Predicting the Interfacial Energy and Morphology of DNA Condensates

TL;DR

This work develops a robust framework that links microscopic details of DNA nanostars to macroscopic condensate morphologies by coupling coarse-grained molecular dynamics with a generalized Flory–Huggins lattice theory. The authors quantify how features such as valence $Z$, arm length $L$, bending rigidity $\ell_p$, Debye length $\lambda_D$, and sticky-end distributions set interfacial energies $\gamma_i$ and $\gamma_{12}$, predicting common Janus-like arrangements and rare nested morphologies. They show how discrete (sticky-end composition) and continuous (crosslinker concentration) design levers can steer interfacial energies and phase contacts, enabling programmable multiphase architectures. The framework provides design principles for constructing complex, functional condensates in vitro and offers a scalable path toward higher-order multiphase assemblies informed by microscopic molecular parameters.

Abstract

The physics and morphology of biomolecular condensates formed through liquid-liquid phase separation underpin diverse biological processes, exemplified by the nested organization of nucleoli that facilitates ribosome biogenesis. Here, we develop a theoretical and computational framework to understand and predict multiphase morphologies in DNA-nanostar solutions. Because morphology is governed by interfacial energies between coexisting phases, we combine Flory-Huggins theory with coarse-grained molecular dynamics simulations to examine how these energies depend on key microscopic features of DNA nanostars, including size, valence, bending rigidity, Debye screening length, binding strength, and sticky-end distribution. The phase behavior of DNA nanostars is quantitatively captured by a generalized lattice model, in which the interplay between sticky-end binding energy and conformational entropy determines the effective interactions. Focusing on condensates comprising two dense phases, we find that Janus-like morphologies are ubiquitous because the interfacial energies between the dense and dilute phases, $γ_{i\in\{1,2\}}$, are typically comparable. In contrast, nested morphologies are rare as they require a large asymmetry in $γ_i$, which arises only for highly dissimilar nanostars such as those differing markedly in valence or size. Moreover, the interfacial energy between the two dense phases, $γ_{12}$, can be modulated either discretely, by varying sticky-end distribution, or continuously, by tuning the crosslinker ratio; the former may even eliminate nested configurations. These findings establish physical design principles for constructing complex condensate architectures directly from microscopic molecular parameters.

Figures (7)

• Figure 1: Structures of DNA nanostars and their coarse-grained representations. Each DNA nanostar consists of a central junction, $Z$ double-stranded arms of length $L$, and $Z$ single-stranded sticky ends. (a–c) DNA nanostars with valence $Z = 3$, $4$, and $6$, respectively. (b, d) Binding between two DNA nanostars. Base-pairing follows standard rules: adenine (“$\!\mathcal{A}$”) pairs with thymine (“$\mathcal{T}$”), and cytosine (“$\mathcal{C}$”) pairs with guanine (“$\mathcal{G}$”). The sticky ends are typically designed to bind only with their own kind, which requires palindromic sequences [the forward strand reads the same as the reverse complement, e.g., “$\mathcal{G\!T\!\!AC}$” in (d)]. An additional unpaired base between the sticky end and the double-stranded arm [the adenine in (d)] facilitates reversible unbinding and thus enhances condensate fluidity jeon2020sequencenguyen2017tuning. (e–g) Coarse-grained model of DNA nanostars, incorporating stretching and bending springs as well as non-bonded interactions. Sticky ends are represented by colored beads: blue beads attract red ones, whereas beads of the same color repel each other. See Methods for modeling details.
• Figure 2: (a, c) Phase diagrams of systems containing a single type of DNA nanostar with identical sticky ends. Here, $\rho$ is the molecular number density of DNA nanostars in each phase, $\Delta E$ is the sticky-end binding energy, $Z$ is the valence, and $L$ is the arm length. The points represent molecular dynamics (MD) simulation results, and the solid curves show the corresponding Flory–Huggins binodal lines obtained with fitted parameters [$M_{\rm eff}$ and $\rho_0$ in Eq. (\ref{['Eq:Flory']}); $z_{\rm eff}$ and $C$ in Eq. (\ref{['Eq:Florychi']})]. Within the coexistence region, the system separates into two phases—a dilute phase and a dense phase—the densities of which correspond to the left and right branches of the binodal, respectively. (b, d) Interfacial energies of different DNA condensates as a function of sticky-end binding energy. The points represent molecular dynamics results, and the solid lines show theoretical predictions from Eq. (\ref{['Eq:florygamma']}), where the characteristic interfacial length scale is taken as $\lambda = \mathcal{C}\rho_0^{-1/3}$. The prefactor $\mathcal{C}=0.64$ is fitted from the data in (b) and subsequently applied in (d). In (c, d), only nanostars with $Z=4$ and $L=5~\rm nm$ are considered, while the persistence length $\ell_{\rm p}$ and Debye length $\lambda_{\rm D}$ are varied to examine their effects on interfacial energy [$\ell_{\rm p}=50~\rm nm$ and $\lambda_{\rm D}=2~\rm nm$ in (a, b)]. All data points in (a–d) are obtained from simulations at overall molecular number densities of $0.42\times10^6~{\rm \mu m}^{-3}$ for $L=5~\rm nm$ and $0.052\times10^6~{\rm \mu m}^{-3}$ for $L=10~\rm nm$, both near their respective critical densities. Error bars represent the standard error of the mean (SEM) from five independent simulations.
• Figure 3: Schematic of the lattice model for DNA-nanostar solutions. Each nanostar occupies one lattice site and interacts with its nearest neighbors. Unoccupied sites are filled with pure solvent, while each occupied site also includes solvent surrounding the nanostar. The central junction of each nanostar (yellow node) is located at the site center, and its sticky ends are distributed within a blue spherical shell that partially overlaps with those of neighboring sites.
• Figure 4: (a) Simulation snapshot of a two-component system of DNA nanostars used to compute interfacial energies. Here, $\gamma_1$ and $\gamma_2$ denote the interfacial energies between the dilute phase and the pink or blue dense phase, respectively, while $\gamma_{12}$ represents the interfacial energy between the pink and blue phases. The simulation box measures $1000\times100\times100~{\rm nm}^3$ [only a portion along the $x$-direction is shown] and contains 4000 pink nanostars (sticky-end distribution 4A2B) and 4000 blue nanostars (4B). Periodic boundary conditions are applied in all directions. (b, c) Interfacial energies for different combinations of DNA nanostars. Pink and blue bars correspond to $\gamma_i$ between dense phase $i$ and the dilute phase; yellow bars represent $\gamma_{12}$ between the two dense phases [see (a)]; and purple bars denote the interfacial energy of the mixed dense phase, $\gamma_{\rm mix}$, where the two components coexist within a single phase. All bar values are obtained from molecular dynamics simulations. Solid lines show theoretical predictions based on Eqs. (\ref{['Eq:Florychii']}) and (\ref{['Eq:Florychiij']}), plotted as a function of $\beta_1$ (the number of yellow sticky ends on the pink nanostar) indicated on the upper horizontal axis. The insets in (b, c) depict the morphologies predicted from interfacial-energy inequalities informed by molecular dynamics calculations. In the mixed-phase regime, $\gamma_1$, $\gamma_2$, and $\gamma_{12}$ are undefined, and only $\gamma_{\rm mix}$ applies. The binding energy of identical sticky ends is fixed at $\Delta E=-19k_{\rm B}T$, and the DNA arm length is $L=5~\rm nm$. Distinct sticky ends repel each other. Error bars indicate the standard error of the mean (SEM) from five independent simulations. (d) Representative ternary phase diagrams corresponding to the systems in (c), showing variations in $\beta_1$. Here, $\phi_0$, $\phi_1$, and $\phi_2$ denote the volume fractions of lattice sites occupied by the solvent, component 1, and component 2, respectively.
• Figure 5: (a) Morphology spectrum for two-component systems of DNA nanostars. (b) Snapshots from molecular dynamics simulations of representative systems. The second row shows the same configurations as the first, but with adjusted transparency to reveal the internal structures. The binding energy of identical sticky ends is fixed at $\Delta E = -19k_{\rm B}T$, and the arm length is $L = 5~\rm nm$ for all nanostars. Different types of sticky ends interact purely repulsively. The simulation box measures $500^3~\rm nm^3$ and contains 1500 pink nanostars and 20000 blue nanostars to clearly visualize the engulfment morphology. Each simulation is run for $4\times10^8$ steps, and the corresponding time evolution is shown in Fig. S8.