Influence of Constraints within a Cyclic Polymer on Solution Properties

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Influence of Constraints within a Cyclic Polymer on Solution Properties Md. Daloar Hossain, James C. Reid, Derong Lu, Zhongfan Jia, Debra J Searles, and Michael J. Monteiro Biomacromolecules, Just Accepted Manuscript • DOI: 10.1021/acs.biomac.7b01690 • Publication Date (Web): 28 Dec 2017 Downloaded from http://pubs.acs.org on December 30, 2017

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Influence of Constraints within a Cyclic Polymer on Solution Properties Md. D. Hossain,1 James C. Reid,1 Derong Lu,1 Zhongfan Jia1, Debra J. Searles1,2 and Michael J. Monteiro,1,2,*

1. Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, Brisbane QLD 4072, Australia 2. School of Chemical and Molecular Biosciences, The University of Queensland, Brisbane, Qld 4072, Australia. *author to whom correspondence should be sent: e-mail:

[email protected]

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ABSTRACT

Cyclic polymers with internal constraints provide new insight into polymer properties in solution and bulk, and can serve as a model system to explain the stability and mobility of cyclic biomacromolecules. The model system used in this work consisted of cyclic polystyrene structures, all with a nearly identical molecular weight, designed with 0 to 3 constraints located at strategic sites within the cyclic polymer, with either 4 or 6 branch points. The total number of branch points (or arms) within the cyclic ranged from 0 to 18. Molecular dynamic (MD) simulations showed that as the number of arms increased within the cyclic structure, the radius of gyration and the hydrodynamic radius generally decreased, suggesting the greater number of constraints resulted in a more compact polymer chain. The simulations further showed that the excluded volume was much greater for the cyclics compared to a linear polymer at the same molecular weight. The spiro cyclic, a structure consisting of three rings joined in series, showed significant excluded volume effects in agreement with experimental data; the reason for which is unclear at this stage. Interestingly, under a size exclusion chromatography flow, the radius of hydration for all the cyclic structures increased compared with the DLS data, and could be explained from the greater swelling of the rings perpendicular to the flow found from previous simulations on rings. This data suggests that the greater compactness, greater excluded volume and structural rearrangements under flow of constrained cyclic polymers could be used to provide a physical basis for understanding greater stability and activity of cyclic biological macromolecules.


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INTRODUCTION Cyclic (or ring) macromolecules represent a class of polymers with no chain-ends, and because of this unique feature cyclic macromolecules (including synthetic polymers and cyclic DNA or peptides) exhibit very different properties in comparison to their linear analogues. Cyclic polymers have a more compact coil conformation due to their lower conformational degree of freedom, and as such have a much greater glass transition temperature (Tg) than linear polymers with the same molecular weight, especially in the low molecular weight range.1-4 Polymer physicists have long recognized that cyclic polymers in the melt will diffuse in a different manner to that of a linear polymer chain, and thus will exhibit very different viscoelastic and phase transition behavior.5,

6

It has been found that cyclic

polymers diffuse two times faster than linear chains with the same molecular weight in the melt due to the cyclic's more compact coil conformation.7 This result is counterintuitive, diffusion of linear chains obeys the well-known reptation model8 and may be expected to diffuse faster. The reptation model suggests that the ends on the polymer chain determine the chains motion constrained within a tube but also allows relaxation of the tube constraints.9, 10 Since cyclic polymers have no chain-ends, reptation as we understand should not occur in the melt. There are many postulates to describe the diffusion process of cyclics, including for example the 'lattice tree' and 'lattice animal' models.11-13 Understanding the influence of constrained cyclic polymers should offer new insight into polymer physical properties, and these insights will provide an understanding into peptide, protein and DNA stability and packing. Jun and Mulder14 showed through simulations that two ring polymers in a confined space demixed more readily than two linear polymers, and suggested that this was the dominant physical explanation for the demixing of cyclic DNA in bacteria during DNA replication. Synthetic cyclic polymers can be made either via the ring-closure or the ring expansion methods.15-17 The ring-expansion method provides a unique synthetic strategy to produce high molecular weight cyclic chains without linear polymer impurities, but control over the molecular weight distribution (MWD) is limited with broad MWDs being produced.18 The ring-closure method can produce low molecular weight cyclics with narrow distributions. Percec and coworkers used the ring closure method ACS Paragon Plus Environment

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to make arrangements of cyclic oligomers with liquid crystal properties, with extensive characterization of their cyclic topologies.19-23 These cyclic products may contain a small amount of linear impurity24, 25 that will, if present, have a large influence on the viscoelastic properties.6 Great efforts have been taken to remove the residual linear starting material from the cyclic product through preparative size exclusion chromatography (SEC) with a quantitative analysis using the log-normal distribution (LND) fitting26, 27 of the MWD.28 The ring-closure method advantageously allows the synthesis of cyclic polymers with a diverse range of chemical compositions and topologies.29-34 During ring closure, a knot may form should the polymer chain consist of three or more entanglements. However, this will only be prevalent at very high molecular weights (a 15% probability at a MW of 1 million) and in a theta solvent.35 No knots will be formed if ring-closure is carried out in a good solvent for the polymer and when using low molecular weight starting linear polymers.36 It is also improbable that other structures (e.g. catenated ring) will form as most ring-closure experiments are carried out under dilute conditions. Cyclic biomacromolecules are ubiquitous in nature, and seem to have physical attributes superior to their linear analogues in solution. Cyclic (or plasmid) DNA, for example, has a greater stability than its linear analogue, and is now widely used to produce protein in a wide range of cell lines. Recently, the discovery of macrocyclic peptides has been predicted to lead to new and stable biological therapeutic agents.37 It has been suggested that the cystine constraints within the cyclic play a much greater role in enzymatic and thermal stability than the underlying cyclic structure; the data also show that cysteine constraints prevent the peptides from denaturing in the presence of significant levels of chaotropes.38 By constraining the peptide topology, the stability, binding affinity and pharmacokinetic properties greatly improves.39 Venom from the black mamba snake, for example, comprises a three-fingered peptide so potent that it can kill a human within 30 min due to its compact and distinct shape. The toxin consists of three loops (or cyclics) that emerge from the nucleus of the protein.40 This family of cyclic and constrained peptides (termed mambalgins) can have therapeutic potential due to their rapid and nanopotency against acute and inflammatory pain. In addition, their high selectivity to specific ion


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channels and receptors could greatly reduce side effects compared to commonly used drugs (e.g. morphine). It seems that cyclic biomacromolecules require intramolecular constraints to impart superior properties compared to linear and monocyclic structures in solution. In our previous work, we found that by coupling cyclic polymeric units in a sequence controlled manner, densely packed multicyclic polymer chains were formed.41 With an increase in the number of cyclic units, the polymer was driven to a compactness approaching the limiting value of linear polymers under theta (θ) conditions. This suggested that excluded volume effects diminished with the greater compactness due primarily to the cyclic polymeric units. In this work, we wanted to determine the influence of internal constraints within a cyclic polymer on their compactness and thus solution properties, analogous to the highly active cyclic peptides. Here, we designed the constraints within the ring of the same molecular weight, in which the constraint placement and type (i.e. number of arms per constraint) were judiciously chosen (see Scheme 1). All the cyclic structures given in Scheme 1 had the same molecular weight, which allowed us to examine the influence of constraints on the polymer dimensions and mobility in dilute solution conditions.


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Scheme 1. Cyclic polystyrene of a similar molecular weight (~19 K) with constraints increasing from 0 to 3, with the total number of arms per cyclic ranging from 0 to 18. The values in parenthesis are the number of monomer units per ring.

(58) (163)

(84)

(84)

(163)

(58) (58)

(a) ≡(OH)-PSTY-N3 , 8e (c) (c-PSTY)2 , 32

(b) c-PSTY-OH, 9e

(d) st-(c-PSTY)3 , 33

0 constraints

1 constraint (19)

(25)

(19)

(25)

(25) (50) (58)

(50)

(57)

(58) (25)

(e) sp-(c-PSTY)3 , 34

(25)

(f) G1-den-(c-PSTY)5 , 35

(25)

(25)

(19)

(19)

(75)

(19)

(19)

(g) G1-st-(c-PSTY)4 , 36

2 constraints

3 constraints


(g) G1-st-(c-PSTY)7 , 37

3 constraints

6

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EXPERIMENTAL Materials The following chemicals were analytical grade and used as received unless otherwise stated: alumina, activated basic (Aldrich: Brockmann I, standard grade, ∼150 mesh, 58 Å), Dowex ion-exchange resin (sigma-aldrich, 50WX8-200), magnesium sulphate, anhydrous (MgSO4: Scharlau, extra pure) potassium carbonate (K2CO3: analaR, 99.9%), silica gel 60 (230-400 mesh ATM (SDS)), pyridine (99%, Univar reagent), 1,1,1-triisopropylsilyl chloride (TIPS-Cl: Aldrich, 99%), phosphorus tribromide (Aldrich, 99%), tetrabutylammonium fluoride (TBAF: Aldrich, 1.0 M in THF), ethylmagnesium bromide solution (Aldrich, 3.0 M in diethyl ether), triethylamine (TEA: Fluka, 98%), 2-bromopropionyl bromide (BPB: Aldrich 98%), 2-bromoisobutyryl bromide (BIB: Aldrich, 98%), propargyl bromide solution (80% wt% in xylene, Aldrich), 1,1,1-(trihydroxymethyl) ethane (Aldrich,96%), sodium hydride (60% dispersion in mineral oil), sodium azide (NaN3: Aldrich, 99.5%), TLC plates (silica gel 60 F254), N,N,N´,N´´,N´´pentamethyldiethylenetriamine (PMDETA: Aldrich, 99%), copper (II) bromide (Cu(II)Br2: Aldrich, 99%). Copper(I)bromide and Cu(II)Br2/PMDETA complex were synthesized in our group. Styrene (STY: Aldrich, >99 %) was de-inhibited before use by passing through a basic alumina column. The following linkers were prepared according to the literature procedure: Methyl 3,5-bis (propargyloxyl) benzoate (12)42 and 1,3,5-tris(prop-2-ynyloxy)benzene (13)43. See Supporting Information for details of the cyclic structure synthesis. All other chemicals used were of at least analytical grade and used as received. The following solvents were used as received: acetone (ChemSupply, AR), chloroform (CHCl3: Univar, AR grade), dichloromethane (DCM: Labscan, AR grade), diethyl ether (Univar, AR grade), dimethyl sulfoxide (DMSO: Labscan, AR grade), ethanol (EtOH: ChemSupply, AR), ethyl acetate (EtOAc: Univar, AR grade), hexane (Wacol, technical grade, distilled), hydrochloric acid (HCl, Univar, 32 %), anhydrous methanol (MeOH: Mallinckrodt, 99.9 %, HPLC grade), Milli-Q water (Biolab, 18.2 MΩm), N,N-dimethylformamide (DMF: Labscan, AR grade), tetrahydrofuran (THF: Labscan, HPLC grade), toluene (HPLC, LABSCAN, 99.8%). ACS Paragon Plus Environment

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Analytical Methodologies Size Exclusion Chromatography (SEC) The molecular weight distributions of the polymers was determined using a Waters 2695 separations module, fitted with a Waters 410 refractive index detector maintained at 35 °C, a Waters 996 photodiode array detector, and two Ultrastyragel linear columns (7.8 x 300 mm) arranged in series. These columns were maintained at 40 °C for all analyses and are capable of separating polymers in the molecular weight range of 500-4 million g/mol with high resolution. All samples were eluted at a flow rate of 1.0 mL min-1. Calibration was performed using narrow molecular weight PSTY standards (PDISEC ≤ 1.1) ranging from 500 to 2 million g/mol. Data acquisition was performed using Empower software, and molecular weights were calculated relative to polystyrene standards.

Absolute Molecular Weight Determination by Triple Detection SEC Absolute molecular weights of polymers were determined using a Polymer Laboratories GPC50 Plus equipped with dual angle laser light scattering detector, viscometer, and differential refractive index detector. HPLC grade N,N-dimethylacetamide (DMAc, containing 0.03 wt % LiCl) was used as the eluent at a flow rate of 1.0 mL.min-1. Separations were achieved using two PLGel Mixed B (7.8 x 300 mm) SEC columns connected in series and held at a constant temperature of 50 °C. The triple detection system was calibrated using a 2 mg mL-1 PSTY standard (Polymer Laboratories: Mwt = 110 K, dn/dc = 0.16 mL.g-1 and IV = 0.5809). Samples of known concentration were freshly prepared in DMAc + 0.03 wt % LiCl and passed through a 0.45 µm PTFE syringe filter prior to injection. The absolute molecular weights and dn/dc values were determined using Polymer Laboratories Multi Cirrus software based on the quantitative mass recovery technique.

Preparative Size Exclusion Chromatography (Prep SEC)


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Crude polymers were purified using a Varian Pro-Star preparative SEC system equipped with a manual injector, differential refractive index detector, and single wave-length ultraviolet visible detector. The flow rate was maintained at 10 mL min-1 and HPLC grade tetrahydrofuran was used as the eluent. Separations were achieved using a PL Gel 10 µm 10 × 103 Å, 300 × 25 mm preparative SEC column at 25 °C. The dried crude polymer was dissolved in THF at 100 mg mL-1 and filtered through a 0.45 µm PTFE syringe filter prior to injection. Fractions were collected manually, and the composition of each was determined using the Polymer Laboratories GPC50 Plus equipped with triple detection as described above.

1

H Nuclear Magnetic Resonance (NMR) Spectroscopy

All NMR spectra were recorded on a Bruker DRX 500 MHz spectrometer using an external lock (CDCl3) and referenced to the residual non-deuterated solvent (CHCl3). A DOSY experiment was run to acquire spectra presented herein by using the gradient strength (gpz6) from 85 to 90 % and gradient pulse length (p30, little delta, δ=p30 x 2) from 1.6 to 2 ms with 256-512 scans.

2D DOSY NMR Spectroscopy for Diffusion Coefficient 2D DOSY experiments were carried out to determine the diffusion coefficients (D) for 8e and cyclic structures (9e, 32-36), all 2D DOSY experiments were conducted at 298 K. NMR spectroscopy was carried out using a Bruker Avance DRX 500 spectrometer operating at 500.13 MHz for protons and equipped with a 5 mm triple-resonance (1H, 13C, 15N) z-gradient probe equipped with actively shielded gradients. The z-gradient was calibrated at 298 K with a HDO sample containing 0.1 mg mL-1 GdCl3. The maximum z-gradient amplitude was 50 G/cm. A 90° pulse calibration was performed for each new sample for DOSY experiments. A bipolar pulse longitudinal eddy current delay (BPPLED) pulse sequence or, if convection was a problem, a bipolar pulse pair double stimulated echo pulse sequence (BPPDSTE) pulse sequence was used. The pulse sequences included a 5 ms delay to allow residual eddy currents to decay. Sine-shaped gradient pulses were utilized to further minimize eddy currents. The ACS Paragon Plus Environment

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pulse gradient duration δ=3.2 (p30 x 2) ms was chosen for diffusion time in order to obtain the minimum residual signal for each component at maximum gradient strength. The diffusion delay ∆ were set to 150 ms. The pulse gradients were incremented from 2 to 95% of the maximum gradient strength in a linear ramp (16 steps). A spectral window of 6000 Hz was accumulated in an acquisition time of 1.38 s. A relaxation delay of 5T1 of the slowest relaxing signal was used (7s). The FIDs were collected into 16 K data points; 128 scans and 4 dummy scans were acquired on each sample. Following acquisition the FIDs were Fourier transformed applying zero-filling to 16K data points and an exponential window function with line broadening factor 1-5 Hz. Data were processed using Bruker XWIN NMR software. The signal decay due to gradients was fitted using:

I=I0 exp(-Dγ2g2δ2(∆-δ/3))

(1)

where I is the resonance intensity measured for a given gradient amplitude, g, I0 is the signal intensity with no gradient applied, γ is the gyromagnetic ratio, δ is the duration of the gradient, and ∆ is the diffusion time. The resulting diffusion coefficients (D) of the polymer signals and the solvent are the result of the fitting procedure (see supporting information Fig S49-62). The hydrodynamic diameter (Rh,DOSY) was determined using the Stokes-Einstein equation:

Rh, DOSY =

kT 6πηD

(2)

where k is the Boltzmann constant (1.380 x 10−23 J K−1), T is the temperature in Kelvin (298 K), η is the viscosity of the solvent in Pascal seconds (5.3 x 10-4 Pa s for CDCl3) and D is the diffusion coefficient obtained from 2D DOSY experiment.

Matrix-Assisted Laser Desorption Ionization-Time-of-Flight (MALDI-ToF) Mass Spectrometry ACS Paragon Plus Environment

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MALDI-ToF MS spectra were obtained using a Bruker MALDI-ToF autoflex III smart beam equipped with a nitrogen laser (337 nm, 200 Hz maximum firing rate) with a mass range of 600-400 000 Da. Spectra were recorded in both reflectron mode (500-5000 Da) and linear mode (5000-20000 Da). Trans2-[3-(4-tert-butylphenyl)-2-methyl-propenylidene] malononitrile (DCTB; 20 mg/mL in THF) was used as the matrix and Ag-(CF3COO) (1 mg/mL in THF) as the cation source of all the polystyrene samples. 20 µL polymer solution (1 mg/mL in THF), 20 µL DCTB solutions and 2 µL Ag-(CF3COO) solution were mixed in an ependorf tube, vortexed and centrifuged. 1 µL of solution was placed on the target plate spot, evaporated the solvent at ambient condition and run the measurement.

Gas chromatography/mass spectrometry analysis (GC-MS) Small organic compounds were analyzed by gas chromatography/mass spectrometry (Thermo Fisher Trace GC Ultra and DSQ II Quadrupole Mass Spectrometer) in electron ionization mode. The analysis was carried out by introducing methanol solution headspace into the GC/MS system by means of direct injection (3 µL by volume) using a gastight syringe.

Dynamic Light Scattering (DLS) Dynamic light scattering measurements were performed using a Malvern Zetasizer Nano Series running DTS software and operating a 4 mW He−Ne laser at 633 nm. Analysis was performed at an angle of 173° and a constant temperature of 25 °C. The hydrodynamic diameter of the polymer structures was measured in CDCl3 and THF (5 mg mL−1). All the samples were filtered by 0.45 µm filter before measurements. The number-average hydrodynamic particle sizes were reported.

Molecular Dynamics Simulation The solutions were modelled with a bead-spring model of the polymer with explicit solvent molecules represented as single particles. Interactions between all particles in the system (polymer beads and solvent molecules) were modelled by a WCA (Weeks, Chandler Anderson) pair potential44 which is a ACS Paragon Plus Environment

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function of the Lennard-Jones parameters, σ and ε. In addition, the polymer beads were bonded using the FENE (finitely extensible nonlinear elastic) model, in configurations described in Scheme 1.45 Solutions of varying concentrations were packed using PACKMOL,46 and molecular dynamics (MD) simulations were carried out using the LAMMPS package.47 The simulations were carried out at in the constant NVT ensemble. Parameters and results are presented in reduced using with the time step dt = 0.001, temperature T = 1.0, and particle density ρ = 0.84. The Lennard-Jones parameter σ = 1 for all pair interactions, εPP = εSS = 1 for polymer-polymer and solvent-solvent interactions, respectively, and εPP was varied to give the required solvent quality. All simulations consisted of 20 polymers in a solution with total particle counts of 200 times the number of polymer beads. Systems were equilibrated for 106-107 time steps before production runs of 107 time steps where Rg and Rh were measured every 1,000 time steps and configurations recorded every 10,000 time steps. Three independent simulations were performed for each polymer.

RESULTS AND DISCUSSION Synthesis of cyclic structures. Our laboratory has recently demonstrated an efficient ring-closure method to produce a wide range of cyclic and multicyclic polymers from 'living' radical polymerization (LRP) and 'click'-type coupling reactions.4, 25, 41, 48, 49 We further elaborated on a new synthesis for creating cyclic polymers with two or three functional groups equidistant from each other, and then coupled with monofunctional cyclics to form a wide range of structures.34 In this work, we used the same methodology to create complex cyclic structures (Scheme 2), all with the same total molecular weight, to gain insight into the influence of the type, number and location of the constraints on the solution and physical properties. Details for the synthesis and characterization of these structures is given in the Supporting Information, as there were some subtle changes in the procedure and the additional synthesis of a new multicyclic structure 37. Importantly, all polymer structures had molecular weights close to 19 K, each with a narrow MWD (i.e.


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dispersity values below 1.06) as shown in Figure 1A. The number of constraints varied from 0 to 3, and the number of constrained arms within the cyclic ranged from 0 to 18.

Scheme 2. Synthetic strategy for the synthesis of cyclic structures with well-defined constraint type and location. 12 (i) Bromination

(i) Azidation (ii) Cyclization

≡

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Biomacromolecules

7 ≡(HO)-PSTYn -Br

(ii) Azidation

13

11, c-PSTYn -N3

9, c-PSTYn-OH

a: n=19 b: n=25 c: n=58 d: n= 84, e: n=163

14, c-PSTYn -≡

Click

15c, c-PSTY58-(≡)2

(58)

Click

11d 7, ≡(HO)-PSTYn -Br

(84)

(84)

(84) Click

32, spiro dicyclic

14d, c-PSTY84-≡

Click

(58)

17, TIPS- ≡ (HO)-PSTYn -N3

12

13

11c

(58)

Linkers

(58)

Click

15c, c-PSTY58-(≡)2

18a, TIPS- ≡ (HO-PSTY19)2-Br 18b, TIPS- ≡ (HO-PSTY25)2-Br Azidation

(ii) Azidation

33, star tricyclic

14c

(50)

(i) Brominatin

(58)

(50)

(58)

(58)

Click

23b, c-PSTY50-(N3)2

34, spiro tricyclic

(i) Deprotection (50)

(ii) Cyclization

19a, TIPS- ≡(HO-PSTY19)2-N3

Click

13 (50)

(50)

19b, TIPS- ≡(HO-PSTY25)2-N3

Click

35, G1 pentacyclic

OH

(25)

(i) Azidation (ii) Deprotection

(i) Brominatin

14b

(iii) Cyclization

(ii) Azidation

Click

25a, TIPS- ≡(HO-PSTY19)3-Br 25b, TIPS- ≡(HO-PSTY25)3-Br

(25)

(25)

24, c-PSTY50-(≡)4

7 Click

(25)

(25)

11b

21b, c-PSTY50-(OH)2

28a, c-PSTY57-(OH)3 28b, c-PSTY75-(OH)3

30a, c-PSTY57-(N3)3

(75) (25)

(25)

36, G1 tetracyclic

30b, c-PSTY75-(N3)3

13 Click

(19)

11a (57)

(19)

(57)

(19)

(19)

Click (19)

31a, c-PSTY57-(≡)3

(19)

37, G1 st heptacylic

Conditions: (a) azidation: NaN3 in DMF at 25 °C, (b) cyclization: CuBr, PMDETA in toluene by feed at 25 °C, (c) bromination: 2-BPB, TEA in THF; 0 °C- RT, (d) deprotection: TBAF in THF at 25 °C. (e) ‘click’: CuBr, PMDETA in toluene at 25 °C.


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(A)

(B) 1.6E-08

5.0E-04

f

f

3.0E-04

d c b g e

1.4E-08 1.2E-08 1E-08

f(N)

d c b g e h

4.0E-04

f(N)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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a

2.0E-04

8E-09

h

a

6E-09 4E-09

1.0E-04 2E-09 0

0.0E+00

3.2

3.5

3.8

4.1

4.4

4.7

5

Log MW

5.3

1.5

2

2.5

3

3.5

4

4.5

Rh,SEC (nm)

Figure 1. Number distribution from size exclusion chromatography (RI detection) of cyclic structures versus (A) Log molecular weight, and (B) hydrodynamic radius (Rh,SEC) using Eq. 3. Curves (a) 8e, (b) 9e, (c) 32, (d) 33, (e) 34, (f) 35, (g) 36 and (h) 37.

To obtain such well-defined structures, the cyclic polymers were designed to have an OH-group in specific locations along the polymer chain. These OH-groups were then converted to either azide or alkyne groups (see Scheme 2), and then coupled together to form a wide range of cyclic structures, including a spiro tricyclic, and 1st generation dendrimers consisting of tricyclic, pentacyclic and heptacyclic. All cyclic polymer precursors were fractionated by preparative size exclusion chromatography (prep-SEC) to remove most if not all linear starting polymers; and coupling these cyclics together produced the crude multicyclic products. After further fractionation of the crude product, all starting materials (including any residual linear polymer) were removed. This purification technique led to the removal of most of the starting and lower molecular weight species (see Figure S38 in SI), in which the formation of near pure structures was supported by MALDI-ToF (Figures S44-S48 in SI). The LND fitting procedure27 on the polymers after prep-SEC gave purities for structure 9e, 32, 33 and 35 of greater than 97%, and greater than 84% for 34 and 36. Structure 37 had a purity of 75.3%, consisting of the pure product and higher molecular weight polymer species. Based on the LND fitting method, there was no evidence of starting material impurities in the products (see Table S2 in SI). The 14 ACS Paragon Plus Environment

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Biomacromolecules

impurities consisted of low percentages of incomplete coupling products; for example, structure 35 (i.e. four azide-cyclics attached to a single tertra-alkyne functional cyclic) after prep-SEC contained about 1.98% of two azide-functional cyclic coupled to the tertra-alkyne functional cyclic with no formation of three azide-cyclic with the alkyne-cyclic (see Table S2 in SI). There was about 1.0% high molecular weight species, which were presumably due to the Glaser coupling of the tertra-alkyne functional cyclic. In all structures, there was no evidence of residual linear polymers that may influence the glass transition temperature of these structures through the threading mechanism.6

Molecular dynamic simulations of cyclic structures A coarse-grained model for molecular dynamic (MD) simulations for the chain conformation of polymer chains in varying solvent quality has been described by Zhou and Daivis50. This model varies the single polymer-solvent interaction parameter, εPS, to change the solvent quality. Increasing εPS from 0.5 to 3 results in the solvent quality going from a good through a theta to a poor solvent. The incorporation of solvent molecules into the model allows the influence of solvent quality on polymer hydrodynamic interactions and spatial configuration of the polymer chain to be determined. This model further provides the radius of gyration (Rg) and hydrodynamic radius (Rh) as a function of solvent quality and appears to give a Gaussian distribution of chain conformations (see Figures S63 and S64 in SI). Here, we used a slightly modified version of this simulation model (bead-spring instead of freely jointed, see Supporting Information for comparison) to provide insights into the change of our cyclic conformation when going from a good solvent to a theta solvent and the influence of constraints within the cyclic structure on the spatial configuration and conformational symmetry. The simulations used two

εPS values of 0.5 and 1.55 to represent a good and theta solvent, respectively. The Rg values in both solvent conditions for the cyclic structures was given in Table 1. A large decrease going from a linear (8e) to a monocyclic (9e) was observed in Rg from 8.76 to 6.53 in a good solvent and a decrease from 7.19 to 5.07 in a theta solvent. Under theta solvent conditions, polymer chains should have a random coil conformation, in which excluded volume effects cancel. Theoretically, the value of Rg,l2/Rg,c2 for ACS Paragon Plus Environment

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linear and monocyclic under theta solvent conditions at the same molecular weight is 2.51 The value calculated from Table 1 for 8e to 9e was 2.01, in good agreement with theory, and further demonstrating that the MD simulations provide an accurate representation of the polymer chain conformation.


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Biomacromolecules

Table 1. Radius of gyration (Rg) and radius of hydration (Rh) determined from coarse-grained molecular dynamic simulations for cyclic structures in a good and theta solvent. Values given in the Table are reduced units. Numbers in parenthesis are free ring values. Structure

# of arms

Rg (Good Solvent) Total

External ring

Rg (Theta Solvent)

Internal ring

Total

External ring

Internal ring

Rh (Good Solvent) Total

External ring

Internal ring

Rh (Theta Solvent) Total

0

8.76

6.98

6.73

5.65

0

6.53

5.07

5.92

4.74

4

6.28

4.55 (4.50)

4.85

3.64 (3.60)

5.72

4.30 (4.26)

4.56

External ring

Internal ring

3.54 (3.52)

6

5.80

3.68 (3.63)

4.54

3.00 (2.97)

5.47

3.59 (3.55)

4.39

3.02 (3.00)

8

6.51

3.67 (3.63)

3.39 (3.32)

4.85

2.99 (2.97)

2.80 (2.74)

5.68

3.58 (3.55)

3.36

4.48

(3.31) 12

5.48

2.18 (2.16)

3.42 (3.32)

4.33

1.92 (1.90)

2.84 (2.74)

5.00

2.40 (2.38)

3.38

4.08

(3.31) 12

5.68

2.17 (2.16)

4.38 (4.20)

4.46

1.91 (1.90)

3.51 (3.40)

5.26

2.39 (2.38)

4.14

4.24

(4.02) 18

5.51

1.83 (1.81)

3.72 (3.56)

4.35

1.65 (1.64)

3.05 (2.92)

5.18

2.12 (2.11)

3.62 (3.49)


4.21

3.01

2.86

(3.00)

(2.81)

2.15

2.88

(2.14)

(2.81)

2.15

3.44

(2.14)

(3.35)

1.95

3.06

(1.94)

(2.96)

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The expansion factor (Rg(good)/Rg(θ)) can be determined from the ratio of Rg in a good solvent to Rg under theta (θ) conditions. The expansion factor was significantly greater for the monocyclic 9e than the linear 8e (see Figure 2A), suggesting that ring polymers have enhanced effective repulsions between their segments and thus greater swelling ability and excluded volume effect compared to its linear analogue. A similar enhanced excluded volume was found for the other cyclic structures, which decreased slightly with the total number of arms within the cyclic. The spiro 34 cyclic had a much greater expansion factor than all other structures. Next we examine the expansion factor changes from Rh(good)/Rh(θ) (Figure 2B), since Rh is more sensitive than Rg to the higher density of monomer units at branch points within the center of the chain. Similar to that found for Rg, the expansion factor determined from Rh increased from linear to cyclic, with a slight decrease from the monocyclic to the cyclic with 18 arms constrained within its structure. Spiro 34 again showed the highest expansion factor, but the difference was not as great as that found from the Rg ratio. The results suggest that the excluded volume effects are much greater for the cyclic than the linear chain analogue, and the greater branching density (i.e. with the increase in the number of arms) within the cyclic structure showed a slight decrease in the swelling of the cyclic within the series of cyclics studied. Using molecular simulations, we also determined the expansion factor of both the internal and external rings within the cyclic structures. Figure 3 showed that the expansion factor based on Rg and Rh increased with the molecular weight of the ring (see Scheme 1 for molecular weight of each ring), regardless of whether the ring was internal or external. This trend was in agreement with experimental values for linear polymer chains as a function of molecular weight52.


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(A)

1.36

(B)

1.34

Rh(good)/Rh(θθ )

Rg(good)/Rg(θθ )

1.28 1.27 1.26

1.32 1.3 1.28 1.26 1.24

1.25 1.24 1.23 1.22 1.21 1.2

1.22

1.19

1.2

1.18

0

2

4

6

8

10

12

14

16

18

20

0

2

4

6

# of arms

8

10

12

14

16

18

20

# of arms

Figure 2. Excluded volume effect as a function of the number of arms within the cyclic structure from MD simulations (A) Ratio of the radius of gyration in a good and θ solvent, and (B) Ratio of the radius of hydration in a good and θ solvent.

(A) 1.35

(B)

1.3

1.3 1.25

1.25

Rh(good)/Rh(θθ )

Rg(good)/Rg(θθ )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Biomacromolecules

1.2 1.15

internal ring external ring

1.1 1.05

1.2 1.15 1.1

internal ring external ring

1.05

1

1

0

20

40

60

80

100

120

140

160

180

0

# monomer units/ring

20

40

60

80

100

120

140

160

180

# monomer units/ring

Figure 3. Excluded volume effect of the internal and external rings within the cyclic structure from MD simulations.


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The number and type of constraints within the cyclic will influence the monomer congestion around the center of mass at the branching point, which can be described using the branching parameter53 gg or gh from the Rg and Rh data, respectively. These are defined as,

gg =

Rgb

2

Rgl

2

(3)

2

R g h = hb2 Rhl

(4)

where Rgb2 is the mean square radius of gyration for the branched chain and Rgl2 is the mean square radius of gyration for the linear chain of the same molecular weight (Eq. 3); similarly the radius of hydration gh is obtained (Eq. 4). Figure 4A showed a sharp decrease in gg to 0.55 from linear to monocyclic, which further decreased to ~0.4 with an increase in the number of branching arms (for 18 arms). A similar trend was observed for gh (Figure 4B), but in this case, the decrease from linear to cyclic was much less, decreasing to 0.77 for the monocyclic. There was also a similar decrease in gh to ~0.55 with the increase in the number of branching arms. The difference between gg and gh arises due to the fact that Rg is heavily weighted by distant pairs of monomer units whereas Rh is weighted to the close pairs of monomer units within the chain.


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(B)

1.05

1.05

0.95

0.95

0.85

0.85

0.75

0.75

gh

(A)

gg

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Biomacromolecules

0.65

0.65

0.55

0.55

0.45

0.45

0.35

0.35

0

2

4

6

8

10

12

14

16

18

20

0

2

# of arms

4

6

8

10

12

14

16

18

20

# of arms

Figure 4. Grafting parameter as a function of the number of arms within the cyclic structure from MD simulations. (A) gg determined from Rg data (Eq. 3) and (B) gh determined from Rh data (Eq. 4).

Solution properties of the cyclic structures The effect of the number of constraint arms on the translational diffusion coefficient (D) in a good solvent can be determined directly from diffusion-ordered NMR spectroscopy (DOSY)54, 55 (see Table 2). An increase in the hydrodynamic radius measured by DLS (Rh,DLS) resulted in the decrease in the diffusion coefficient as shown in Figure 5A (larger structures in solution diffuse much slower than smaller ones). This suggests that the size data from two different methods (i.e. NMR and DLS) are well correlated. Comparison of Rh,DLS for structures 9e and 34, for example, showed that Rh,DLS was larger for the tricyclic spiro structure 34 even though each cyclic was very much smaller than the monocyclic 9e (see Scheme 1), which was the reverse to that found by simulations (see Rh in a good solvent in Table 1). This result suggested that the diffusion and size of 34 in dilute solution was enhanced by excluded volume effects. Figure 5B showed that the branching parameter (gh), with a similar trend to simulations, decreased with the number of branching arms. Spiro 34 was higher and close to that of the linear chain, which was more pronounced than the simulation gh (see Figure 4B).


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Table 2. Characterization of the cyclic structures by size exclusion chromatography (SEC), DOSY NMR, and dynamic light scattering (DLS).

Structure

# of arms

8e 9e 32 33 34 35 36 37

a

Purity by LND (%)

SEC (RI)

SEC (Triple detection) Mn PDI

D x1010 (m2 s-1)

Rh (nm) THF

Rh,θ (SEC-RI) a

Mn

PDI

SECa

DLS

1.06 1.04

18300 18330

1.004 1.003

1.28 2.14

3.29 2.85

3.01 2.45

1.72 1.52

(nm)

0 0

>99.00

17300 13430

4 6

98.50 99.00

13320 12850

1.04 1.04

19140 19700

1.003 1.017

1.99 2.60

2.84 2.78

2.42 2.18

1.51 1.48

8 12

91.23 97.02

14050 12890

1.06 1.04

19080 18900

1.001 1.005

1.63 2.19

2.93 2.79

2.86 2.06

1.55 1.49

12

84.15

13920

1.05

19680

1.002

2.11

2.91

2.33

1.54

18

75.30

14920

1.13

19440

1.05

NA

3.03

2.14

1.60

Rh from SEC determined using Eq. 5 (a = 0.5 for theta solvent conditions).

(A) 2.80E-10

(B)

2.60E-10

1.05 0.95

2.40E-10 0.85

2.20E-10

gh,THF

Diffusion Coef., DTHF (m2s-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 34

2.00E-10 1.80E-10 1.60E-10

0.75 0.65 0.55

1.40E-10 0.45

1.20E-10 1.00E-10

0.35

1.9

2.1

2.3

2.5

2.7

2.9

3.1

0

2

Rh (DLS, good) (nm)

4

6

8

10

12

14

16

18

20

# of arms

Figure 5. (A) Influence of hydrodynamic radius by DLS in THF on the diffusion coefficient (measured by DOSY NMR in CDCl3), and (B) Grafting parameter (gh) determined from DLS data in THF as a function of the number of arms within the cyclic structure.


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Biomacromolecules

The Rh of the cyclics determined by DLS in THF showed that Rh,DLS was less than that of the linear polymer at similar absolute molecular weights (Figure 6). As the number of arms increased the value of Rh,DLS decreased, with the spiro 34 cyclic found to have a significantly greater Rh,DLS (close to the value for the linear chain) than all other cyclics. The reason for the large difference in solution properties between 34 and all the other cyclics is unclear, and requires a more comprehensive investigation. We also calculated Rh from SEC using the hydrodynamic polystyrene (PSTY) coil radius equivalence (i.e. from using a PSTY calibration curve).4,

56, 57

In general, a cyclic PSTY structure has a lower

hydrodynamic volume than its linear analogue of the same molecular weight. SEC can be used to determine Rh in THF based on polystyrene standards using the Mark-Houwink relationship between molecular weight and intrinsic viscosity. The hydrodynamic radius (Rh) can be calculated using the following relationship

Rh3,SEC =

3KM na+1 10πN A

(5)

where K = 0.0141 cm3g-1, a = 0.7 (in a good solvent), NA is Avogadro's number and Mn is the numberaverage molecular weight found using a linear PSTY calibration curve. The K and a values used in this work were determined by light scattering58 for molecular weights ranging from 13,000 to 2.2 x 106, which was in the range of molecular weights studied here. The average Rh,SEC and Rh,DLS are shown in Table 2. Figure 1B also showed that the size (i.e. Rh,SEC) distribution for all cyclic structures was narrow, ranging from 2 to 4 nm. It was found from Figure 6 that Rh,SEC increased slightly with the number of arms and was much higher than the Rh,DLS values. The difference can be attributed to fluid flow within an SEC column compared to simple Brownian diffusion in a static solution. Steady-state extensional flows stretch polymer chains in which entropic effects drive these chains back to random coils (coil-to-stretch transition). Experiments with linear and ring DNA suggests that the ring DNA chains are less prone to ACS Paragon Plus Environment

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Page 24 of 34

stretching than their analogous linear chains.59 Recent simulations by Sing and coworkers60 found that a monocyclic ring structure had non-intuitive and profound properties under a flow compared to their equilibrium structure. Profoundly, at medium to high flow strength, the rings open perpendicular to the flow. This phenomenon may exist in our SEC system, in which the rings within the cyclic structure increase in size due to this open loop conformation with flow.


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3.4

SECTHF (Eq. 3)

3.2 3

Rh (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Biomacromolecules

2.8 2.6 2.4

DLSTHF

2.2 2

0

2

4

6

8

10

12

14

16

18

20

# of arms

Figure 6. Influence of the number of arms on the hydrodynamic radius (Rh). Curves a: Rh determined by DLS in THF, b: Rh determined from the SEC data using Eq. 5.

CONCLUSION Utilizing the new polymer synthetic method from our laboratory, we constructed cyclic polymer chains with the same molecular weight, in which the location of the constraints and the number of arms per constraint could be precisely controlled. A range of cyclic architectures were synthesized with the same molecular weight with low dispersity values, and their chain conformation determined by MD simulations and from experiments. Simulations showed that excluded volume effects were much greater for the cyclic structures than the linear analogue due to its greater compactness and chain repulsion interactions. The spiro 34 structure had a much greater excluded volume than all cyclic structures studied; the reason for this is unclear at this stage and more work will be required to elucidate the reason for this anomaly. The data further showed a slight decrease in the ability of the cyclics to swell with the increase in the number of constrained arms within the structure. As these structures have many branching points (i.e. number of arms), the simulations showed that the branching parameter, gg or gh, ACS Paragon Plus Environment

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Page 26 of 34

decreased with an increase in the number of arms. The hydrodynamic radius experimentally determined by DLS showed that Rh decreased as the number of arms increased. Again the Rh for spiro 34 was much higher than all the other cyclics and similar to the linear polymer. Interesting, under an SEC flow, the Rh,SEC values for all the cyclic structures increased, and could be explained from the internal and external rings opening perpendicular to the flow in accord with pervious dynamic simulations60. Our data suggests that the more compact nature of cyclic macromolecules due to internal constraints may explain why non-symmetrical cyclic peptides, e.g. those found in the snake venom, are more potent than either linear or monocyclic analogs (i.e. with a spherical shape) under systemic blood flow. With this knowledge, synthetic cyclic polymers with judiciously selected constraints could be designed as scaffolds to produce a new class of therapeutic peptides.

Acknowledgment. M.J.M acknowledges financial support from the ARC Discovery grant (DP140103497). Supporting Information Available: Synthesis and characterizations of all polymers, including 1H NMR spectra, SEC traces, and MALDI-ToF spectra.

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For Table of Contents Use Only to

Influence of Constraints within a Cyclic Polymer on Solution Properties Md. D. Hossain,1 James C. Reid, 1 Derong Lu, 1 Zhongfan Jia, 1 Debra J. Searles1,4 and Michael J. Monteiro1,4,*

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(e) sp-(c-PSTY)3 , 34


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Influence of Constraints within a Cyclic Polymer on Solution Properties

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