Polyelectrolytes

We have extended a model for empty capsid assembly (Wales, 2005 (link); Fejer et al., 2009 (link); Johnston et al., 2010 (link)) to describe assembly around NAs. A complete listing of the interaction potentials is provided below; here we present a concise description of our model. The pseudoatoms in the capsid subunit model are illustrated in Figure 1. Subunit assembly is mediated through an attractive Morse potential between Attractor (‘A’) pseudoatoms located at each subunit vertex. The Top (‘T’) pseudoatoms interact with other ‘T’ psuedoatoms through a potential consisting of the repulsive term of the LJ potential, the radius of which is chosen to favor a subunit-subunit angle consistent with a dodecahedron (116°). The Bottom (‘B’) pseudoatom has a repulsive LJ interaction with ‘T’ pseudoatoms, intended to prevent ‘upside-down’ assembly. The ‘T’, ‘B’, and ‘A’ pseudoatoms form a rigid body (Wales, 2005 (link); Fejer et al., 2009 (link); Johnston et al., 2010 (link)). See Schwartz et al. (1998) (link), Rapaport et al. (1999) (link), Rapaport (2004 (link), 2008 (link)), Hagan and Chandler (2006) (link), Hicks and Henley (2006) (link), Nguyen et al. (2007) (link), Wilber et al., (2007 (link), 2009a (link), 2009b) (link), Hagan (2008) (link), Nguyen and Brooks (2008) (link), Nguyen et al. (2009) (link), Elrad and Hagan (2010) (link), Johnston et al. (2010) (link), Hagan et al. (2011) (link), Mahalik and Muthukumar (2012) (link), Hagan (2013) for related models.
To model electrostatic interaction with a negatively charged NA or polyelectrolyte we extend the model as follows. Firstly, to better represent the capsid shell we add a layer of ‘Excluder’ pseudoatoms which have a repulsive LJ interaction with the polyelectrolyte and the ARMs. Each ARM is modeled as a bead–spring polymer, with one bead per amino acid. The ‘Excluders’ and first ARM segment are part of the subunit rigid body. ARM beads interact through repulsive Lennard–Jones interactions and, if charged, electrostatic interactions modeled by a Debye–Huckel potential. Comparison to Coulomb interactions with explicit counterions is shown in Figure 3D. We also show that the results do not change significantly when experimentally relevant concentrations of divalent cations are added to the system (Figure 3D). The ability of the Debye–Huckel model to provide a reasonable representation of electrostatics in the system can be understood based on the relatively low packing fractions (see Table 1) within the assembled capsids and the fact that the relevant experimental and physiological conditions correspond to moderate to high salt concentrations.
Simulations were performed with the Brownian Dynamics algorithm of HOOMD, which uses the Langevin equation to evolve positions and rigid body orientations in time (Anderson et al., 2008 (link); Nguyen et al., 2011 (link); LeBard et al., 2012 (link)). Simulations were run using a set of fundamental units. The fundamental energy unit is selected to be $E_{\text{u}}\equiv 1k_{\text{B}}T$ . The unit of length $D_{\text{u}}$ is set to the circumradius of a pentagonal subunit, which is taken to be $1D_{\text{u}}\equiv 5$ nm so that the dodecahedron inradius of $1.46D_{\text{u}}=7.3$ nm gives an interior volume consistent with that of the smallest $T=1$ capsids. Assembly simulations were run at least 10 times for each set of parameters, each of which were concluded at $2\times {10}^8$ time steps. The following parameters values were used in all of our dynamical assembly simulations: ${\lambda }_{\text{D}}=1$ nm, box size = 200 × 200 × 200 nm, subunit concentration = 12μM. During calculation of the thermodynamic optimal polymer length $L_{\text{eq}}^{\ast }$ , calculations were run at least $1\times {10}^7$ timesteps, with equilibrium assessed after convergence. Standard error was obtained based on averages of multiple $\left(\ge 3\right)$ independent simulations. Separate calculations of $L_{\text{eq}}^{\ast }$ were also performed using using the Widom test-particle method (Widom, 1963 (link)) as extended to calculate polymer residual chemical potentials (Kumar et al., 1991 (link); Elrad and Hagan, 2010 (link)) (described in more detail below). Snapshots from simulations were visualized using VMD (Humphrey et al., 1996 (link)).

Plastic substrates
(Hostaphan, 125 μm thick PET, purchased from Mitsubishi) and paper board (KKC paperboard grammage 274
g m^–2, 400 μm thickness, Klabin) were used as substrates for the manufacturing of the rOECDs. The
surface energy of the Klabin paperboard was 28.5
± 2.3 mN m⁻¹ (disperse 26.7 ± 1.2 mN m⁻¹, polar 1.8 ± 1 mN m⁻¹). Successful
cross hatch tests were also performed to evaluate the adhesion of
screen printed silver lines, that is, no silver was removed from the Klabin paperboard. PET films were preshrunk in a belt oven
for 6 min at 130 °C to improve the heat stability of the substrates. Similarly, the paper boards
were preheated at 120 °C for 4 min prior to screen printing.
Due to the tendency of the paper to change dimensions upon humidity
uptake (up to 0.5%, see Figure S1 in the Supporting Information), the paper substrates
were additionally run through the oven for 2 min at 120 °C directly
before every printing step. Furthermore, to minimize the buckling
of the paper substrate and facilitate the printing process, the paper
boards were hot pressed at 130 °C for approximately 40 s.
Screen printing of the different layers was performed using a DEK
Horizon 03iX screen printer and frames with polyester meshes. Screens
with different mesh counts (threads per centimeter and thread diameter)
were used in the different layers: 100–40 for the electrolyte,
120–34 for PEDOT:PSS, carbon and silver, and 140–31
for the insulating layers. The screen layout is shown in Figure S2. The approximate thicknesses of the
screen printed layers are carbon 9 μm, electrolyte 13 μm,
insulator 15 μm, PEDOT:PSS 0.5 μm and silver 11 μm.^{41 (link)}A schematic of the rOECD architecture
is presented and compared
with the conventional OECD architecture in Figure 1. For the reverse OECD architecture presented
herein, the first layer screen printed onto the substrate was a carbon
paste (7102 purchased from DuPont), which served
as the counter electrode. Thereafter two layers of electrolyte (E003, a polyelectrolyte-based ink formulation for screen
printing, commercially available from RISE) were
screen printed, including subsequent curing after each screen printing
step. The reason for printing two layers is to minimize the risk of
pinholes. To define the active areas of the display segments, two
layers of an insulator (UVSF 173 purchased from Marabu) were deposited in the following screen printing
steps, including a subsequent curing step after each screen printing
step. As the pixel electrode, or color changing electrode, two layers
of an ink containing PEDOT:PSS (poly(3,4-ethylenedioxythiophene) doped
with poly(styrene sulfonic acid)), S V4 (purchased
from Clevios) or EL-P 5015 (purchased
from Agfa), were screen printed on top, and into
the cavities, of the insulating layer. These are all the functional
layers required to enable electrochromic switching in the display
segments, but to lower the overall resistance of the display, and
therefore to shorten the switching time, a silver conductor (Ag 5000 from DuPont) was subsequently screen
printed along the outline of the display segments. Two layers of an
insulating ink were then screen printed on top, one opaque layer for
the graphical pattern (color matched UVSW-based ink
provided by Marabu) and one transparent layer for
the mechanical protection of the display (UVSW 904 purchased from Marabu). The green-colored UVSW-based ink used as mechanical protection in some of
the rOECDs (Figure 7) was color matched and provided by Marabu. The
different inks were cured prior to the printing of the following layer;
the insulating layers were cured with UV light, at a dose of approximately
800 mJ cm^–2, while the other layers were heat cured
at 120 °C for 2 min. The electrolyte layers were heat treated
at 60 °C for 2 min and then cured with UV light (∼800
mJ cm^–2).
Two different rOECD types were manufactured:
Type A, containing
one layer each of the S V4 and EL-P 5015 PEDOT:PSS inks as electrochromic
layers, and Type B, containing two layers of the S V4 PEDOT:PSS ink.

This procedure is identical to point 3.4. with the difference that CaCO₃ core was dissolved in a 0.2 M EDTA solution. The produced polyelectrolyte microcapsules were incubated for 1 h in Am:MASGA solution. After that, the supernatant was decanted, and the precipitate was washed with water. The microcapsules were obtained with an average diameter of 4.5 ± 1 μm.