Stochasticity of poly(2-oxazoline) oligomer hydrolysis determined by tandem mass spectrometry

Understanding modification of synthetic polymer structures is necessary for their accurate synthesis and potential applications. In this contribution, a series of partially hydrolyzed poly(2-oxazoline) species were produced forming poly[(2-polyoxazoline)-co-(ethylenimine)] (P(EtOx-co-EI)) copolymers; EI being the hydrolyzed product of Ox. Bulk mass spectrometry (MS) measurements accurately measured the EI content. Tandem mass spectrometry analysis of the EI content in the copolymer samples determined the distribution of each monomer within the copolymer and corresponded to a theoretically modelled random distribution. The EI distribution across the polymers was shown to be effected by the choice of terminus, with a permanent hydrolysis event observed at an OH terminus. A neighbouring group effect wasn't observed at the polymer length analysed (approximately 25-mer species), suggesting that previously observed neighbouring group effects require a larger polymer chain. Although clearly useful for random polymer distribution this approach may be applied to many systems containing non-specific modifications to determine if they are directed or random locations across peptides, proteins, polymers, and nucleic acids.

Section S1: Mass spectrometry conditions The hydrolysed sample was dissolved into purified water obtained from a Direct-Q3 Ultrapure Water System (Millipore, Lutterworth, United Kingdom) at 20 μM and acidified for analysis via addition of 0.5% formic acid (v/v) (Sigma-Aldrich, Dorset, United Kingdom). All experiments were performed on a 12 T solariX Fourier transform ion cyclotron resonance mass spectrometer (Bruker Daltonik, GmbH, Bremen, Germany) using a nano-electrospray (nESI) ion source in positive-ion mode. The ECD was carried out with the use of an indirectly heated hollow cathode with a current set at 1.5 A, with a pulse length of 0.2 s and bias 1.2 V. All data were recorded using 4 mega-word (2 22 , 22 bit) transients (1.6777 s) achieving approximately 500,000 resolving power at m/z 400 for the intact mass spectrometry with a mass cut off at m/z 147 and 400,000 resolving power at m/z 400 for the tandem mass spectrometry with a low mass cut off at m/z 100. All mass spectra were internally calibrated by the intact polymer peaks across the polymer distribution, or by internal calibration of fragment peaks in ECD spectra (peaks used for calibration are marked). The peaks used for internal calibration were crosschecked using both the a and x fragment series. The Bruker SNAP algorithm was used for peak picking with the polyoxazoline monomer used as the repeat unit (C 5 H 9 NO). The Bruker SNAP algorithm matches a calculated isotope distribution adjusted to a repeat unit with increasing mass. [1] Section S2: Additional analysis notes  Figure 3 are the fragment intensities comparing the peak area of the 0-EI containing fragment and the 1-EI containing fragment at each monomer position. By calculating the total peak area of fragments at each monomer position the relative proportions of differing EI amounts can be compared to one another generating a plot, Figure 3C. The theoretical plot, Figure 3D, assumes completely random hydrolysis, calculated using the same method discussed in the experimental but with a single hydrolysis event randomly distributed across a 20-monomer species. Deviation from the theoretical plots indicates deviation from completely random hydrolysis events during the synthetic process. Figure 3C shows the analysis comparing the area of each modified/unmodified peak pair. The total areas of the a n peaks in both the 0-EI and 1-EI series were summed at the ratio between the two compared. The results, presented in Figure 3, closely align with the theoretical plot, Figure 3D. Showing the presence of the 1-EI group trending upwards linearly across the length of the polymer chain.

Section S2: Theoretical plotting of random distributions
The use of tandem mass spectrometry to localize non-specific modification positions graphically has been effectively carried out using DNA, [2] we extend this by predicting and then fitting to, random distributions. The fragmentation data was compared to the statistically distributed fragmentation patterns. The statistically distributed hydrolysis maps were calculated by combination of PEI units within a polymer chain using a modified Heap's algorithm. [3] The total number of arrangements was calculated and the fragment intensities were calculated by code included in the SI. Figure 1 shows a theoretical model of 2 EI units evenly distributed across five monomer units using the Heap's algorithm and how, at different fragmentation points, the total proportion of each species will vary. Put simply: Random hydrolysis events (H) will evenly distribute across all possible combinations. All possible combinations will be statistically represented during the analysis.
At monomer position 1 measuring back to the α (left) methyl terminus 40% of fragments have one hydrolysis event (H) as only one monomer unit is present; a doubly hydrolysed species can't be present. The remaining 60% of fragments possible have not undergone a hydrolysis event. One hydrolysis event (H) represents the presence of and EI species. Depending on whether the fragment contains 0, 1, or 2 hydrolysis events (H) dictate whether that fragment is a 0-EI, 1-EI, or 2-EI containing species respectively.
Moving to monomer position 2 60% of measured fragment oligomers contain one hydrolysis event (H). 30% of fragments contain no hydrolysis events and 10% of fragments contained 2 hydrolysis events.
Fragmentation at each monomer and the resulting oligomer unit can be analyzed in the same way and the proportions compared.
If the practical data shows similar binomial distribution to the theoretical plot then they hydrolysis is random, if there is a large shift in the distribution then it is not random.
Practically, the peak areas at each monomer position are compared. For example, the 0-EI a 3 , 1-EI a 3 , and 2-EI a 3 fragment peak areas are compared to one another. The peak area is calculated within the DataAnalysis program and the same peak picking is used for all assignments. As the measurement is relative to other peaks in a given summed spectrum, deviations in signal to noise from spectrum to spectrum do not influence the techniques use, and fragments are similar enough in abundance and resolved well enough that S/N variation has little effect on individual monomer positions.
Section S3: Synthesis of Poly(oxazoline) and species Scheme S1: Overview of synthesis of P(Ox-co-EI)-OH, through hydrolysis of POx.

Instrumentation
Size Exclusion Chromatography P(EtOx)-OH was measured on an Agilent Infinity II MDS instrument equipped with differential refractive index (DRI), viscometry (VS), dual angle light scatter (LS) and multiple wavelength UV detectors. The system was equipped with 2 x PLgel Mixed C columns (300 x 7.5 mm) and a PLgel 5 µm guard column. The eluent is CHCl 3 with 2 % TEA (triethylamine).
Samples were run at 1 ml min -1 at 30 °C. Poly(methyl methacrylate), and polystyrene standards (Agilent EasyVials) were used for calibration. Ethanol was added as a flow rate marker. P(EtOx)-N 3 was measured on an An Agilent Infinity II MDS instrument equipped with differential refractive index (DRI), viscometry (VS), dual angle light scatter (LS) and multiple wavelength UV detectors was used for SEC analysis. The system was fitted with 2 x PLgel Mixed D columns (300 x 7.5 mm) and a PLgel 5 µm guard column. The eluent used was DMF with 5 mmol NH 4 BH 4 additive. Samples were run at 1 ml min -1 at 50 °C. Poly(methyl methacrylate) standards (Agilent EasyVials) were used for calibration between 955,500 -550 g mol -1 .
Analyte samples were filtered through a GVHP membrane with 0.22 μm pore size before injection. Respectively, experimental molar mass (M n, SEC ) and dispersity (Đ) values of synthesized polymers were determined by conventional calibration using Agilent GPC/SEC software.

Nuclear Magnetic Resonance
Proton nuclear magnetic resonance spectra ( 1 H NMR) were recorded on a Bruker Advance 300 spectrometer (300 MHz), with chemical shift values (δ) reported in ppm, and the residual proton signal of the solvent used as internal standard. 1 H NMR of P(EtOx) homopolymers was measured in CDCl 3 . 1 H NMR of P(EtOx-co-EI) copolymers was measured in CD 3 OD

Synthesis
Synthesis of ω-hydroxyl-poly (2-ethyl-2- The vial was sealed and placed into a Biotage Initiator+ Eight microwave reactor and heated to 120 °C for a pre-determined time (see Table S  The degree of hydrolysis determined by 1 H-NMR was calculated using the integration values (I) and Equation S1 ( Equation S1 : Calculation of total hydrolysis as a % of pEI content.       Figure S 3: x-series fragmentation diagram P(Ox 19 -co-EI 1 )-N 3 reverse of Figure 3C in text