Supplementary Material for Binary superlattice design by controlling DNA-mediated interactions

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1 Supplementary Material for Binary superlattice design by controlling DNA-mediated interactions Minseok Song #, Yajun Ding #, Hasan Zerze, Mark A. Snyder, Jeetain Mittal Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA 1815, USA # These authors contributed equally to this work. To whom correspondence should be addressed; jeetain@lehigh.edu. 1

2 I. SUPPORTING INFORMATION TEXT A. Effective pair potential model for DNA-functionalized particles The effective pairwise interactions between DNA-functionalized particles (DFPs) are derived from previously published simulation data using a sequence-specific coarse-grained model [1]. Advanced sampling techniques (replica exchange molecular dynamics and umbrella sampling) were used to obtain free energy or potential of mean force (PMF) as a function of interparticle distance. We use the following expression to fit these data to represent various contributions to the interparticle interactions between DFPs, (i) repulsive interactions between particle cores, (ii) repulsive interactions due to DNA chain overlap, and (iii) attractive interactions due to DNA hybridization. U(r) = ɛ o ( σ o r r shift ) n + A 1 + exp(a 1 (r A 2 )) B 1 + exp(b 1 (r B 2 )) (1) Figure S1 shows an example comparison between the simulation data and eq. 1. By varying B, we can model potentials with different attractive well depths if particle size and overall grafting density is held constant. Even though the PMFs represented by eq. 1 are reflective of nanosized particles, the qualitative shape of the potential is quite similar to the one measured experimentally for micron-sized particles [2]. We simply rescale the potential to reflect features of micron-sized particles with an appropriate DNA length used in the experimental part of this work. Specifically, we have used the following values for various parameters in eq. 1: ɛ = 1.ɛ, σ =.2σ, r shift =.8σ, n = 36, A = 11.3ɛ, A 1 =.σ 1, A 2 = 1.17σ, B 1 = 1.5σ 1 and B 2 = 1.31σ. B was changed from to 1.32 to vary the attractive well depth between and 1.ɛ, respectively. B. Nearest neighbor analysis (NNA) To distinguish the formation of various binary superlattices, we calculate the average number of like (AA and BB) and unlike contacts (AB), defined as N K = n i K /n with K = {AB, AA, BB}. Where, n is the total number of particles analyzed in a given lattice and 2

3 n i K is the number of contacts (AB, AA or BB) between particle i and its nearest neighbors. [1] Y. Ding, J. Mittal, J. Chem. Phys. 11 (21). [2] W. B. Rogers, J. C. Crocker, Proc. Natl. Acad. Sci. 18, (211). 3

4 II. SUPPORTING INFORMATION FIGURES Potential of mean force [k B T] REMD Umbrella sampling Sampling MCJ Eq Pair distance [σ] Figure S 1. Potential of mean force (PMF) between two DNA-functionalized particles, with each particle grafted by 16 ssdna strands with sequence TTTTTTATGTATCAAGGT or TTTTT- TACCTTGATACAT. Mean Potential Energy E AA /E AB = E AA /E AB =.97 E AA /E AB =.22 E AA /E AB =.31 E AA /E AB =.22 E AA /E AB =.535 E AA /E AB =.65 E AA /E AB = Temperature Figure S 2. Mean potential energy as a function of temperature from molecular dynamics simulation for different E AA /E AB = E BB /E AB. These data are used as a guide to define putative melting temperature and to conduct additional simulations to study self-assembly behavior of binary superlattices.

NN = HexagonalNN = 6 A B C 2 N NN 3 Square 1 NN NN NNAB 3.5 3 NN = 6 N 2 1 A [arb. units] 3.5-12 3-16 2.5-2 2 A [arb. units] NN = NNNN =6= 3 3.5 NAB NAB units] A [arb. 23 2.5 1 2-8 -8-12 3 2.

(Top) Average number of particles with nearest -16 neighbors (NNs) equal to and 6. (Bottom) Average number of unlike contacts (NAB ) as a -2 function of EAA /EAB = E BB /EAB.

5 NN = HexagonalNN = 6 A B C 2 N NN 3 Square 1 NN NN NNAB NN = 6 N 2 1 A [arb. units] A [arb. units] NN = NNNN =6= NAB NAB units] A [arb (a) (a).2..6 (b).8 1 EAA/EAB = EBB/EAB (b).2. (c).6.8 EAA/EAB = EBB/EAB (c) 1 Figure S 3. Nearest neighbor analysis (NNA). (Top) Average number of particles with nearest -16 neighbors (NNs) equal to and 6. (Bottom) Average number of unlike contacts (NAB ) as a -2 function of EAA /EAB = E BB /EAB. For low pair energies, square lattices (NN = ) are observed order.2.whereas.6hexagonal.8lattices1(nn = 6) are observed with near-perfect compositional (NAB = ), E /E = E /E AA AB BB at intermediate and high pair energies. The compositional orderab for hexagonal lattices also depend on the interparticle interaction strength. 5

6 (a) Number of common neighbors Rcut = (2,1,1) = (,2,1) Number of bonds in the longest chain of bonds Number of bonds btw. common neighbors (b) Reference particle Similarly, of the neighbors have CNA indices of (2,1,1) Similarly, of the neighbors have CNA indices of (,2,1) Red: Reference & Neighbor, Green particles: common neighbors, Green lines: Bonds btw. common neighbors As Rcut Bs 6 neighbors have CNA indices of (2,,) (c) Crystal Rcut / Dp CNA indices (all particles) CNA indices (only A or B particles) Square 1.6 { x (2, 1, 1) and x (, 2, 1) } - Hexagonal 1.6 { 6 x (2,, ) } - Alternating string { x (,, ) } Honeycomb { 6 x (3, 1, 1) and 3 x (, 2, 1) } or { 6 x (2,, )} Kagome { x (2,, ) and x (3,, ) }, or { no neighbor } Square kagome { 2 x (2,, ) and 1 x (2, 1, 1) and 2 x (3, 1, 1) and 1 x (, 2, 1) and 2 x (, 2, 2) } or { x (3, 1, 1) and x (, 2, 2) and 2 x (, 3, 3) } or { 2 x (,, ) } Figure S. Common neighbor analyses (CNA). (a) Illustration of the determination of CNA indices for a perfect square lattice and the definition of index components. (b) The CNA index determination in a compositionally ordered lattice (illustrated in a perfect honeycomb) for a specific particle type to be used in the identification of the compositionally ordered 2D crystals. (c) Reference CNA indices and frequencies for perfect 2D crystals. 6

7 Figure S 5. Experimental melting profiles for a suspension of the DNA-functionalized particles. When the fraction of α-strands on B-type particles is increased, the melting curve of the binary system (γ A γ B ) shifts to left whereas that of the unary system (γ A = γ B ) shifts to the right. Figure S 6. Evolution of pair correlation function (PCF) as a function of (a) DNA blending ratio, γ B (γ A = ) and (b) particle number ratio, n. Reference PCFs for perfect square and hexagonal lattices are shown. 7

8 Figure S 7. Evolution of pair correlation function (PCF) separated by particle identity (AA: panels a and b, BB: panels c and d) as a function of (a,c) DNA blending ratio, γ B (γ A = ) and (b,d) particle number ratio, n. Reference PCFs for perfect honeycomb and Kagome lattices are shown. 8

arxiv: v1 [cond-mat.soft] 5 Mar 2015

arxiv: v1 [cond-mat.soft] 5 Mar 2015 arxiv:5.677v [cond-mat.soft] 5 Mar 5 Insights into DNA-mediated interparticle interactions from a coarse-grained model, a) Yajun Ding and Jeetain Mittal Department of Chemical and Biomolecular Engineering,