Molecular basis of cooperativity in pH-triggered supramolecular self-assembly

Supramolecular self-assembly offers a powerful strategy to produce high-performance, stimuli-responsive nanomaterials. However, lack of molecular understanding of stimulated responses frequently hampers our ability to rationally design nanomaterials with sharp responses. Here we elucidated the molecular pathway of pH-triggered supramolecular self-assembly of a series of ultra-pH sensitive (UPS) block copolymers. Hydrophobic micellization drove divergent proton distribution in either highly protonated unimer or neutral micelle states along the majority of the titration coordinate unlike conventional small molecular or polymeric bases. This all-or-nothing two-state solution is a hallmark of positive cooperativity. Integrated modelling and experimental validation yielded a Hill coefficient of 51 in pH cooperativity for a representative UPS block copolymer, by far the largest reported in the literature. These data suggest hydrophobic micellization and resulting positive cooperativity offer a versatile strategy to convert responsive nanomaterials into binary on/off switchable systems for chemical and biological sensing, as demonstrated in an additional anion sensing model.

Microscopic reversibility of pH titration of PEO-b-PDPA copolymers. a, pH titration; b, fluorescence emission intensity as a function of pH of TMR conjugated PEO-b-PDPA block copolymers; c-d, 1 H NMR spectra of micelle to unimer transitions of PEO-b-PDPA copolymers (opposite to the titration direction as shown in Fig. 4b and 4d).

Development of the cooperative deprotonation model
We adopted an allosteric model to describe the cooperative deprotonation process (Fig.  5a). The sequential neutralization of fully protonated polymers can be characterized by a series of microscopic Ki, which corresponds to the ith dissociation constant of the polyatomic acids.

Cooperative parameters
In the simplest case of dibasic acid (n=2), the neutralization of protons can be characterized by two microscopic dissociation constant K 1 and K 2 as defined by Supplementary Equation 2 and 3, where 2 and ½ are statistical factors 1 .
At molecular level, the cooperativity of dibasic acid dissociation process can be described by the interaction parameter which is defined as 2 : For the dissociation of polyatomic acid as in our system, a series of cooperative parameters  are defined by Equation 1 as shown in the main text. The apparent dissociation constant K is defined as geometric mean of individual dissociation constants 3  . This equation allows the theoretical-experimental correlation between the microscopic cooperative parameter and macroscopically measurable pKa (logarithmic K). For polymeric polyatomic acid, the pKa can be defined as the pH where 50% of the ionizable amines are protonated 4-6 . The theoretical modeling suggests that cooperative dissociation of fully protonated PEO-b-PR with more ammonium groups per polymer chain will have higher K (or Ka) and lower pKa.
Hill Coefficient. Practically, Hill plot is used to evaluate the allosteric cooperativity. First, the sequential neutralization of fully protonated UPS nanoprobes are described in dissociation isotherms. Here we use (pH -pKa) as the x-axis and protonation degree ( A ) as the y-axis to plot the dissociation isotherms. In this case, the point at which 50% of tertiary amines are protonated occurs at 0 on the x-axis 7 . Increase of pH leads to dissociation of protons, corresponding to the decreased A as shown in Figure 5b The deprotonation is opposite process of protons binding to tertiary amines, which means the K=1/K´. So the cooperativity in allosteric deprotonation of fully charged PEO-b-PR copolymers can be quantified by plotting log( A /(1- A )) versus (pKa-pH) in a Hill plot: The Hill coefficient n H , corresponding to the slope of this plot measured at 50% saturation, is a useful parameter to quantify the cooperativity strength. The allosteric systems with positive cooperativity have the number of binding sites n as the limit of n H . In the absence of cooperativity, the n H is equal to 1. Positive cooperaitvity gives a slope larger than 1 (n H >1), which corresponds to narrower ligand concentration range nacessary for receptors to go from bound free state to fully occupied state. The Hill plot modeling suggests that polyatomic acids with more ammonium groups per polymer chain will have higher n H and sharper pH transition.

Syntheses of methacrylate monomers
Methacrylate monomers were synthesized following a published method. [2] Synthesis of 2-(dipropylamino) ethyl methacrylate (DPA-MA) is described here as an example. First, ethanolamine (12.2g, 0.2 mol) and bromopropane (49.2 g, 0.4 mol) were dissolved in 400 mL acetonitrile, and Na 2 CO 3 (53.0 g, 0.5 mol) was added to the solution. After overnight reaction, the solution was filtered to remove the precipitated NaBr salt and extra Na 2 CO 3 . CH 3 CN solvent was removed by rotovap. The resulting residue was distilled in vacuo (40~45 °C at 0.05 mm Hg) as a colorless liquid to obtain 2-(dipropylamino) ethanol. Then 2-(dipropylamino) ethanol (21.3g, 0.1 mol), triethylamine (10.1 g, 0.1 mol), and inhibitor hydroquinone (0.11g, 0.001mol) were dissolved in 100 mL CH 2 Cl 2 and methacryloyl chloride (10.4g, 0.1 mol) was added dropwise into a three-neck flask. The solution was refluxed overnight. After reaction, the solution was filtered to remove the precipitated triethylamine-HCl salts, and CH 2 Cl 2 solvent was removed by rotovap. The resulting residue was distilled in vacuo (47-53 °C at 0.05 mm Hg) as a colorless liquid. After synthesis, the monomer was characterized by 1 H-NMR. All the NMR spectra were obtained in CDCl 3 using tetramethylsilane (TMS) as the internal reference on a Varian 500MHz spectrometer. The characterization of the DPA methacrylate monomers is as follows:

Syntheses of dye conjugated PEO-b-PR block copolymers
AMA monomer was incorporated in the copolymers for the conjugation of dyes (Scheme S1b) following procedures reported previously [3] . Synthesis of PEO-b-(PR-r-AMA) copolymers followed the procedure described above. Three primary amino groups were introduced into each polymer chain by controlling the feeding ratio of AMA monomer to the initiator (ratio = 3). In a representative procedure, PEO-b-(PR-r-AMA) (50mg) was dissolved in 2 mL DMF. Then the NHS-ester (3.0 equivalence for TMR-NHS, RhoG or Cy5-NHS) was added. After overnight reaction, the copolymers were purified by preparative gel permeation chromatography (PLgel Prep 10 m 10E3 Å 300×250 columns by Varian, THF as eluent at 5 mL/min) to remove the free dye molecules. The produced PEO-b-(PR-r-Dye) copolymers were lyophilized and kept at -20 ℃ during storage.

TEM and DLS characterization
Samples for TEM and DLS analyses were prepared in situ by pH titration. The morphology and size of nanoparticles were characterized by transmission electron microscopy (TEM, FEI Tecnai G2 Spirit Biotwin model). Hydrodynamic diameter (D h ) and scattering count rates were determined by dynamic light scattering (DLS, Malvern Nano-ZS Model, He-Ne Laser, =633 nm).

Fluorescence characterization
The fluorescence emission spectra were obtained on a Hitachi fluorometer (F-7500 model, Tokyo, Japan). The fluorescent images of PEO-b-PDBA-RhoG and Lysosensor Green solutions at different pH values (200 μg/mL for each sample) were obtained using the Maestro imaging system (CRI, Inc., Woburn, MA) with a proper band pass excitation filter and long-pass emission filter according to the instrument manual. All measurements were conducted at room temperature.

Perchlorate Anion Sensing
TMR-conjugated PEO-b-PR copolymer stock solutions were prepared following a solvent evaporation method as previously published 8 . In the example of PEO-b-PDPA micelle solution, 40 mg of the dye-conjugated copolymer was first dissolved in 2 mL THF and then added into 8 mL distilled water dropwise under sonication. The THF was removed through ultrafiltration with (100 kD) membrane for several times. Then the distilled water was added to adjust the polymer concentration to 5.0 mg/mL as a stock solution. TMR conjugated PEO-b-PDPA stock solution (2 mL) was first diluted to 2.