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Programming colloidal phase transitions with DNA strand displacement

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Science  06 Feb 2015:
Vol. 347, Issue 6222, pp. 639-642
DOI: 10.1126/science.1259762

DNA control of bonding interactions

Colloidal particles have been used as atom mimics and are often connected together using complementary DNA strands. Rogers and Manoharan controlled the strength of the colloidal “bond” by using a set of competing strand displacement reactions. They capitalized on the reversible chemical equilibrium between the DNA strands connecting different particles to control the temperature dependence of the equilibrium state.

Science, this issue p. 639

Abstract

DNA-grafted nanoparticles have been called “programmable atom-equivalents”: Like atoms, they form three-dimensional crystals, but unlike atoms, the particles themselves carry information (the sequences of the grafted strands) that can be used to “program” the equilibrium crystal structures. We show that the programmability of these colloids can be generalized to the full temperature-dependent phase diagram, not just the crystal structures themselves. We add information to the buffer in the form of soluble DNA strands designed to compete with the grafted strands through strand displacement. Using only two displacement reactions, we program phase behavior not found in atomic systems or other DNA-grafted colloids, including arbitrarily wide gas-solid coexistence, reentrant melting, and even reversible transitions between distinct crystal phases.

Like atoms, colloidal particles suspended in a fluid can form bulk phases such as gases and crystals. These particles can also be directed to form new states of matter (1) through careful tuning of their interparticle interactions—for example, by grafting DNA strands onto the particles to create specific attractions (2, 3). Such DNA-grafted particles have been called “programmable atom-equivalents” (4), a moniker that highlights the experimenter’s ability to dictate, or “program,” the self-assembled structures through the DNA sequences. The implied analogy to computer programming is a useful way to conceptualize how information in the sequences is translated to structure: Much as one can program a computer to perform complex tasks by writing statements that are compiled to machine code, one can “program” a colloid to form a complex structure by designing nucleotide sequences (statements) that are “compiled” into specific interparticle interactions (machine code). Recent advances in our understanding of this compilation process, in the form of design rules (5) or mean-field models (68) relating the effective interactions directly to the nucleotide sequences (9), have enabled the assembly of crystal phases not found in ordinary colloids (5, 1013) and could be extended, in principle, to the assembly of prescribed nonperiodic structures (14, 15).

Structure, however, is just one aspect of self-assembly; more generally, self-assembly describes a phase transition between a disordered and an ordered state, or a pathway on a phase diagram. Thus far, only a subset of the full colloidal phase diagram has been programmed: the equilibrium structure of the ordered state as a function of density and composition. Programmatic control over the phase behavior in the orthogonal thermodynamic dimension—the temperature—remains elusive. Typically, the attraction between two DNA-grafted particles decreases steeply and monotonically with increasing temperature (16, 17). As a result, the suspension displays phase behavior resembling that of simple atoms rather than programmable ones: It is fluid at high temperature and solid at low temperature (Fig. 1A). Our goal here is to develop a comprehensive approach to programming the full phase diagram of colloidal suspensions: We seek to design a set of interaction “primitives” that can be combined to program both the structure of equilibrium phases and their temperature-dependent transitions. In other words, we aim to program the equilibrium self-assembly pathways, just their endpoints.

Fig. 1 Strand-displacement reactions program phase behavior by modifying the local chemical equilibrium between DNA-grafted particles.

(A) In the absence of displacing strands, the strength of the DNA-induced attraction (ΔFa) decreases monotonically with increasing temperature T, resulting in simple phase behavior in the ϕ-T space, where ϕ is the particle volume fraction. The fluid-solid coexistence region is shown in gray. (B) A single displacement reaction eliminates the temperature dependence of ΔFa/kB T over a range of temperatures, thereby widening the fluid-solid coexistence region. (C) Adding a second strand-displacement reaction allows ΔFa/kBT to vary nonmonotonically with T, inverting the colloidal phase behavior and creating a reentrant fluid phase. The elementary reaction steps in orange are drawn schematically.

We achieve this goal by adding information to the buffer in the form of free DNA strands. We refer to these as displacing strands because their sequences are designed to be complementary to subunits of the grafted strands; they can therefore react with a double-stranded bridge, displacing one of the grafted strands and forming a nonbridging duplex (Fig. 1B). This hybridization reaction, known as toehold exchange or strand displacement, is widely used in the DNA nanotechnology field to construct dynamic assemblies and devices (18, 19). Strand displacement has also been used to melt or change the lattice constants of nanoparticle-based materials (2023). Here, rather than modifying the structure of an already assembled material, we use strand-displacement reactions to control the equilibrium assembly process. The additional degrees of freedom that we introduce allow us to design temperature-dependent interaction potentials with tunable shape, steepness, and specificity (Fig. 1, B and C). Returning to the computer programming analogy, the free DNA sequences act as the language for programming the transitions between phases, much as the grafted sequences program the structure of the phases. Because we separate the functions of the grafted and free strands, the two mechanisms can be controlled independently.

To understand how displacing strands affect the interparticle potential, consider the hybridization reactions shown in Fig. 1. Given that hybridization of complementary strands happens on time scales much shorter than that of particle motion, we can assume that interacting DNA strands are in chemical equilibrium (68). More precisely, the DNA-induced colloidal attraction is determined by the spatially varying hybridization yield of DNA bridges, whose temperature dependence comes from the free energy change ΔG/RT [for details, see (7, 24, 25)]. In the absence of displacement, the free energy change of the hybridization reaction Embedded Image, given by ΔG/RT = ΔHAB/RT – ΔSAB/R, is monotonic with a steepness set by ΔHAB, because the enthalpy change ΔHAB and entropy change ΔSAB are largely independent of temperature (Fig. 1A).

With displacing strands, the free energy difference between bridged and unbridged states can be modified owing to the additional reaction pathways Embedded Image and Embedded Image. Because the enthalpic changes of displacement reactions can be tuned through the base sequences of the displacing strands, the free energy change ΔG/RT can be designed to have various nonlinear dependences on temperature (figs. S1 and S2). Furthermore, the entropic changes of the displacement reactions can be adjusted by changing the molar concentrations of the displacing strands, providing a way to tune the magnitude of ΔG/RT independently of its dependence on temperature.

A single displacement reaction (Fig. 2A) allows precise control over the thermodynamics of the fluid-solid transition. We control the temperature dependence of the free energy change ΔG/RT, and thus of the interaction potential, by changing the displacing strand sequence. Using the nearest-neighbor model, which relates DNA sequences to hybridization free energies (9), we predict the enthalpic changes of displacement and bridge formation. If we choose the appropriate sequences such that these enthalpic changes are the same Embedded Image, we can eliminate the temperature dependence entirely over a range of temperatures (fig. S1). We thereby establish a dynamic equilibrium in which the bridging and nonbridging duplexes exchange freely by toehold-exchange hybridization, without an enthalpic barrier.

Fig. 2 A single displacement reaction eliminates the temperature dependence of binding.

(A) Competition between bridge formation and strand displacement results in stable coexistence between fluid and solid phases that persists over a wide range of temperatures. (B) Representative confocal fluorescence micrographs of a binary suspension of DNA-grafted particles at various temperatures. (C) Experimentally measured particle singlet fraction (symbols) shows the broadening of the melting transition with increasing concentration of free strand D1 (indicated on plot) (25). Error bars denote SD of three measurements. A model based on local chemical equilibrium (curves), together with a separate model of the singlet fraction (16), reproduces our results to within the inherent uncertainty of the nearest-neighbor model (9, 25, 32). DNA sequences and predicted free energies are given in tables S1 and S2.

This single-displacement scheme, where Embedded Image, eliminates the boundary between the coexistence region and the solid phase, resulting in coexistence between fluid and solid that persists even at low temperatures (Fig. 2B). In the absence of the displacing strand, we find a single, steep melting curve with an approximate width of 1°C, consistent with earlier reports (16). The melting transition softens with increasing concentration of the free strand (Fig. 2C), widening by 10°C or more. Furthermore, the singlet fraction remains nonzero and constant down to room temperature. Because the entropy of the free strands can be adjusted by changing their molar concentration, the singlet fraction, and thus the interaction strength, can still be tuned.

This single-displacement scheme solves a long-standing problem in DNA-directed self-assembly: the steep dependence of the interparticle attraction on temperature (17), which frustrates equilibrium self-assembly. Previous experiments and simulations have shown that crystal nucleation and growth occur over a range of interaction strengths only 1 to 2 kBT wide, corresponding to a temperature window roughly 1°C wide (6, 26). In contrast, with a single displacement reaction, we find that nucleation and growth of binary crystals occurs over a range of temperatures wider than 10°C—an improvement of at least an order of magnitude relative to displacement-free schemes. Expanding the temperature window of equilibrium assembly makes it easier to grow crystals and obviates the need for precision temperature control, temperature gradients, or complex annealing schemes (10, 11, 13).

Our model of DNA-mediated attractions in the presence of strand displacement quantitatively reproduces these measurements (Fig. 2C). Taking the grafting density, free-strand concentration, ionic strength, and DNA sequences as inputs, we reproduce the measured singlet fractions to within the inherent uncertainty associated with the nearest-neighbor model (25). This level of agreement supports our physical picture—that the changes in the temperature dependence result directly from molecular-scale displacement reactions—and demonstrates that the emergent phase behavior can be predicted and therefore programmed.

With two-displacement reactions (Fig. 3A), we can make the free energy not only a nonlinear function of temperature but also a nonmonotonic one, with interesting consequences for the phase behavior: The resulting suspensions display multiple fluid-solid transitions and inverted phase behavior, in which the stable, low-temperature phase is a fluid that freezes upon heating before melting again at higher temperatures. Such reentrant behavior results from a competition between entropy and enthalpy. The low-temperature fluid is stabilized enthalpically: Because each bridge can be replaced by two nonbridging duplexes of the same length, the most favorable state contains few or no bridges between particles, thus maximizing the total number of base pairs. At higher temperatures, entropy favors the solid phase, because formation of a single bridge liberates two displacing strands. At even higher temperatures, the solid phase melts again, owing to thermal dissociation of DNA bridges.

Fig. 3 Two strand-displacement reactions program a tunable reentrant melting transition.

(A) Hybridization of free displacing strands induces a second melting transition. (B) Representative confocal fluorescence micrographs show re-entrant melting of a binary suspension of DNA-grafted particles. (C) Singlet fraction f measurements (symbols) show that the reentrant melting transition can be tuned by changing the displacing strand concentrations CD0 for equimolar mixtures of D1 and D2 (indicated on plot) (25). Error bars denote SD of three measurements. Our local chemical equilibrium model (curves) reproduces our results to within the inherent uncertainty of nearest-neighbor predictions (9, 25, 32). (D) The displacing strand concentration–temperature coexistence envelope is delimited by the temperature and CD0 where 0.15 < f < 0.85 (gray). Symbols show experimental data: orange for f > 0.85, blue for f < 0.15. We achieve coexistence over roughly 10°C when CD0 = 250 μM. DNA sequences and hybridization free energies are shown in tables S3 and S4.

Our experiments (Fig. 3B) show that the resulting reentrant melting transition is tunable and can be programmed independently of the solid-phase symmetry. By adjusting the concentrations of the displacing strands, we control the temperature window in which the solid phase is stable (Fig. 3C). Higher concentrations of displacing strands shift the local chemical equilibrium toward nonbridging duplexes, leading to a narrower window (Fig. 3D). Strand concentrations exceeding a critical limit prevent freezing entirely. The crystals that we assemble have the expected cesium chloride (CsCl) symmetry (fig. S3). Because energetic arguments suggest that intraspecies attractions as weak as ~1 kBT would lead to formation of Cu-Au crystals instead of the observed CsCl crystals (13, 27), we conclude that our approach does not result in undesired cross-talk between intra- and interspecies attractions.

Of course, the principal feature of DNA-grafted particles is the ability to create multiple particle species that interact with each other in specific ways. Strand displacement allows us to modify each interaction and thereby program pathways between different self-assembled structures. To demonstrate this feature of our approach, we combine the displacement-free and two-displacement schemes to program a reversible pathway between two compositionally distinct equilibrium ordered phases. Specifically, we design a system containing three different particle species with a temperature-dependent interaction matrix, implemented through six DNA sequences (table S5), four of which are grafted to particles and two of which are displacing strands that modulate interactions between species 2 (green in Fig. 4A) and the other two species. At low temperatures, the interaction matrix favors cocrystallization of species 2 and 3, as confirmed by confocal fluorescence microscopy (Fig. 4B). At high temperatures, it favors cocrystallization of species 1 and 2. At intermediate temperatures, we program an intervening fluid phase by tuning the displacing strand concentrations, which allows us to easily nucleate and grow either crystal by lowering or raising the temperature. Because the system is in equilibrium at each temperature, the observed phase transitions are completely reversible.

Fig. 4 The zero- and two-displacement reaction schemes are combined to program a pathway between two colloidal crystals.

(A) Strand displacement yields a temperature-dependent specificity matrix defining favorable (gray) and unfavorable (white) interactions in a ternary suspension. Measured pair interactions (symbols) in this experimental system agree quantitatively with our model calculations (curves). Error bars denote SD of three measurements. (B) Confocal fluorescence experiments (25) show CsCl binary crystals of species 2 (green) and 3 (blue) in coexistence with a fluid of species 1 (red) at low temperature (left), and CsCl crystals of species 1 (red) and 2 (green) in coexistence with a fluid of species 3 (blue) at high temperature (right), separated by a homogeneous fluid phase of all three species at intermediate temperature (middle), as predicted. The two crystals have the same symmetry, as determined by the lattice distance Embedded Image in the {110} plane, but different compositions; D is the particle diameter. Hybridization free energies are shown in table S6.

These last experiments demonstrate that the specificity afforded by Watson-Crick base pairing, which is used to program the structure of equilibrium self-assembled phases, can itself be programmed to depend on temperature, enabling reconfigurable materials in which particles change their interactions and reconfigure their structure in response to temperature. The approach is limited only by the freezing and boiling points of the buffer: Because the transition illustrated in Fig. 4 is roughly 10°C wide, one could conceivably design transitions between at least 10 distinct solid phases in the 0° to 100°C temperature range, which could each be directed to self-assemble independently and on cue simply by changing the temperature. Moreover, incorporation of thermally driven solid-solid transitions could also enable the sequential self-assembly of other crystal phases not accessible by direct nucleation from the fluid, but which have the lowest free energy at a given temperature (13). These systems represent an additional direction in self-assembly, in which information supplied to the buffer can program equilibrium pathways between many different target structures within a closed system.

The zero-, one-, and two-displacement reaction schemes constitute a set of primitives that can be combined to further program thermal pathways to self-assembly. We have demonstrated one such combination—a zero-displacement reaction combined with a two-displacement reaction—but many others are possible, owing to the specificity of DNA hybridization. A key feature of our approach is that it separates the functions of the grafted strands, which encode the interaction matrix, and the free displacing strands, which control the temperature dependence of the interaction matrix. Other competitive binding schemes have been proposed (2830), but none results in independent control of the temperature-dependent phase transitions and the symmetry of the equilibrium phases. This independent control, which is crucial to fully program self-assembly, could make it possible to assemble complex materials in multiple stages. For example, particles might first self-assemble into a scaffold that would disassemble after helping the final, prescribed structure to assemble. Similar strategies are used in biological systems such as bacteriophages (31) and could prove to be more robust than current one-step approaches to assembly. More generally, our demonstration that strand displacement alters the local chemical equilibrium between DNA-grafted particles opens the door to the inclusion of more complex strand displacement–based devices into colloidal assembly. For example, incorporation of DNA-based logic gates, cascaded circuits, or catalytic amplifiers (19) could make it possible nonequilibrium self-assembly pathways in colloidal matter.

Supplementary Materials

www.sciencemag.org/content/347/6222/639/suppl/DC1

Materials and Methods

Figs. S1 to S3

Tables S1 to S6

References (3340)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: We thank S. Magkiriadou, J. Collins, Z. Zeravcic, and M. Brenner for helpful discussions. Supported by the Harvard MRSEC through NSF grant DMR-0820484, NSF grant DMR-1435964, and an Alfred P. Sloan Research Fellowship. See the supplementary materials for additional data.
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