Tuning Net Charge in Aliphatic Polycarbonates Alters Solubility and Protein Complexation Behavior

A synthetic strategy yielded polyelectrolytes and polyampholytes with tunable net charge for complexation and protein binding. Organocatalytic ring-opening polymerizations yielded aliphatic polycarbonates that were functionalized with both carboxylate and ammonium side chains in a post-polymerization, radical-mediated thiol–ene reaction. Incorporating net charge into the polymer architecture altered the chain dimensions in phosphate buffered solution in a manner consistent with self-complexation and complexation behavior with model proteins. A net cationic polyampholyte with 5% of carboxylate side chains formed large clusters rather than small complexes with bovine serum albumin, while 50% carboxylate polyampholyte was insoluble. Overall, the aliphatic polycarbonates with varying net charge exhibited different macrophase solution behaviors when mixed with protein, where self-complexation appears to compete with protein binding and larger-scale complexation.

. 1 H-NMR spectrum of the crude aliquot of the APC precursor synthesis, showing residual monomer relative to the polymer (600 MHz, in CDCl 3 with TMS). The -CH 3 protons of the monomer and the polymer (peaks E in Figure  S1) were integrated to determine the degree of conversion as 96.4%.

Syntheses and Purifications of APC Polyampholytes
APC polyampholytes, APC (+/-) 90/10, 80/20, 70/30 and 50/50 were synthesized following the same general procedures outlined in the "Synthesis" section of the main text, while the specific modifications are summarized in Table S1.

Dialysis purification of APC(+)100
For purification by dialysis, regenerated cellulose membranes with molar mass cutoff of 3,500 kDa (Spectrum) were first equilibrated in methanol and then loaded with filtered polymer solution (0.45 µm PTFE syringe filter) dissolved in MeOH. The dialysis bath was a 1.5 L beaker filled with methanol. The first methanol bath was exchanged the next morning after equilibrating overnight, the second bath was exchanged at the end of the day, and the third methanol bath equilibrated again over night. The dialysis bag was removed, and the polymer was dried under high vacuum. To fully dry the polymer after the yield check, the polymer was freeze/thaw cycled in liquid nitrogen while under high vacuum. This caused the polymer to flake off the sides of the vial. 1 H NMR indicated that the polymer sample had a methanol mol fraction of 11.1 % and a polymer repeat unit mol fraction of 88.9 %, despite days of drying under high vacuum at room temperature.

Dialysis purification of polyampholytes
The dialysis procedure for the polyampholyte was different. The dialysis membrane was first hydrated and equilibrated in water, and then filled with polymer dissolved in methanol. A 250 mL graduated cylinder, filled with methanol, served as the dialysis bath. The first 250 mL bath was discarded after 30 min, and the dialysis bag and graduated cylinder were rinsed with methanol. The bag was put into a second ≈ 250 mL methanol bath. After ≈ 80 min the second methanol bath was discarded, the bag was rinsed with methanol, and then placed in a third ≈ 250 mL methanol bath which was equilibrated overnight resulting in the swelling of the bag. The third bath was discarded and replaced with a fourth ≈ 250 mL bath. The bag remained in the fourth bath for 2 h to 3 h at which time the fourth bath was discarded and replaced with a fifth and final ≈ 250 mL methanol bath. The polymer was removed from the dialysis bag, concentrated by rotary evaporation at room temperature, and transferred to a tared vial. In total, five ≈ 250 mL methanol baths were used in dialysis over a ≈ 22.5 h period where the first bath was discarded in less than 1 h and the fourth bath was equilibrated overnight.   Figure S4. APC (+) 100 at 2.5 mg/mL, the same sample shown in Figure 4a of the main text, which was monitored by DLS every hour for overnight at 25 °C. The red dotted line represents the as-prepared solution (0 h).     The SANS data of APC (+) 100 and APC (+) 93 in PBS-D 2 O are shown in Figure S11. Notably, salt suppresses the correlation peaks as in Figure 6 of the main text. At low q, I(q) ~ q -d was used to model the upturn; at high q, the curves are best fit to the polydisperse Debye model, which assumes a Schulz-Zimm molecular weight distribution of the polymer. The overall model function reads:

Time-Resolved DLS of APC polyelectrolytes in Aqueous Solution
In the fitting, M w /M n is fixed at 1.38. The fitting results are summarized in Table S2. Notes: a Calculated based on the degree of polymerization (DP) and NMR functionalization of each polymer. b Calculated by the difference between the positively charged amino acids K (lysine) and R (arginine), and the negatively charged D (aspartic acid) and E (glutamic acid), in their amino acid sequences. c Calculated by multiplying the DP with the charge fraction. d Calculated by the net charge divided by the molar mass.

SANS on BSA with APC (+) 100 and 93 in PBS-D 2 O
The structure of bovine serum albumin was originally found to have a prolate ellipsoid shape with a semi-major axis of 70 Å and semi-minor axis of 20 Å by small-angle neutron scattering. 1 This was consistent with earlier sedimentation equilibrium measurements. 2

S12
The main text shows SANS data of the BSA. The ellipsoid model was used without modification in the NIST Igor Pro SANS analysis software. 3 The main parameters of interest are the semimajor (a) and semi-minor (b) radii of the BSA prolate ellipsoid ( Figure S13) and the effects of polymer complexation to BSA. Additional parameters are needed or may be estimated including the particle concentration and scattering length density () associated with the ellipsoid model. In this case the  c of BSA was fixed to 3.8 10 -6 Å -2 , consistent with prior studies 1 ,  s of the D 2 O PBS buffer was 6.3 10 -6 Å -2 . The least squares curve fitting results are shown in Table 2 which includes a flat scattering background due to incoherent scattering arising from primarily the protons from the BSA after the D 2 O buffer scattering was subtracted from the data. The uncertainty () represent one standard deviation of the fit. Our results differ slightly from the literature for BSA with semi-axes of 60 Å and 23 Å. We attribute these differences to the different D 2 O buffers used between the studies as well as a convoluted effect that may be caused by BSA dimers. The BSA fit result could not recover the feature between q = 0.15 Å -1 to 0.25 Å -1 . This may be caused by the presence of BSA dimers, S13 which were not removed. This feature appears in the BSA as well as the complex and therefore not associated with the polymer and further attempts to include would only lead to more parameters. We then fix the BSA structure and contrast factor as the core of the core-shell ellipsoid model and fit the BSA with the expected bound APC polycations as shown in Table S4 using an estimated  sh for the APC polymer as 1.0 10 -6 Å -2 . Figure S13 shows the basic geometric factors defined along two views of the prolate ellipsoid.
The fit results are summarized in Table S4 and in Table 2. The initial major core radius was held fixed at 60.3 Å and the major shell thickness resulted in 86.5 Å, a 26.2 Å increase. Interestingly, with the initial minor core radius held fixed at 23.5 Å, there was little change in the minor shell radius after complexation with APC(+)100. Similar results are observed with APC(+)93.
The increase in the radius of the shell relative to the core represents a change due to the polycation binding. We assume there are negligible free polycation chains in the solution following the complexation with BSA, as the scattering data are best fit by a single model of core-shell ellipsoid, rather than a combined model of ellipsoid and Gaussian coil.
The main equations for the prolate ellipsoid core-shell model may be found in the original sources 4 and the NIST Igor Pro data analysis software package. 3 We reproduce the key equations that do not include the structure factor, S(q), contributions that consider interparticle interactions and correlations due to the dilute solutions used and high salt concentrations that screen the long range electrostatic interactions. The scattered intensity I(q) involves an orientational average of the single-particle form factor, as a function of the integration variable (), with prefactors of | ( )| 2 the particle volume fraction, , volume of the particle V t , and a background (I b ) from solvent scattering and incoherent scattering arising primarily from the protons, The volume fraction of the particles is inter-related to the number density (n) of particles by  = nV t , which must be considered when using the Igor Pro Models as input or fitting the scale prefactor concentration.
The amplitude of the scattering by a core-shell ellipsoid is defined by, .
Eq. 3 The neutron contrast prefactors represent the scattering length density difference between core and shell in the first term and shell and solvent in the second term. The volumes of the core (V c ) and total core-shell (V t ) ellipsoid are defined by, Eq 4 and Eq 5, respectively, with semi-axis defined earlier and shown in Figure S13.
Eq. 4 ( , ) = over the common integration variable,  = cos w, where w is the orientation angle between the scattering vector q and semi-major axis a. As can be seen many of the variables appear as products and therefore are highly correlated. These correlations were minimized by keeping many of the parameters that may be estimated based upon the chemical composition or literature results, such S15 as scattering length densities. In the present case, the concentration was also fit which can lead to correlations to the geometric parameters. However, once the geometric parameters for the BSA core were fixed the only fit parameters would be the semi-axis of the core-shell ellipsoid and prefactor, was very close between the two polymers consistent with the sample preparation. The small contribution from the incoherent background after subtracting the solvent scattering is another parameter. This SEC provides relative molar mass which differs from the SEC in THF with absolute molar mass measurement via light scattering detection. Aqueous SEC traces for freshly prepared from the solid APC(+)93 purified by precipitation and no methanol dialysis is similar to the APC(+)100 that was purified by both precipitation and methanol dialysis. We provide this as the test that the polymers, as freshly prepared, are not substantially affected by methanolysis after post-S16 polymerization modification. The relative mass-average molar mass for the APC(+)93 is Mw = 17,200 Da with 1.29 polydispersity and APC(+)100 was 11,800 Da with 1.16 polydispersity, such data are not comparable to GPC in THF with absolute molar mass via light scattering detection, but provide confidence for the series of polymers to enable a net-charge study.