemical energy, the system is inherently non-equilibrium. Focusing on a scenario where the equilibrium interactions would lead to condensation into a liquid droplet, and despite the relative simplicity of the interaction rules, these systems display a wealth of interesting and novel behaviors such as oscillations of droplet size and molecular sorting, and raise the possibility of spatio-temporal control of chemical reactions on the nanoscale.

Properties of Rouse polymers with actively driven regions.

We study theoretically the physical properties of Rouse polymers when a subset of monomers along the backbone is subjected to an additional driving force of exponentially correlated fluctuating noise. In other words, the polymers are made up of two kinds of particle, one of which has an additional coupling to an active bath that subjects those particles to extra forces. We analyze properties of these active polymers, such as the end to end distance and the local structure induced by active kicks. We then proceed to quantify how the dynamics of such polymers depend on the proportion of monomers which are being actively driven, and show how the dynamics transitions from the normal Rouse like behavior to substantially faster dynamics. Finally we analyze some of the non-equilibrium properties induced in these systems, such as the irreversibility.

Effect of Grafting on Aggregation of Intrinsically Disordered Proteins.

A significant part of the proteome is composed of intrinsically disordered proteins (IDPs). These proteins do not fold into a well-defined structure and behave like ordinary polymers. In this work, we consider IDPs that have the tendency to aggregate, model them as heteropolymers that contain a small number of associating monomers, and use computer simulations to compare the aggregation of such IDPs that are grafted to a surface or free in solution. We then discuss how such grafting may affect the analysis of in vitro experiments and could also be used to suppress harmful aggregation.

Darwinian selection of host and bacteria supports emergence of Lamarckian-like adaptation of the system as a whole.

BACKGROUND: The relatively fast selection of symbiotic bacteria within hosts and the potential transmission of these bacteria across generations of hosts raise the question of whether interactions between host and bacteria support emergent adaptive capabilities beyond those of germ-free hosts. RESULTS: To investigate possibilities for emergent adaptations that may distinguish composite host-microbiome systems from germ-free hosts, we introduce a population genetics model of a host-microbiome system with vertical transmission of bacteria. The host and its bacteria are jointly exposed to a toxic agent, creating a toxic stress that can be alleviated by selection of resistant individuals and by secretion of a detoxification agent ("detox"). We show that toxic exposure in one generation of hosts leads to selection of resistant bacteria, which in turn, increases the toxic tolerance of the host's offspring. Prolonged exposure to toxin over many host generations promotes anadditional form of emergent adaptation due to selection of hosts based on detox produced by their bacterial community as a whole (as opposed to properties of individual bacteria). CONCLUSIONS: These findings show that interactions between pure Darwinian selections of host and its bacteria can give rise to emergent adaptive capabilities, including Lamarckian-like adaptation of the host-microbiome system. REVIEWERS: This article was reviewed by Eugene Koonin, Yuri Wolf and Philippe Huneman.

Dynamics of active Rouse chains.

We consider how active forces modeled as non-thermal random noise affect the average dynamical properties of a Rouse polymer. As the power spectrum of the noise is not known we keep the analytical treatment as generic as possible and then present results for a few examples of active noise. We discuss the connection between our results and recent experimental studies of dynamics of labeled DNA telomeres in living cells, and propose new chromatin tracking experiments that will allow one to determine the statistical properties of the active forces associated with chromatin remodeling processes.

Effect of non-specific interactions on formation and stability of specific complexes.

We introduce a simple model to describe the interplay between specific and non-specific interactions. We study the influence of various physical factors on the static and dynamic properties of the specific interactions of our model and show that contrary to intuitive expectations, non-specific interactions can assist in the formation of specific complexes and increase their stability. We then discuss the relevance of these results for biological systems.

A physical model describing the interaction of nuclear transport receptors with FG nucleoporin domain assemblies.

The permeability barrier of nuclear pore complexes (NPCs) controls bulk nucleocytoplasmic exchange. It consists of nucleoporin domains rich in phenylalanine-glycine motifs (FG domains). As a bottom-up nanoscale model for the permeability barrier, we have used planar films produced with three different end-grafted FG domains, and quantitatively analyzed the binding of two different nuclear transport receptors (NTRs), NTF2 and Importin ß, together with the concomitant film thickness changes. NTR binding caused only moderate changes in film thickness; the binding isotherms showed negative cooperativity and could all be mapped onto a single master curve. This universal NTR binding behavior - a key element for the transport selectivity of the NPC - was quantitatively reproduced by a physical model that treats FG domains as regular, flexible polymers, and NTRs as spherical colloids with a homogeneous surface, ignoring the detailed arrangement of interaction sites along FG domains and on the NTR surface.

Universal protein distributions in a model of cell growth and division.

Protein distributions measured under a broad set of conditions in bacteria and yeast were shown to exhibit a common skewed shape, with variances depending quadratically on means. For bacteria these properties were reproduced by temporal measurements of protein content, showing accumulation and division across generations. Here we present a stochastic growth-and-division model with feedback which captures these observed properties. The limiting copy number distribution is calculated exactly, and a single parameter is found to determine the distribution shape and the variance-to-mean relation. Estimating this parameter from bacterial temporal data reproduces the measured distribution shape with high accuracy and leads to predictions for future experiments.

Communication: pair interaction ordering in fluids with random interactions.

We use molecular dynamics simulations in 2D to study multi-component systems in the limiting case where all the particles are different (APD). The particles are assumed to interact via Lennard-Jones potentials, with identical size parameters but their pair interaction parameters are generated at random from a uniform or from a peaked distribution. We analyze both the global and the local properties of these systems at temperatures above the freezing transition and find that APD fluids relax into a non-random state characterized by clustering of particles according to the values of their pair interaction parameters (particle-identity ordering).

Nanoscale stiffness topography reveals structure and mechanics of the transport barrier in intact nuclear pore complexes.

The nuclear pore complex (NPC) is the gate for transport between the cell nucleus and the cytoplasm. Small molecules cross the NPC by passive diffusion, but molecules larger than ∼5 nm must bind to nuclear transport receptors to overcome a selective barrier within the NPC. Although the structure and shape of the cytoplasmic ring of the NPC are relatively well characterized, the selective barrier is situated deep within the central channel of the NPC and depends critically on unstructured nuclear pore proteins, and is therefore not well understood. Here, we show that stiffness topography with sharp atomic force microscopy tips can generate nanoscale cross-sections of the NPC. The cross-sections reveal two distinct structures, a cytoplasmic ring and a central plug structure, which are consistent with the three-dimensional NPC structure derived from electron microscopy. The central plug persists after reactivation of the transport cycle and resultant cargo release, indicating that the plug is an intrinsic part of the NPC barrier. Added nuclear transport receptors accumulate on the intact transport barrier and lead to a homogenization of the barrier stiffness. The observed nanomechanical properties in the NPC indicate the presence of a cohesive barrier to transport and are quantitatively consistent with the presence of a central condensate of nuclear pore proteins in the NPC channel.

Stepwise visualization of membrane pore formation by suilysin, a bacterial cholesterol-dependent cytolysin.

Membrane attack complex/perforin/cholesterol-dependent cytolysin (MACPF/CDC) proteins constitute a major superfamily of pore-forming proteins that act as bacterial virulence factors and effectors in immune defence. Upon binding to the membrane, they convert from the soluble monomeric form to oligomeric, membrane-inserted pores. Using real-time atomic force microscopy (AFM), electron microscopy (EM), and atomic structure fitting, we have mapped the structure and assembly pathways of a bacterial CDC in unprecedented detail and accuracy, focussing on suilysin from Streptococcus suis. We show that suilysin assembly is a noncooperative process that is terminated before the protein inserts into the membrane. The resulting ring-shaped pores and kinetically trapped arc-shaped assemblies are all seen to perforate the membrane, as also visible by the ejection of its lipids. Membrane insertion requires a concerted conformational change of the monomeric subunits, with a marked expansion in pore diameter due to large changes in subunit structure and packing.

Model inspired by nuclear pore complex suggests possible roles for nuclear transport receptors in determining its structure.

Nuclear transport receptors (NTRs) mediate nucleocytoplasmic transport via their affinity for unstructured proteins (polymers) in the nuclear pore complex (NPC). Here, we have modeled the effect of NTRs on polymeric structure in the nanopore confinement of the NPC central conduit. The model explicitly takes into account inter- and intramolecular interactions, as well as the finite size of the NTRs (∼20% of the NPC channel diameter). It reproduces various proposed scenarios for the channel structure, ranging from a central polymer condensate (selective phase) to brushlike polymer arrangements localized at the channel wall (virtual gate, reduction of dimensionality), with the transport receptors lining the polymer surface. In addition, it predicts a new structure in which NTRs become an integral part of the transport barrier by forming a cross-linked network with the unstructured proteins stretching across the pore. The model provides specific and distinctive predictions for the equilibrium spatial distributions of NTRs for these different scenarios that can be experimentally verified by, e.g., superresolution fluorescence microscopy. Moreover, it suggests mechanisms by which globular macromolecules (colloidal particles) can cause polymer-coated nanopores to switch between open and closed configurations, a possible explanation of the biological function of the NPC, and suggests potential technological applications for filtration and single-molecule sensing.