Kinetics of DNA-coated sticky particles

Kun-Ta Wu, Lang Feng, Ruojie Sha, Rémi Dreyfus, Alexander Y. Grosberg, Nadrian C. Seeman, and Paul M. Chaikin

Phys. Rev. E 88, 022304 – Published 12 August 2013

Abstract

DNA-functionalized particles are promising for complex self-assembly due to their specific controllable thermoreversible interactions. However, there has been little work on the kinetics and the aggregation rate, which depend on the rate of particle encounters and the probability that an encounter results in particles sticking. In this study, we investigate theoretically and experimentally the aggregation times of micron-scale particles as a function of DNA coverage and salt concentration. Our 2- $μ$ m colloids accommodate up to 70 000 DNA strands. For full coverage and high salt concentration, the aggregation time is 5 min while for 0.1 coverage and low salt it is 4 days. A simple model using reaction-limited kinetics and experimental oligomer hybridization rates describes the data well. A controlling factor is the Coulomb barrier at the nanometer scale retarding DNA hybridization. Our model allows easy measurements of microscopic hybridization rates from macroscopic aggregation and enables the design of complex self-assembly schemes with controlled kinetics.

Received 16 October 2012

DOI:https://doi.org/10.1103/PhysRevE.88.022304

Authors & Affiliations

Kun-Ta Wu¹, Lang Feng¹, Ruojie Sha², Rémi Dreyfus³, Alexander Y. Grosberg¹, Nadrian C. Seeman², and Paul M. Chaikin¹

¹Center for Soft Matter Research, New York University, New York, New York, USA
²Chemistry Department, New York University, New York, New York, USA
³Complex Assemblies of Soft Matter, CNRS-Rhodia-UPenn UMI 3254, Bristol, Pennsylvania 19007, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 88, Iss. 2 — August 2013

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematic representation of the system. The aggregation kinetics relates to the microscopic hybridization time of single DNA strands S and S $^{'}$ . (b) Time evolution of the singlet fraction vs temperature for a surface coverage of 1 DNA per ${(59 nm)}^{2}$ , $χ = 0.05$ . (c) Same data as in (b) plotted as singlet fraction vs time for different temperatures.Reuse & Permissions
Figure 2
(a) Singlet fraction vs time for each sticky-end DNA coverage ratio $χ$ at a corresponding fixed temperature. From left (blue) to right (red), $χ = 1, 0.75, 0.5, 0.4, 0.3, 0.2, 0.1, 0.05, and 0.025$ respectively. The corresponding temperatures are 42 $^{\circ} C$ , 40 $^{\circ} C$ , 38 $^{\circ} C$ , 36 $^{\circ} C$ , 36 $^{\circ} C$ , 33 $^{\circ} C$ , 25 $^{\circ} C$ , 22 $^{\circ} C$ , and 12 $^{\circ} C$ respectively. The solid curves are the fit curves from Eq. (1). The intersection of the dashed line and the solid curve indicate the characteristic aggregation time $τ$ . (b) The characteristic aggregation time $τ$ vs. possible bonding configurations $N_{G}$ . The blue dots are the experimental data. The red curve is determined by Eq. (9) with $λ = 1 nm$ , $τ_{DLA} = 313 s$ , and $τ_{DNA}^{(0)} = 230 μ s$ .Reuse & Permissions
Figure 3
The characteristic aggregation time $τ$ vs Debye Hükel screening length $λ_{D}$ for $χ = 0.1$ . The blue dots are the experimental data. The red curve is determined by Eq. (9) with $χ = 0.1$ , equivalently $N_{G} = 25$ . The dashed curves indicate the uncertainty of the model due to the uncertainties of $τ_{DLA}$ , $τ_{DNA}^{(0)}$ , $χ$ , and total DNA coverage on the particles.Reuse & Permissions
Figure 4
(a) A pair of spheres with reaction patches held in contact. The red patches are a ligand for the green sphere (left) and a receptor for the blue sphere (right). The two spheres are held in contact and are allowed to rotational diffuse. The ligand-receptor reaction will be triggered when the ligand and the receptor touch each other by the rotational diffusion of the spheres. (b) A pair of complementary DNA strands attached to colloidal surfaces. Since the backbones of the DNA strands can rotate freely, the spatial diffusion space of the each sticky end is the surface of a hemisphere with a radius $L$ . The overlapping area of the two hemispheres is the red ring. These two DNA sticky ends can only hybridize when they are both in the ring. Hence, the ring is like the reaction patch in (a). (c) The angle for the sticky end to rotationally diffuse its own size.Reuse & Permissions
Figure 5
(a) The schematic diagram of our temperature gradient setup. (b) Monitored temperatures through a 27-day experiment. The upper (red) dots and lower (blue) dots are the temperatures measured through the right sensor and the left sensor as a function of time respectively. Over the period of 27 days, the averages of the measured temperatures from the left sensor and the right sensor are (10.1 $\pm$ 0.1) $^{\circ} C$ and (25 $\pm$ 0.01) $^{\circ} C$ , respectively.Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics