Hydrodynamic Analysis Resolves the Pharmaceutically-Relevant

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Hydrodynamic Analysis Resolves the Pharmaceutically-Relevant Absolute Molar Mass and Solution Properties of Synthetic Poly(ethylene glycol)s Created by Varying Initiation Sites Ivo Nischang, Igor Perevyazko, Tobias C. Majdanski, Juergen Vitz, Grit Festag, and Ulrich S. Schubert Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b03615 • Publication Date (Web): 11 Dec 2016 Downloaded from http://pubs.acs.org on December 11, 2016

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Analytical Chemistry

Hydrodynamic Analysis Resolves the PharmaceuticallyRelevant Absolute Molar Mass and Solution Properties of Synthetic Poly(ethylene glycol)s Created by Varying Initiation Sites Ivo Nischang,*,a,b Igor Perevyazko,*,a,b,c Tobias Majdanski,a,b Jürgen Vitz,a,b Grit Festag,a,b Ulrich S. Schubert*,a,b a

Laboratory of Organic and Macromolecular Chemistry (IOMC), Friedrich Schiller University Jena, Humboldtstraße 10, 07743 Jena, Germany; [email protected]; [email protected]

b

Jena Center for Soft Matter (JCSM), Friedrich Schiller University Jena, Philosophenweg 7, 07743 Jena, Germany

c

Department of Molecular Biophysics and Physics of Polymers, St. Petersburg State University, Universitetskaya nab. 7/9, 199034, Saint Petersburg, Russia; [email protected] The solution behavior originating from molecular characteristics of synthetic macromolecules plays a pivotal role in many areas, in particular the life sciences. This situation necessitates the use of complementary hydrodynamic analytical methods as the only means for a complete structural understanding of any macromolecule in solution. To this end, we present a combined hydrodynamic approach for studying in-house prepared, low dispersity poly(ethylene glycols)s (PEGs), also known as poly (ethylene oxide)s (PEOs) depending on the classification used, synthesized from varying initiation sites by living anionic ring opening polymerization. The series of linear PEGs in the molar mass range of only a few thousand to 50 000 g mol-1 have been studied in detail via viscometry, and sedimentation-diffusion analysis by analytical ultracentrifugation. The obtained estimations for intrinsic viscosity, diffusion coefficients, and sedimentation coefficients of the macromolecules in the solution-based analysis clearly showed selfconsistency of the followed hydrodynamic approach. This self-consistency is underpinned by appropriate and physically-sound values of hydrodynamic invariants, indicating adequate values of derived absolute molar masses. The classical scaling relations of Kuhn-Mark-Houwink-Sakurada of all molar-mass dependent hydrodynamic estimates show linear trends, allowing for interrelation of all parametric macromolecular characteristics. Differences among these are ascribed to the observation of α-end and chain-length dependent solvation of the macromolecules, identified from viscometric studies. This important information allows for analytical tracing of variations of scaling relationships and a physically-sound estimation of hydrodynamic characteristics. The demonstrated self-sufficient methodology paves an important way for a complete structural understanding and potential replacement of pharmaceutically-relevant PEGs by alternative macromolecules offering a suite of similar or tractably distinct physicochemical properties.

The area of advanced materials has diversified rapidly with the inception of a variety of synthetic methods to create soft matter components for life science and energy application platforms. The structure and chemical identity of such components is crucial for the resultant implementation. In the case of macromolecular and multi-functional constructs, this requires an exact knowledge and detailed reconciliation of the absolute molar mass, functionality, and conformation in a particular solution of interest. The majority of studies concerning the characterization of synthetic macromolecules allude to size exclusion chromatography (SEC).1 SEC falls short in its suitability for more complex macromolecular systems since calibration of the SEC system is based on more or less suitable reference standards, whose absolute properties, in particular its hydrodynamic volumes, need to be known in advance.2 Notwithstanding, together with mass spectrometry (MS) and the diversity of spectroscopic techniques such as nuclear magnetic resonance (NMR), SEC is the standard in almost any laboratory.3

The pitfalls of common analytical methods in terms of accuracy and suitability are difficult to overcome, in particular since we are interested in investigations of the particular solvated-state of macromolecules, reference-free and without instrument calibration based on standards. This as well should enable the study of macromolecules in solutions that may closely resemble their intended use. The aim should be a reference-free characterization of macromolecules in solution.2 Thereby, the inherent roadblock for a fundamental solution characterization of advanced life-science material precursors urgently needs to be overcome. Several sophisticated options of choice for characterization of macromolecules in solution are found in the overarching family of light scattering4 and hydrodynamic methods, as well as developments concerned with Taylor dispersion analysis.5,6 Among the diversity of hydrodynamic methods, a key role should be reserved for sedimentation velocity analysis using an analytical ultracentrifuge.7 Analytical ultracentrifugation is a classical analytical technique that found its inception with pioneering work by Svedberg,8-10 who received the noble prize

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in chemistry as early as 1926. It can be used to study the solution behavior of nearly any macromolecular, respectively colloidal system in a wide range of solute concentrations and in a large variety of solvents.10-12 However, though analytical ultracentrifugation is wellknown and a classical, indispensable tool in biochemistry and biophysics, its application for studying synthetic macromolecules is still rather limited up to now.13-17 With respect to macromolecular characterization science, the information extracted from sedimentation-velocity experiments in the ultracentrifuge can be combined with orthogonal hydrodynamic methods used in classical macromolecular science, e.g. viscometry and diffusion measurements.16,18 This combined approach applied for homologous series including that of existent and potentially up-and-coming pharma-polymers will provide most reliable and comprehensive information on the macromolecular characteristics, void of the necessity or existence of a notoriouslyneeded reference standard. Therefore, we chose a contemporary example of varying αend functionalized, in-house prepared poly(ethylene glycol)s (PEGs) including the methoxyPEG (mPEG) as a macromolecule approved by the Federal Drug Administration (FDA) for diverse medical uses and being a prominent candidate for a broad range of applications in the life sciences.19 This is mainly due to its stealth properties, biocompatibility, and limited toxicity.19-21 PEGs have conquered many applications ranging from pharmacy, as industrial lubricant, coating materials, etc.. Though PEGs are commercially available in a manifold of purities and α-end group identities, limited information on their behavior in solution studied by straightforward hydrodynamic methods is available.22-25 Our recent experimental accessibility to such macromolecules in a desirable molar mass range for pharmaceutical applications and with varying α-end groups, made them an excellent objective of study. This should create a baseline for forthcoming characterization work related to more complex functional variants,26 conjugates to proteins,27,28 and potential alternatives sought for their replacement.20,29,30 To this end, we report on the potential of sedimentation velocity experiments in the pharmaceutically-relevant molar mass range in combination with intrinsic viscosity measurements. Through the provided unique key analytical approach that, in its entirety, relies on first principle measurements, we found distinct and self-consistent insights for these watersoluble macromolecules.

EXPERIMENTAL SECTION Chemicals and Materials. Several series of α-end group functionalized PEGs were prepared in-house (Scheme 1) via an anionic ring opening polymerization (AROP) of ethylene oxide from respective initiation sites. Their preparation is described in the Supporting Information. The first series comprised diphenylmethane PEGs (DPMPEG 1-7), the second methoxyPEG (mPEG 1-7) as a gold standard for pharmaceutical applications and used widely in the PEGylation of proteins,31 and the third example new iso-fructose PEGs (isoFruPEGs 1-3) in their respective protected and deprotected form. Ultrapure water was freshly acquired from a Thermo ScientificTM BarnstedTM GenPureTM xCAD Plus water purification system (Thermo Electron LED GmbH, Langenselbold, Germany) and used throughout all experiments.

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Size Exclusion Chromatography. Details for size exclusion chromatography, used calibration standards, and molar mass estimations can be found in the Supporting Information. Viscosity Measurements. Viscosity measurements were performed with an AMVn viscometer (Anton Paar, Graz, Austria). The capillary/ball combination of the measuring system allowed the determination of respective flow times for the solvent water, , and for macromolecule solutions of varying concentrations, . Relative viscosities, , were determined at a tilting angle of the capillary of 50°, and at concentrations of the macromolecules in solution in a range that resulted in values of / 1.2 2.5. Extrapolations of viscosity to zero concentration were performed by using both the Huggins (eq 1) and the Kraemer equation (eq 2): 1 ⋯ 1 ln ⋯ 2 c

The average values of both extrapolations were considered as the value of intrinsic viscosity, . Scheme 1. Graphical representation of poly(ethylene glycol)s (PEGs) with the ω-hydroxyl group (green) and a variety of α-ends originating from varying initiation sites, that are (1) the diphenyl methane (DPMPEG), (2) methoxy (mPEG), and (3) iso-Fructose (iso-FruPEG) in the protected (a), and deprotected form (b).

Partial Specific Volume Determinations. The partial specific volume, , can be defined as the change of the solution volume when a macromolecule is dissolved in a solvent at constant temperature and pressure. This is either assessed experimentally32 or by computational tools.33 In the present work, the partial specific volume was estimated via density measurements.32 The density measurements were carried out in the density meter DMA 4100 (Anton Paar, Graz, Austria). Here, the density of varying concentrations of macromolecules in aqueous solution were studied. Typically, these determinations were in the concentration range of 1 2%, while approaching zero concentration, i.e. the respective solvent density, . The slope of the resultant curve, 1 0 , is also known as the buoyancy factor. Analytical Ultracentrifugation. Sedimentation velocity experiments were performed with a ProteomeLab XL-I analytical ultracentrifuge (Beckman Coulter, Brea, CA), using double-sector aluminum centerpieces with a 12 mm optical path length. The centerpieces were placed in a four-hole rotor (An60 Ti). A typical rotor speed of 50 000 rpm was used. The cells were filled with ca. 420 µL of sample solution and 440 µL of the solvent water (Figure 1a). Three concentrations of each sample in water were centrifuged within a concentration


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range of a factor between of at least three to six. Sedimentation was followed by the interference optical detection system (with resulting sedimentation profiles such as in Figure 1b). Before the acquisition run, the rotor was equilibrated and the formation of a sedimentation front was allowed for a typical time of one hour at " 20 °$. The sedimentation profiles were recorded at the same temperature for a timescale of at least 24 hours using the interference optics, with a sedimentation profile scan for each cell performed every 3 minutes.

lecular species with a given concentration in solution.36 In simple words, eq 3 can be utilized to describe the time-radial concentration distribution *, of species having a sedimentation coefficient, %, and a diffusion coefficient, ,, in the centrifugal field - * (where - is the angular velocity) acting on the sector-shaped cell volume under given boundary conditions:35 . 1 / / 01, - *%2 *3 3 . * /* /*

Numerical solution of eq 3 based on sedimentation velocity data from varying concentrations resulted in differential distributions of %. The first moment of the resultant distributions of %, (such as in Figure 1c) showed varying concentration dependence. The values of sedimentation at an infinitely diluted solution, % , were then estimated either (i) by average values of % if there was no apparent concentration dependence, or by linear approximation of individual first moments of % and extrapolating to zero concentration, following the relationship: % 56 %56 1 ' 4

Figure 1. Conceptual approach to estimate molar masses and related quantities by sedimentation velocity experiments. (a) Picture of the ultracentrifuge interior containing rotor and cells with the detector assembly for interference detection, (b) Sedimentation profiles at varying timescales used to estimate distribution of sedimentation coefficients, %, at varying concentrations from the continuous % distribution model shown in (c) for three descending concentrations of DPMPEG 2 (black, blue, and green line). Further details on this macromolecule are found in Table S1.

Sedimentation Velocity - Data Analysis. For the analysis of the sedimentation velocity data, the continuous % model with a Tikhonov−Phillips regularization procedure in the Sedfit program was applied.34 Depending on sedimentation velocity, every fifth or tenth scan was used for evaluation of sedimentation coefficients to ensure acceptable accuracy.34 The % model is based on the numerical solution of the Lamm equation (eq 3),35 assuming the same apparent translational frictional ratio, &/&'() , values for each sedimenting macromo-

where ' is the concentration sedimentation coefficient (Gralen coefficient).37 Estimated values of % were then used to calculate the intrinsic sedimentation coefficient % by eq 5: % % 5 1 8 were is the viscosity of the solvent water. Similarly to the values of %, the apparent translational frictional ratio, &/&'() , at varying solution concentrations was found to either fluctuate around a mean value (for small molar masses), respectively showed a pronounced decreasing trend at reduced solution concentration (for larger molar masses).16,38 The translational frictional ratio at ‘zero’ concentration (i.e. at infinite dilution), &/&'() was either taken as an average of values at varying concentrations if there was no apparent concentration dependence, or estimated by linear approximation following the relationship: &/&'() &/&'() 1 9 : 6 were 9 is the concentration frictional ratio coefficient. We note that &/&'() is an intrinsic function of both the molecular shape (originating from conformation, flexibility) and the solvation. & is the translational frictional coefficient of the macromolecule and &'() describes the frictional coefficient of the corresponding spherical particle of the same anhydrous volume and mass.39 The translational diffusion coefficient, , , was then calculated using the following relationship: "1 8 6⁄ , 7 =⁄ ⁄ = 9?√2 AB& ⁄&'() : C % 6⁄ where is the Boltzmann constant, " is the temperature, and 8 , are the density, and viscosity of the solvent water. Based on , we can then define the intrinsic diffusion coefficient ,: , , 8 "

RESULTS AND DISCUSSION Overarching, a combination of different hydrodynamic methods was used for evaluating the molecular properties of the varying α-end group functionalized PEGs in aqueous solution, i.e. (i) intrinsic viscosity, , estimations by the Huggins and Kraemer extrapolations, (ii) sedimentation-diffusion anal-



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ysis by means of analytical ultracentrifugation and derived hydrodynamic parameters such as % , B&⁄&'() : , and , . First, we discuss the primary experimental data as well as the estimations and then we move to the evaluation and subsequent discussion of the absolute molar mass, size, conformation, and solvation of the macromolecules. Finally, we performed a reference analysis of the PEGs by three different SEC systems calibrated with commercially available standards as a notoriously-used hydrodynamic characterization technique of almost any type of synthetic macromolecule. Intrinsic Viscosity. Figure S1 shows plots for determination of intrinsic viscosities after the Huggins and Kraemer equations (eqs 1 and 2). All plots are linear over the studied concentration range resulting in values for in a range of F 10 80 G= H56 for the DPMPEG 1-7, F 10 60 G= H56 for the mPEG 1-7, and F 8 20 G= H56 for the iso-FruPEG 1-3 in their protected and deprotected form. Clearly, the intercept of both correlations, characterizing , is readily similar for each macromolecular species studied here. The overall estimates for are summarized in Table S1). Partial Specific Volume. The partial specific volume υ was calculated from the corresponding density measurements as Δ /Δ 1 0 ). Figure S2a-c shows plots of the measured density increment of each series of the PEG. A global fit to the cumulative data of each α-end PEG (Scheme 1) led to unresolvable deviations for the macromolecules’ α-end group identity. Average values of the partial specific volume were found being 0.835 J 0.006 G= H56 for the DPMPEG and 0.834 J 0.008 G= H56 for the mPEG, while they were on average 0.827 J 0.001 G= H56 for the iso-FruPEGs, both in their protected and deprotected form. Estimations of values for each single here studied macromolecule showed fluctuations around their average values, without a significant trend in the macromolecule series (Figure S2d). The values of as well agree well with reports of related macromolecules in the literature.22 Sedimentation Coefficients, Translational Frictional Ratios, and Diffusion Coefficients. Example distributions of sedimentation coefficients of particular concentrations of the macromolecules studied here are shown in Figure 2a-c. All distributions of sedimentation coefficients show a single species with a very narrow population of sedimentation coefficients, indicating a narrow unimodal molar mass distribution. Values for % (eq 4) and B&⁄&'() : (eq 6) of each of the macromolecules were derived from plots shown in Figures S3 and S4. These are summarized in Table S1. It is clearly seen that % and &⁄&'() within the present set of macromolecules showed a range in between % 0.1 1 K (Figures 2 and S3, Table S1), and frictional ratios between B&⁄&'() : 1 3 (Figure S4, Table S1). The here obtained results are then used to examine their physical soundness and, consequently, to calculate associated properties of the macromolecules. Consistency of Experimental Data - Hydrodynamic Invariants. The interrelation between the basic hydrodynamic characteristics ( (eqs 1 and 2), % (eq 5), and , (eq 8)) can be evaluated by calculating the hydrodynamic ants, L MN H G % 5 O 56 GPQ56/= , for all populations of macromolecules:40 6 L R%, S= TU. 9 with R being the universal gas constant.

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The determined and studied values of qualify as an independently determined hydrodynamic parameter (based on rotational friction) from that of the sedimentation-diffusion analysis performed on sedimentation velocity experiments in the ultracentrifuge to derive % and , (both based on translational friction). The low fluctuations of L values around their averages in the present study (Figure S5, Table S1) allow to conclude that satisfactory correlations between the molecular characteristics obtained from different measurements are seen. We found that hydrodynamic invariants assume values of L 3.42 J 0.16 V 1056 for the DPMPEG 1-7, respec-

Figure 2. Example normalized distributions of sedimentation coefficients, %, at the macromolecules’ (Scheme 1) smallest concentrations in ultracentrifugation. (a) DPMPEG 1-7, (b) mPEG 1-7, and (c) iso-FruPEG 1-3 in protected (solid lines) and deprotected (dotted lines) form. Details on the macromolecules can be found in Table S1.

tively L 3.51 J 0.25 V 1056 for the mPEG 1-7, and L 3.50 J 0.17 V 1056 for the three rather small isoFruPEG 1-3 examples, in both their protected and deprotected form. As well, the values are in the upper range known for flexible linear chain macromolecules.40 With these consistent


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results between differently estimated hydrodynamic characteristics at hand, we can then move to the consistently estimated prime parameter of interest, i.e. the absolute molar mass. Absolute Molar Mass and Hydrodynamic Diameter. The absolute molar mass, W',9 , was estimated based on the modified Svedberg equation (eq 10), that contains a set of distinct, experimentally and numerically determined parameters. These are: (i) the frictional ratio, &⁄& '() (eq 6), (ii) the intrinsic sedimentation coefficient % derived from eq 5 via % (eq 4), obtained from the numerical solution to the Lamm equation of sedimentation velocity data (eq 3), and the estimated partial specific volume from density measurements. The molar mass based on &⁄& '() , %, and is defined by: W',9 9?√2XY A% A& ⁄& '() C C

=⁄

√ 10

where XY is the Avogadro constant. Eq 10 resembles the classical Svedberg equation, W',Z % R"/, 1 8 ,8,10,39 that inherently requires knowledge of % and , to estimate the molar mass, W',Z . In the here presented self-sufficient analysis, &⁄& '() is used as a hydrodynamic parameter to estimate translational diffusion coefficients, , (eq 7), respectively directly the absolute molar mass W',9 (eq 10). As being shown for the here studied macromolecules as well as demonstrated before for other macromolecules,16,17,38 the estimated values of frictional ratios (consequently diffusion coefficients, eq. 7) by numerical solution of the Lamm equation (eq 3) are correct, which, in turn, qualifies sedimentation velocity as a practical absolute method. This situation can be inferred by the discussed values of the hydrodynamic invariants (eq. 9) that bring into consideration values of intrinsic viscosities, , and intrinsic sedimentation coefficients, %. However, for certain macromolecule systems with stronger non-ideality and/or for rigid chain macromolecules, the evaluation of frictional ratios by this approach may fall in accuracy.14 In this case independent measurements of the translational diffusion coefficients are required. The hydrodynamic size, .) , in a first approximation can be estimated using the determined values of intrinsic sedimentation coefficient, %, and frictional ratio &⁄& '() . This is possible by combining the Svedberg equation (W',Z % R"/, 1 8 ), with the Stokes-Einstein equation (, "/&, where & is the translational frictional coefficient): .) 3√2[% AB&⁄&'() : C

=⁄

11

This equation contains the frictional ratio, B&⁄&'() : , therefore accounting for the asymmetry and solvation of the macromolecule,39 based on the hydrodynamic equivalent sphere concept. Clearly, the radius of a hydrodynamic equivalent sphere can differ substantially from the size of the real macromolecule.41 Nevertheless, this approach can be useful for a general assessment of hydrodynamic sizes of macromolecules. Scaling Relationships and Gross Conformation in solution. With the comprehensive data presented in the previous sections, we finally can move to the discussion about the most probable conformation of the macromolecules in solution and how the different hydrodynamic characteristics relate to each other. This information can be obtained by establishing so called Kuhn-Mark-Houwink-Sakurada relationships.42-44 These scaling relationships may take the following general form: _`,a

\] O],^ \^

12

where \] is one of the particular hydrodynamic characteristic such as , % , &⁄& '() , , , or .) . \^ is another hydrodynamic characteristic from this set, or simply the values of the corresponding molar masses, W',9 . Figure 3 shows double logarithmic dependences of the discussed hydrodynamic characteristics vs. W',9 . The estimated

Figure 3. Double logarithmic plots of experimentally determined hydrodynamic parameters \] (eq 12) where the index M refers to (black symbols), % (blue symbols), B&⁄&'() : (green sym bols), and , (red symbols) and \^ where the index k refers to absolute values of the molar mass, W',9 (eq 10). Symbol assignment: DPMPEG (empty circles), mPEG (filled circles), and isoFruPEG (filled (protected) and empty (deprotected) grey stars). The data in plots were fitted linearly to determine the resultant constants O],^ and exponents b],^ (see Table 1).

values of exponents, b],^ , from linear fits to these plots are displayed in Table 1 and the constants O],^ in the footnote. The obtained magnitude of average exponents for intrinsic viscosity,23,25 for sedimentation,23 and diffusion,24 are in the same range as those reported separately in the literature, despite the fact that a limited, respectively different, range of molar masses has been investigated here. An interrelation of these exponents of each series of the PEGs (i.e. bB9⁄9cde : & bZ , f

bh & bZ , b' & bZ , see footnote of Table 1) demonstrates rea-

sonable agreement and indicates self-consistency of the here performed analysis. Table 1. Constants O],^ and exponents b],^ (eq 12) with standard error in

brackets. The index M refers to , % , A&S&%ij C , , , or .) and the index k refers to W',9 .

bh

b'f

mPEG

0.63 (± 0.03)

0.43 (± 0.02)

DPMPEG

0.73 (±0.03)

0.41 (± 0.02)

a

PEG

b

c

bB9⁄9cde:

bZf

ble

0.21 (±0.01)

-0.52 (± 0.01)

0.55 (±0.01)

0.28 (±0.02)

-0.63 (± 0.02)

0.62 (± 0.02)

0

a Structure of the α-end is shown in Scheme 1. Interrelation of exponents mbZf m B& ⁄&'() : 1/3, mbZf m 1 bh /3, and mbZf mb'f 1 is given within the experimental error. b Constants: Oh 8.6 n 105 G= H56; O'f 1.0 n 105 K; OB9⁄9cde: 28.4 n 105 ; OZf 89.7 n 105o G % 56 ; Ole f

3.7 n 105 NG Constants: Oh 3.0 n 105 G= H56 ; O'f 1.3 n 105 K; O&⁄&%ij 13.9 n 105 ; OZf 253.6 n 105o G % 56 ; Ole c

f

1.8 n 105 NG



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Though the accuracy of estimated exponents from double logarithmic plots and their values will be limited and may require a larger molar mass range (eq 12), all exponents suggest random coil conformation.45 We as well note that calculated values of the hydrodynamic invariants, L , suggested existence of flexible linear chain macromolecules (vide supra). However, the here presented analysis gives further distinct insight. It can clearly be seen in Figure 3 that (black symbols) and % (blue symbols) increase with W',9 , while the slopes of for the series of the DPMPEG (empty circles) and mPEG (filled circles) appear reasonably distinct (Table 1). The slopes for % are practically indistinguishable between the series of the mPEG and DPMPEG within the experimental error. Figure 3 shows as well one of our prime interest and concerns the frictional ratios &⁄&'() (green symbols) and their dependence on W',9 . &⁄&'() estimates increase linearly within the W',9 range studied in this double logarithmic plot. The increase can be explained in view of a deviation of a flexible backbone macromolecule from that of a spherical particle of the same anhydrous volume and mass. Small values of &⁄& '() close to one indicate that the macromolecules behave in first approximation like a spherical particle, while larger values indicate significant deviation of molecular shape from that of spherical and/or the macromolecule is strongly hydrated (solvated).39 This would also be expected for a random coil conformation of flexible linear chain macromolecules. Some difference in the slopes of the DPMPEG (empty circles) and mPEG (filled circles) also for , and .) can be discerned and cannot be explained by experimental error (Table 1). These differences may be related to the influence of different α-end groups of the studied macromolecules (vide infra). Solvation of the macromolecules and their impact on hydrodynamic characteristics. In order to explain the differences in scaling relationships found for a rather small molar mass range studied here, we first focus our attention on . can be described by the well-known Flory equation:46,47 〈j〉 =/ ∅ 13 W',9 where ∅ is the Flory-parameter and 〈j〉 is the average mean square chain end-to-end distance of the population of the macromolecules. In fact, in first approximation resembles the hydrodynamic volume 〈j〉 =/ (eq 13), a strong function of solvation and swelling, affecting the macromolecule of a given molar mass. The qualitative description of solvation and swelling may be assessed by the viscometric Huggins, , and Kraemer, , constants for each absolute molar mass, W',9 , in the present study. The data to extract and are available from our viscometric measurements by the slope of the respective dependences of plots shown in Figure S1 (eqs 1 and 2). Flexible macromolecule chains possess values in the range of 0.2 to 0.8, most frequently about 0.3 in good solvents. Typically there is a general tendency of to increase for more poor solvents. The Kraemer constant, , is usually negative. In our case, the calculated Huggins constant, , shows an increase while moving toward the smaller molar masses (Figure 4a). This effect is most pronounced for the series of the DPMPEG, while being attenuated for that of the mPEG and iso-FruPEG. While an increase in with decreasing molar mass can be identified for the entirety of series, aggravated by the hydro-

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phobic α-end group, the trend may indicate an increasingly poorer solvation of the macromolecules at the lower molar masses. We note that for two molar mass examples of the DPMPEGs the Kraemer constant, , is actually positive as seen by their positive slopes in Figure S1a, distinct from the entirety of all studied macromolecules here. Furthermore, the following relationship should hold between the dimensionless constants and : 0.5;48 a situation found for the larger molar masses of each series of PEGs, irrespective of their α-end group (Scheme 1 and Figure 4b). However, differences in α-end group identity appear significantly pronounced at lower molar masses. In fact, among different hydrodynamic characteristics, is expected to be very sensitive to size changes and the here presented scaling relationships indicate a pronounced difference of intrinsic viscosities of macromolecules differing in their αend group (Figure 3, empty and filled black circles, Table 1). It is therefore safe to assume that for the DPMPEG is re-

Figure 4. (a) Plots of the Huggins constants, (eq 1) derived from intrinsic viscosity, , measurements shown in Figure S1 in dependence of the absolute molar mass, W',9 (eq 8). (b) Plots of the difference of (eq 2) and the Kraemer constants, (eq 2), , in dependence of W',9 (eq 10). The dotted line is shown as a guide to the eye. Symbols: DPMPEG 1-7 (empty circles), mPEG 1-7 (filled circles), and iso-FruPEG 1-3 (filled (protected) and empty (deprotected) grey stars).

duced due to poorer solvation and, as a consequence, significantly larger values of the Huggins constant, . Solvation by itself then is dependent on the molar mass (Figure 4a). The influence of the DPM α-end group on the macromolecules vanishes at molar masses approaching highest values for the here studied and presented set of PEGs, i.e. approaching 30 000 to 50 000 g mol-1 (Figure 3, empty vs. filled black circles), at a range where also differences between the solvation for


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macromolecules with different α-end groups vanishes (Figure 4a). Poorer solvation of the macromolecules also significantly impacts , (Figure 3, empty vs. filled red circles) and, consequently, .) (see Figure S6 of the Supporting Information). This shows that we start to resolve differences in hydrodynamic characteristics between the mPEG and DPMPEG within a small molar mass range. This situation demonstrates unprecedented experimental resolution provided by analytical ultracentrifugation in combination with viscometric studies of nanometer-sized macromolecular species (Figure 3). Hydrodynamic Volume Estimations. The constitution of macromolecules in solution may be described by hydrodynamic volume estimations, s) .2 It follows from eq 13, that s) ~〈j〉 =/ ~W',9 . The estimate W',9 is plotted against W',9 in Figure S7. The curves represent, in a comprehensible way, the significantly smaller hydrodynamic volume of the smaller molar mass DPMPEGs as compared to the mPEGs, while this difference vanishes at molar masses approaching 50 000 g mol-1. This result is consistent with the situation that the hydrodynamic volume is strongly affected by solvation of the macromolecules. Not surprisingly, this situation originates from significantly poorer solvation for the smaller molar mass DPMPEGs as compared to the mPEGs (Figures 3, 4, S7). The iso-FruPEGs somewhat correlate well with that of the mPEGs (Figures 3, 4, S7), in agreement with the entirety of hydrodynamic characteristics presented in this work. The similarity in hydrodynamic characteristics is deemed important for their use in potential medical settings, since the iso-FruPEGs in their deprotected form may resemble promising candidates for targeting cancer.49 It is worth noting that the hydrodynamic volume of PEGs as well influences the elution times in SEC50 and, based on the hydrodynamic volume concept, enables absolute calibration of SEC systems operated in the same solvent.2 Correlation of the Absolute Molar Mass with Standard Analytical Methods - Size Exclusion Chromatography. In a final attempt to find overarching validity of our data, we performed the standard size exclusion chromatography (SEC) of varying α-end functionalized PEGs (Scheme 1), whose com-

Figure 5. Correlation of the weight-average molar mass, Wu , of the here studied PEGs obtained by SEC to that of absolute values of the molar mass, W',9 (eq 10) for the DPMPEG 1-7 (empty circles), mPEG 1-7 (filled circles), and iso-FruPEG (filled (protected) and empty (deprotected) grey stars). The dotted line is plotted as a guide to the eye and represents an ideal correlation (i.e. equality) of average Wu values from SEC and W',9 values derived from sedimentation velocity analysis.

prehensive solution properties, in particular its absolute molar masses, W',9 , have been studied here in water without any prior knowledge. Three different SEC systems available in our laboratory have been utilized. These were calibrated via PEG/PEO standards within a suitable molar mass range, as specified in the Supporting Information. Calibration curves are shown in Figure S8 and individual elution profiles of the macromolecules in Figure S9. The determined weight-average molar masses (Wu ) for each macromolecule from these three different SEC systems were averaged and then correlated to absolute molar masses, W',9 (eq 10). Based on the here presented analysis, W',9 , should closely relate to the Wu , since the estimation of sedimentation coefficients, %, is based on the first moment of the % distribution (e.g. Figures 1c and 2).34,51,52 Furthermore, the distributions of sedimentation coefficients are really narrow and fairly symmetrical (Figure 2). Figure 5 clearly shows that the absolute values of W',9 show a good correlation to the Wu determined by SEC. We note that while the agreement is excellent for molar masses below 15 000 g mol-1 (see inset in Figure 5), a systematic overestimation of SEC can clearly be seen for the larger molar masses. Here also, the variation among SEC systems is largest as indicated by the error bars. While the origins of such differences may be manifold and require further investigations, we believe they may originate from standard molar masses, whose way of determination is very often based on SEC itself, being imprecise.

CONCLUSION We have presented a comprehensive study of the determination of absolute properties of varying α-end PEGs in the pharmaceutically-relevant molar mass range prepared via different initiation sites. Estimations of absolute molar masses, relying on first principle absolute methods, and the associated solution hydrodynamics of the macromolecules have been exemplified for the most common solvent water. For the present set of macromolecules our combined study of (i) intrinsic viscosity as a measure for rotational friction, and (ii) sedimentation behavior and diffusion as a measure for translational friction have resolved, for the very first time, differences related to specific α-end functionalities of the PEG. While the mPEG is the prime example for biopharmaceutical applications (in particular for PEGylation reactions as approved by the FDA), the de-protected iso-FruPEGs have potential for targeting cancer. Finally, the here presented methodology will work for any desirable solvent, respectively buffer system, if estimations of the hydrodynamic characteristics and their consistency is checked for, as shown by the present approach. We are currently working on resolving the impact of PEGylation on protein hydrodynamics. As well, the search of potential candidates for PEG replacement is of great interest, gaining also increased attention in providing alternatives for biopharmaceutical research and applications. The tractable differences resolved by the here provided methodology offer a promising perspective for such alternatives being studied in a quantitative manner.

ASSOCIATED CONTENT Supporting Information Additional information as noted in text. This material is available as a single file free of charge via the Internet at http://pubs.acs.org.listing



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AUTHOR INFORMATION Corresponding Author * [email protected] * [email protected] * [email protected]

ACKNOWLEDGMENT The authors acknowledge support of this study from the Thüringer Ministerium für Wirtschaft, Wissenschaft und Digitale Gesellschaft (TMWWDG, ProExzellenz II, NanoPolar) for funding the Solution Characterization Group (SCG) at the Jena Center for Soft Matter (JCSM), Friedrich Schiller University Jena, Germany.

REFERENCES (1) Bouvier, E. S. P.; Koza, S. M. TrAC-Trends Anal. Chem. 2014, 63, 85-94. (2) Grubisic, Z.; Rempp, P.; Benoit, H. J. Polym. Sci., Part B: Polym. Lett. 1967, 5, 753-759. (3) Crotty, S.; Gerislioglu, S.; Endres, K. J.; Wesdemiotis, C.; Schubert, U. S. Anal. Chim. Acta 2016, 932, 1-21. (4) Wyatt, P. J. Anal. Chim. Acta 1993, 272, 1-40. (5) Cottet, H.; Biron, J. P.; Cipelletti, L.; Matmour, R.; Martin, M. Anal. Chem. 2010, 82, 1793-1802. (6) Cipelletti, L.; Biron, J. P.; Martin, M.; Cottet, H. Anal. Chem. 2015, 87, 8489-8496. (7) Lebowitz, J.; Lewis, M. S.; Schuck, P. Protein Sci. 2002, 11, 2067-2079. (8) Svedberg, T. Endeavour 1947, 6, 89-95. (9) Svedberg, T. J Phys. Colloid Chem. 1947, 51, 1-18. (10) Svedberg, T. Magy Kem Lapja 1972, 27, 101. (11) Schubert, D.; Tziatzios, C.; Schuck, P.; Schubert, U. S. ChemEur. J. 1999, 5, 1377-1383. (12) Chen, M.; Colfen, H.; Polarz, S. ACS Nano 2015, 9, 69446950. (13) Rasa, M.; Schubert, U. S. Soft Matter 2006, 2, 561-572. (14) Perevyazko, I.; Seiwert, J.; Schomer, M.; Frey, H.; Schubert, U. S.; Pavlov, G. M. Macromolecules 2015, 48, 5887-5898. (15) Pechar, M.; Pola, R.; Laga, R.; Braunova, A.; Filippov, S. K.; Bogomolova, A.; Bednarova, L.; Vanek, O.; Ulbrich, K. Biomacromolecules 2014, 15, 2590-2599. (16) Pavlov, G. M.; Perevyazko, I. Y.; Okatova, O. V.; Schubert, U. S. Methods 2011, 54, 124-135. (17) Pavlov, G. M.; Perevyazko, I.; Schubert, U. S. Macromol. Chem. Phys. 2010, 211, 1298-1310. (18) Meier, M. A. R.; Hofmeier, H.; Abeln, C. H.; Tziatzios, C.; Rasa, M.; Schubert, D.; Schubert, U. S. E-Polymers 2006. (19) Dingels, C.; Schoemer, M.; Frey, H. Chemie in Unserer Zeit 2011, 45, 338-349. (20) Knop, K.; Hoogenboom, R.; Fischer, D.; Schubert, U. S. Angew. Chem. Int. Ed. 2010, 49, 6288-6308. (21) Zalipsky, S. Adv. Drug Deliv. Rev. 1995, 16, 157-182. (22) Luo, Z. L.; Zhang, G. Z. J. Phys. Chem. B 2009, 113, 1246212465. (23) Bailey, F. E.; Kucera, J. L.; Imhof, L. G. J. Polym. Sci. 1958, 32, 517-518. (24) Brown, W.; Stilbs, P.; Johnsen, R. M. J. Polym. Sci., Part B: Pol. Phys. 1983, 21, 1029-1039. (25) Gregory, P.; Huglin, M. B. Makromol. Chem. 1986, 187, 1745-1755. (26) Dimitrov, P.; Hasan, E.; Rangejov, S.; Trzebicka, B.; Dworak, A.; Tsvetanov, C. B. Polymer 2002, 43, 7171-7178. (27) Dozier, J. K.; Distefano, M. D. Int. J. Mol. Sci. 2015, 16, 25831-25864. (28) Gokarn, Y. R.; McLean, M.; Laue, T. M. Mol. Pharm. 2012, 9, 762-773. (29) Mero, A.; Pasut, G.; Via, L. D.; Fijten, M. W. M.; Schubert, U. S.; Hoogenboom, R.; Veronese, F. M. J. Control. Release 2008, 125, 87-95.

Page 8 of 9

(30) Qi, Y. Z.; Chilkoti, A. Curr. Opin. Chem. Biol. 2015, 28, 181193. (31) Roberts, M. J.; Bentley, M. D.; Harris, J. M. Adv. Drug Deliv. Rev. 2012, 64, 116-127. (32) Kratky, O.; Leopold, H.; Stabinger, H. Methods Enzymol. 1973, 27, 98-110. (33) Durchschlag, H.; Zipper, P. J. Appl. Crystallogr. 1997, 30, 803-807. (34) Schuck, P. Biophys. J. 2000, 78, 1606-1619. (35) Lamm, O. Die Differentialgleichung der Ultrazentrifugierung; Almqvist & Wiksell, 1929. (36) Brown, P. H.; Schuck, P. Biophys. J. 2006, 90, 4651-4661. (37) Gralen, N. Sedimentation and diffusion measurements on cellulose and cellulose derivatives. University of Uppsala 1944. (38) Pavlov, G. M.; Amoros, D.; Ott, C.; Zaitseva, I. I.; de la Torre, J. G.; Schubert, U. S. Macromolecules 2009, 42, 7447-7455. (39) Cölfen, H. Analytical ultracentrifugation V; Springer, 2003; Vol. 113. (40) Tsvetkov, V. N.; Lavrenko, P. N.; Bushin, S. V. J. Polym. Sci. Pol. Chem. 1984, 22, 3447-3486. (41) Lee, H.; Venable, R. M.; MacKerell, A. D.; Pastor, R. W. Biophys. J. 2008, 95, 1590-1599. (42) Pavlov, G. M. Polym. Sci., Ser. A 2005, 47, 1129-1134. (43) Leon, A.; Lopez, M.; Gargallo, L.; Radic, D.; Horta, A. J Macromol. Sci. Phys. 1990, B29, 351-359. (44) Velickovic, J.; Vasovic, S. Makromolekul. Chem. 1972, 153, 207-218. (45) Harding, S. E. Biophys. Chem. 1995, 55, 69-93. (46) Newman, S.; Flory, P. J. J. Polym. Sci. 1953, 10, 121-123. (47) Flory, P. J.; Fox, T. G. J. Am. Chem. Soc. 1951, 73, 19041908. (48) Pamies, R.; Cifre, J. G. H.; Martinez, M. D. L.; de la Torre, J. G. Colloid Polym. Sci. 2008, 286, 1223-1231. (49) von der Ehe, C.; Rinkenauer, A.; Weber, C.; Szamosvari, D.; Gottschaldt, M.; Schubert, U. S. Macromol. Biosci. 2016, 16, 508521. (50) Trathnigg, B.; Yan, X. J. Chromatogr. A 1993, 653, 199-206. (51) Dam, J.; Schuck, P. Numerical Computer Methods, Pt E 2004, 384, 185-212. (52) Harding, S. E.; Schuck, P.; Abdelhameed, A. S.; Adams, G.; Kok, M. S.; Morris, G. A. Methods 2011, 54, 136-144.


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Hydrodynamic Analysis Resolves the Pharmaceutically-Relevant

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