Linker-Mediated Phase Behavior of DNA-Coated Colloids

Open Access

Linker-Mediated Phase Behavior of DNA-Coated Colloids

Janna Lowensohn, Bernardo Oyarzún, Guillermo Narváez Paliza, Bortolo M. Mognetti, and W. Benjamin Rogers

Phys. Rev. X 9, 041054 – Published 13 December 2019

Abstract

The possibility of prescribing local interactions between nano- and microscopic components that direct them to assemble in a predictable fashion is a central goal of nanotechnology research. In this article, we advance a new paradigm in which the self-assembly of DNA-functionalized colloidal particles is programmed using linker oligonucleotides dispersed in solution. We find a phase diagram that is surprisingly rich compared to phase diagrams typical of other DNA-functionalized colloidal particles that interact by direct hybridization, including a reentrant melting transition upon increasing linker concentration, and show that multiple linker species can be combined to prescribe many interactions simultaneously. A new theory predicts the observed phase behavior quantitatively without any fitting parameters. Taken together, these experiments and model lay the groundwork for future research in programmable self-assembly, enabling the possibility of programming the hundreds of specific interactions needed to assemble fully addressable, mesoscopic structures, while also expanding our fundamental understanding of the unique phase behavior possible in colloidal suspensions.

Received 14 March 2019
Revised 13 August 2019

DOI:https://doi.org/10.1103/PhysRevX.9.041054

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Classical statistical mechanics Phase behavior Phase diagrams Self-assembly

Colloids DNA

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Authors & Affiliations

Janna Lowensohn ¹, Bernardo Oyarzún², Guillermo Narváez Paliza¹, Bortolo M. Mognetti ², and W. Benjamin Rogers ^1,*

¹Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
²Université Libre de Bruxelles, Interdisciplinary Center for Nonlinear Phenomena and Complex Systems, Campus Plaine, Code Postal 231, Boulevard du Triomphe, B-1050 Brussels, Belgium

^*wrogers@brandeis.edu

Popular Summary

Inspired by nature’s ability to make complex structures, self-assembly has emerged as a powerful technique for synthesizing nanoscale materials. DNA-coated colloids provide a particularly promising approach to realizing this vision since the base sequences grafted to particles can be designed to encode the formation of a chosen structure. Although significant progress has been made in programming one or two colloidal species to form different crystal lattices, prescribing the myriad interactions required to assemble fully addressable, aperiodic structures remains an unsolved challenge. To address this problem, we develop a paradigm for programmable self-assembly in which the instructions are encoded using short sequences of DNA dispersed in solution.

Combining experiments and theory, we find that this system has a number of interesting features, such as new phase transitions, and is significantly easier to program than existing DNA-coated colloids. As proof of principle, we demonstrate how interactions between dozens or even hundreds of particle species can be programmed and tuned independently. Furthermore, we develop a model to predict these interactions quantitatively from the base sequences and molar concentrations of the dispersed pieces of DNA that link together particles.

Our results enable new directions in programmable self-assembly, namely the pursuit of fully addressable structures built from many particle species. The generic phase behavior that we find is also universal for other systems in which multivalent interactions arise because of weak crosslinkers. Thus, our models could help shed light on similar phase transitions found in the condensation of biological molecules such as nucleic acids and proteins.

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Issue

Vol. 9, Iss. 4 — October - December 2019

Subject Areas

Soft Matter

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Figure 1
Linker-mediated binding. (a) Our experimental system is comprised of three DNA sequences: Strands $A$ and $B$ are grafted to $1 − μ m$ -diameter colloidal particles, and strands $L_{a b}$ , which bind $A$ to $B$ , are dispersed in solution. (b) These three DNA sequences produce a symmetric interaction matrix, in which the linker encodes the pair interaction between particles $A$ and $B$ . (c) The resulting phase behavior is temperature dependent: The system phase separates upon decreasing temperature, as shown by optical micrographs. We define the melting temperature ( $T_{m}$ ) as the temperature at which 50% of the particles are unbound. Experiments are for a 19-nucleotide linker at a concentration of $1 μ M$ ; the melting temperature is $43 ° C$ .
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Figure 2
Phase behavior of linker-mediated assembly. (a) The temperature-linker concentration phase diagram is characterized by three distinct regimes: a gas phase at low linker concentrations (region I), a solid-gas transition at intermediate linker concentrations (region II), and a reentrant gas phase at the highest linker concentrations (region III). Circles show measurements of the melting temperatures at different linker concentrations; $x$ ’s show samples that are gas at all temperatures. We define the reentrant concentration $C_{l, re}^{0}$ as the linker concentration above which the solid melts. The arrow labeled “equivalence” shows the linker concentration at which there is one linker molecule per grafted molecule in the system. Data are for the 17-nt linker and particles with a DNA grafting density of $2000 DNA / μ m^{2}$ . The curve is a guide to the eye. We hypothesize that the phase behavior in (a) results from the molecular-scale reactions shown in (b).
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Figure 3
Effects of linker affinity and grafting density on the phase behavior. (a) Experimental measurements of the melting temperature as a function of the linker concentration for four linkers having different lengths $n$ : 17 nt (black), 19 nt (gray), 21 nt (blue), 23 nt (orange). All linkers are symmetric and $(n - 1) / 2$ bases of each linker are complementary to each grafted strand. (b) Measurements of the melting temperature as a function of the concentration for the 21-nt linker for four different grafting densities: 2000 (circles), 500 (squares), 100 (upward triangles), and 20 (stars) DNA strands per $μ m^{2}$ . The grafting densities of $A$ and $B$ are equal to one another. The reentrant concentrations are shown as points intersecting the linker-concentration axis and have a precision of roughly a factor of 2. Lines in (a) and (b) are guides to the eye.
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Figure 4
Predictions of the melting temperature $T_{m}$ and number of bound molecular species per contact between particles versus linker concentration. (a) The full theory predicts a phase diagram that matches experimental measurements (points) quantitatively above linker concentrations of roughly 10 nM. (b) Predictions of the number and type of bound molecular species—either bridges (solid lines) or half-bridges (dashed lines)—between a pair of interacting particles help explain our observations. Orange curves show the number of molecular species at the melting transition [the orange path in (a)]; blue curves show the number of bridge and half-bridge species at a fixed temperature: $T = 35 ° C$ [the blue path in (a)]. Linker concentrations with a constant number of bridges at the melting transition correspond to the weak-binding limit. The horizontal gray line shows the maximum number of possible bound species; the vertical gray line shows the reentrant concentration.
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Figure 5
Melting temperatures and reentrant concentrations collapse onto master curves. (a) shows roughly 200 measurements of the melting temperature (points) for different combinations of linker concentration, linker length, and grafting density. Color indicates linker length: 17 nt (black), 19 nt (gray), 21 nt (blue), and 23 nt (orange). Symbols indicate grafting density: 2000 (upward triangle), 1000 (plus), 500 (square), 200 (asterisk), 100 (circle), 50 (downward triangle), and 20 (star) DNA strands per $μ m^{2}$ . (b) The same data collapse when rescaled according to Eq. (1). (c) The measured reentrant concentrations collapse and exhibit a power-law dependence on the grafting density $Ψ$ , as given by Eq. (2). Filled symbols correspond to unequal grafting densities. The solid black curves in (b),(c) show predictions of the full theory. The black curve in (b) is generated by rescaling the full-theory predictions at intermediate concentrations below $C_{l, re}^{0}$ .
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Figure 6
Effects of multiple competing linker sequences on pair interactions. (a) Fully addressable self-assembly of a 19-particle dipyramid requires specifying 60 independent pair interactions shown in the interaction matrix with some particles needing up to 12 pair interactions. The number of specific interactions per particle $N$ is shown to the left of the matrix. (b) We test the feasibility of this design by devising a simplified experimental system consisting of two particle species, $A$ and $B$ , and three linker sequences $L_{a b}$ , $L_{a}$ , and $L_{b}$ . The monovalent linkers $L_{a}$ and $L_{b}$ compete with the divalent linker $L_{a b}$ and simulate the role of other linkers binding $A$ and $B$ to other particle species. (c) Measurements of the change in melting temperature of particles $A$ and $B$ for increasing concentrations of a single competing linker $L_{a}$ (points). Colors indicate different concentrations of $L_{a b}$ : $100 μ M$ (black), $10 μ M$ (gray), $1 μ M$ (orange), and 100 nM (blue). (d) Measurements of the change in the melting temperature for two competing linkers with $C_{l, cmp}^{0} \equiv C_{l, A}^{0} = C_{l, B}^{0}$ versus $(C_{l, cmp}^{0})^{2} / C_{l}^{0}$ . Curves in (c),(d) show predictions from the full theory; $x$ ’s show experimental concentrations at which the particles fail to aggregate. All particles have a surface density of $2000 DNA / μ m^{2}$ , and the reentrant concentration is indicated by the arrow. The reentrant concentration indicated by $C_{l, re}^{0}$ in (c),(d) is calculated by the full theory in the absence of competitors.
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