Crafting Stable Antibiotic Nanoparticles via Complex Coacervation of Colistin with Block Copolymers

To combat the ever-growing increase of multidrug-resistant (MDR) bacteria, action must be taken in the development of antibiotic formulations. Colistin, an effective antibiotic, was found to be nephrotoxic and neurotoxic, consequently leading to a ban on its use in the 1980s. A decade later, colistin use was revived and nowadays used as a last-resort treatment against Gram-negative bacterial infections, although highly regulated. If cytotoxicity issues can be resolved, colistin could be an effective option to combat MDR bacteria. Herein, we investigate the complexation of colistin with poly(ethylene oxide)-b-poly(methacrylic acid) (PEO-b-PMAA) block copolymers to form complex coacervate core micelles (C3Ms) to ultimately improve colistin use in therapeutics while maintaining its effectiveness. We show that well-defined and stable micelles can be formed in which the cationic colistin and anionic PMAA form the core while PEO forms a protecting shell. The resulting C3Ms are in a kinetically arrested and stable state, yet they can be made reproducibly using an appropriate experimental protocol. By characterization through dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS), we found that the best C3M formulation, based on long-term stability and complexation efficiency, is at charge-matching conditions. This nanoparticle formulation was compared to noncomplexed colistin on its antimicrobial properties, enzymatic degradation, serum protein binding, and cytotoxicity. The studies indicate that the antimicrobial properties and cytotoxicity of the colistin-C3Ms were maintained while protein binding was limited, and enzymatic degradation decreased after complexation. Since colistin-C3Ms were found to have an equal effectivity but with increased cargo protection, such nanoparticles are promising components for the antibiotic formulation toolbox.

1. SAXS modeling, fuzzy-surface complex coacervate model in detail 1.1.Mass balance contributions Based on the zeta potential measurements, we assumed that there is stoichiometric chargematching inside the core, reducing the number of parameters and fixing the fmix0 parameter, which was defined as the molar fraction of polymer in the polyelectrolyte core.To explain the model, we defined several parameters for the mass balances of SCP and C3M structures.With a sound mass balance, it is possible to get more information from the scattering curves since there are many characteristics from the scattering contributions from complex coacervates, free peptide and polymer, clusters, internal structures, and blob scattering among the whole Qrange.First, the volumes of the core (Vcp) and the fuzzy-interface PEO-shell (Vsp), the total volume (Vtot), and the volume fraction (ϕ) are calculated (Eq.S1-4).
In which Vcp is the mean core block volume from one average complex of colistin and the PMAA block in Å 3 , fmix0 is the molar fraction of polymer inside the core, MCol0 the molecular weight of colistin excluding sulfate salt, dCol the density of colistin, MPMAA, the molecular weight of the anionic block of the polymer, dPMAA the density of the anionic block of the polymer and NA Avogadro's number.
In which Vsp is the effective volume of the PEO block of one chain in Å 3 , MPEO is the molecular weight of the neutral PEO block of the polymer, and dPEO is the density of the PEO block of the polymer.

(S3)
Vtot is the total effective volume from both contributions from one average chain in the complex coacervate.

(S4)
In which ϕ is the volume fraction, cCol, the concentration of colistin and cPoly, the concentration of polymer and daverage, the average specific density of the components making up the system.When going off the charge-matching, we assume that the internal charge ratio remains constant while the external charge ratio will change in the aqueous environment around the complex coacervates, causing a mismatch in molar fractions inside and outside the core.To grasp the effect of these changes the molar fraction of polymer in the aqueous phase is calculated (fmix) (Eq.S5).

(S5)
In which fmix is the molar fraction of polymer in the aqueous phase surrounding the complex coacervates, fCol is the free fraction of colistin, which is the first fitting parameter in our model.MCol is the molecular weight of colistin, including the sulfate salt.Based on the fmix fraction, the free fraction of polymer (fPoly) and the fraction of complex coacervates (fCoa) can be calculated (Eq.S6, S7).fPoly, the free fraction of polymer not incorporated into micelles, and fCoa, the fraction of complex coacervates inside the whole system, were calculated from terms already explained previously.The C3Ms are treated as having an inhomogeneous internal structure with a fuzzy surface.Therefore, the density distribution is described by a profile with graded interfaces 1 .
Based on these fuzzy surfaces, the radii of the complex coacervates are explained as follows (Eq.S8-10).
Rcore (the radius of the core), Rout (the outer radius of the coacervate), and Rtot (the total complex coacervate radius) are calculated with these formulas.In these, the σin and σout are Gaussian core-shell interface smearing and Gaussian shell-solvent interface smearing, respectively, while Rin is the core radius.These three parameters are fitting parameters.
1.2.Scattering contributions For the calculations of the scattering contributions, the scattering length densities (SLDs) need to be calculated based on the mass balances.First, the SLDs of the separate components were calculated using the Thomson radius.For polymer blocks, the respective monomers were taken to calculate the SLDs (Eq.S11).
In which the M0PMAA is the monomer mass of PMAA.The SLDs were all fixed parameters, including the solvent.We can divide the scattering model into three scattering contributions: complex coacervate scattering, free component scattering, and an internal structure factor from the internal anionic spacing inside the polyelectrolyte core.The three components are combined into one formula for the scattering intensity.

Complex coacervate scattering
The complex coacervate scattering is based on the scattering formula of centrosymmetric particles, which can generally be written as follows (Eq.S14).

𝐼(𝑄
In which n is the number density of scatterers, the Δρ the SLD contrast, the Vp is the volume of the particle, P(Q) is the form factor of the particle, and S(Q) is the structure factor of the particle.In the case of complex coacervate scattering, n can be written as follows (Eq.S15).
Vcoa is the volume of one coacervate complex (several chains), excluding the water incorporated.The scattering amplitude of a fuzzy sphere (Acore), which is the form factor if it is squared, can be described as follows 2,3 and integrated into the formula for centrosymmetric particles, excluding the structure factor and volume fraction, as these are added later in the total equation (Eq.S16-20).
0 = ( In which the ICoa(Q) is the scattering contribution from the complex coacervates, P is the aggregation number, the number of molecules that make up one micelle, which is a fitting parameter, and Acore(Q) is the scattering amplitude of the fuzzy core.Other parameters were mentioned previously.This scattering equation is not yet complete.For the complex coacervates, if there is any cluster formation, a structure factor is needed to explain the scattering.The structure factor for clusters, S(Q)cluster, is described by the following equations 4 (Eq.S21-26).
=   − (  ) In which Nclu is the number of clusters and fdist is the distance correlation of the clusters.If necessary for fitting, these two parameters were fitting parameters.Apart from the structure factor, there is also a scattering contribution from the blob scattering from the polyelectrolytes in the core.The blob scattering is described in the following equation (Eq.S27).
In which the fblob is the fraction of blob scattering, and ξ is the correlation length of the blobs.Both these parameters are fitting parameters in the model.
1.4.Free component scattering Outside the complex coacervate surroundings there is a free component scattering fraction for either polymer or colistin and potentially even added components like serum proteins or enzymes.Again, the equation for centrosymmetric particles could be used.In this case, we use a form factor instead of a scattering amplitude.In the free component scattering, the Debye form factor P(Q) for polymers and polyelectrolytes describes the scattering 5 (Eq.S28).In the case of the presence of globular proteins, an ellipsoid form factor is used 6,7 (Eq.S29-S31).

𝑃(𝑄
In which the Rg is the radius of gyration of the polymer/polyelectrolyte/globular protein.The ellipsoid of revolution has two minor core radii of R and major axis R, respectively.For the free chains of polymer and colistin, the Debye form factor was taken and implemented in their scattering equation P(Q)Poly and P(Q)Col.Additionally, P(Q)Ellipsoid was implemented for the scattering of additional scattering from enzymes and HSA.The scattering contributions can be summarized as the following equations, assuming S(Q) = 1 and excluding the volume fraction from this equation (Eq.S32-35).

𝐼(𝑄)
The scattering from the free chains of polymer, colistin, and other added components are described here, including each a form factor specific to the chain itself.For the added components, to obtain the SLD and Rg for the form factor, the contributions were first fitted by the Debye model using the least-squares fit routines.The Debye model in the general form can be written as follows (Eq.S36).

𝐼(𝑄
For the added scattering components, these two equations were used in which the Rg and Δρ were fitted, after which they were used in the fuzzy-surface complex coacervate model. 1.5.Internal structure scattering The model up until now describes the complex coacervates already decently apart from the high Q area.In the complex coacervates, we see an internal structure from the bump in scattering around 0.22 Å -1 , which can be described by positional charges in polyelectrolyte complexes.To add that to the scattering model, we have taken a scattering contribution as a pseudo-structure factor S(Q)internal on top of the existing scattering contributions, which was written as follows (Eq.S37).

𝑆(𝑄)
In which S(Q)internal is the pseudo-structure factor, C fractal scattering, Qlocal is the position of the structure peak, and W is the relative width of the local Q.These three parameters were fitted in the model.

Combining all scattering components
Combining all these separate components results in the following scattering equation (Eq.S38).

𝐼 (𝑄) = 𝜑 ⋅ 𝑓 𝐶𝑜𝑎 (𝑓 𝑐𝑙𝑢 ⋅ 𝑆(𝑄) 𝑐𝑙𝑢𝑠𝑡𝑒𝑟 ⋅ 𝐼 𝐶𝑜𝑎 (𝑄) + (1 − 𝑓
The first part of the scattering equation considers the complex coacervate scattering for the volume fraction and fraction of complex coacervates and includes the cluster structure factor if it is necessary to explain the data.The second part takes the free scattering of the polymer and colistin, considering the volume fraction and the fractions of free fractions in the aqueous environment around the complex coacervates.The last part is additional scattering from the pseudo-structure factor, factored by the fraction of complex coacervates.If there is another component added (enzyme or serum protein), the volume fraction of this component and additional Debye scattering are added on top of the existing scattering.
Since the mass balance and the scattering equation are complete for fitting, we can calculate the molecular weights of the complex coacervates.First, the molecular weights (Mw) of the complex coacervates could be calculated with the following formula (Eq.S39).
In which Mw is the molecular weight of one complex coacervate structure.In addition, the concentration of colistin taken up by the complex coacervates (cColC3M) can be calculated (Eq.S40).

𝑐 𝐶𝑜𝑙𝐶3𝑀 = (1 − 𝑓 𝐶𝑜𝑙 ) ⋅ 𝑐 𝐶𝑜𝑙 (S40)
The cColC3M is calculated to get an idea of the efficiency in the encapsulation of colistin for the charge ratios, where a bigger value means a higher encapsulation efficiency.However, the volume fraction of water in these complexes is also of importance.To get more information about the volume fractions of water inside of the complex coacervates, we calculate the water volume fraction (fw) (Eq.S41).
2. Results and Discussion 2.1.DLS measurements at different charge ratios (f+) of complex coacervates made from different block lengths of PEO-b-PMAA The DLS measurements of the sizes of the complex coacervates can be found in Figures S1,  S2, and S3.In addition, the autocorrelation function of representative DLS measurements is shown (Figure S4).

SAXS concentration independence and density profiles of charge ratios
The concentration independence of 0.33 ≤ f+ ≤ 0.83 for P1-colistin-C3Ms (Figure S5) and density profiles of different charge ratios of P1-colistin-C3Ms (Figure S6) are shown.2.3.Varying ionic strength and pH for P1-colistin-C3Ms at f+ = 0.50 The ionic strength is varied in two experimental setups.In the first, the colistin-C3Ms at f+ = 0.50 are prepared in a stopped-flow mixer at a mixing speed of 6.7 mL/s in either regular TRIS buffer (0.05M, pH = 7.4) or TRIS buffer with added 0.15 M NaCl (to mimic physiological conditions) (Figure S7).Secondly, the annihilation effect of salt was assessed by preparing C3Ms before adding salt (Figure S8).Lastly, the preparation of colistin-C3Ms at different pH values was investigated (Figure S9).

Figure S7
. X-ray scattering patterns to demonstrate ionic strength dependency in mixing for P1-colistin coacervate complexes at 5.0 mg/mL, using a stopped-flow device at a mixing rate of 6.7 mL/s.Preparation of P1colistin C3Ms in the presence of higher ionic strength results in swollen lower-defined particles (increased size, water volume fraction, and polydispersity index).All other properties, like encapsulation, aggregation number, and free colistin fraction are similar (Table S4).

Figure S8
. X-ray scattering patterns to indicate the ionic strength dependency in annihilation caused by salt addition for P1-colistin coacervate complexes at 5.0 mg/mL, measured on an in-house SAXS at the University of Oslo (RECX).Until physiological levels of NaCl (until 0.15 NaCl), the C3Ms become less defined (increased PDI) and start swelling (Rtot, higher fw).After physiological levels, the complex coacervates are smaller and comprised of a very small number of molecules (Table S5).S6).

CMC determination
Two ways of CMC determination are shown using surface tension to measure a concentration series (Figure S10) and SAXS (Figure S11).The SAXS pattern starts deviating between 0.63 mg/mL and 0.31 mg/mL since the distinguishable features are lost.Therefore, the CMC can be assumed to be around 0.3-0.6 mg/mL.

Antimicrobial properties
Other bacteria were assessed for antimicrobial properties during the experiment (Figure S12A), while the negative control did not show any inhibition (Figure S12B).

Figure S7
. Other bacteria were found to be unsuitable for accurate antimicrobial activity testing.E. coli was found to give the clearest results (Fig. 4A).S. indica grew over the inhibition zones, making precise measurements difficult (A), and B. subtilis served as a control, no inhibition zones could be observed (B).

Enzymatic breakdown of trypsin
Colistin and colistin-C3Ms were also analyzed for breakdown with trypsin.It was found that trypsin did not break down colistin sufficiently (Figure S13). .Small-angle X-ray scattering patterns of enzymatic breakdown of colistin (3.4 mg/mL) versus colistin C3Ms (total concentration 5.0 mg/mL) in the presence of trypsin.Theoretical SAXS patterns were calculated based on either the added scattering from C3Ms and enzymes (0% enzyme breakdown, orange squares) or colistin, polymer, and enzyme separately summed up (100% break down, blue circles).The effect of enzymatic degradation after 24 hours at 37°C was measured by either adding Trypsin to colistin followed by complexation with polymer (indicated by green triangles) or the addition of enzyme to C3Ms (indicated by grey diamonds).The SAXS patterns were fitted by using the fuzzy-surface complex coacervate model for complex coacervates with added Debye scattering of the corresponding enzymes.It can be observed that trypsin does not seem to break down colistin.

Freeze-drying C3Ms
Freeze-dried colistin C3Ms at f+ = 0.50 were compared to non-freeze-dried counterparts using SAXS to check if freeze-drying is a viable method for sterilization (Figure S14).

Figure S9.
Compared freeze-dried C3Ms (blue circles) versus ordinary C3Ms (orange squares) at f+ = 0.50 at 5.0 mg/mL.Even though the curve changes slightly, the SAXS pattern is similar, especially considering the structure, showing that freeze-drying is a viable method to acquire sterile samples for cell testing.

Figure S2 .
Figure S2.DLS measurements over time of P2-colistin coacervate complexes at several ratios at 0.33 ≤ f+ ≤ 0.83.f+ < 0.33 and f+ > 0.83 were not possible to be measured because of instability and immediate aggregation.

Figure S3 .
Figure S3.DLS measurements over time of P3-colistin coacervate complexes at several ratios at 0.33 ≤ f+ ≤ 0.83.f+ < 0.33 and f+ > 0.83 were not possible to be measured because of instability and immediate aggregation.

Figure S4 .
Figure S4.Autocorrelation function including CONTIN fits of a representative sample of DLS measurements performed on several PEO-b-PMAA block length complex coacervates at f+ = 0.50.

Figure S5 .
Figure S5.SAXS curves of P1-colistin-C3Ms to show concentration independence between 5.0 mg/mL, 2.5 mg/ml, and 1.3 mg/mL.Four different ratios are plotted, of which the three concentrations are all scaled to 5.0 mg/mL, and then scaled again to improve visuals: f+ = 0.33 is scaled by a factor 1, f+ = 0.50 by a factor 10, f+ = 0.67 by a factor 100 and f+ = 0.83 by a factor 1000. Slight differences can be observed in the scattering pattern but within experimental differences.

Figure S6 .
Figure S6.Density profiles obtained from the fuzzy-surface complex coacervate model.Several charge ratios are shown, including their fuzzy-surface parameters where the core transforms into the fuzzy-interface shell.Larger f+ values cause a decrease in the density of the core, especially in the SCP --region (f+ < 0.40).

Figure S9 .
Figure S9.X-ray scattering patterns showcasing the pH dependency of P1-colistin coacervate complexes at 5.0 mg/mL.A decrease in pH leads to a decreased I0, an increase in PDI, and a loss of internal peak structure (TableS6).

Figure S5 .
Figure S5.CMC determination of P1-colistin coacervate complexes at f+ = 0.50.With the pendant drop method, the surface tension was determined at several concentrations of P1-colistin coacervate complexes, by which two regions could be determined: high slope and low slope.The intercept is the CMC of the coacervate complexes, which was determined to be 0.3 mg/mL by linear regression of both lines.

Figure S6 .
Figure S6.Determination of CMC at f+ = 0.50 by using SAXS.SAXS patterns are shown at seven different concentrations and scaled to 5.0 mg/mL.The SAXS pattern starts deviating between 0.63 mg/mL and 0.31 mg/mL since the distinguishable features are lost.Therefore, the CMC can be assumed to be around 0.3-0.6 mg/mL.

Figure S8
Figure S8.Small-angle X-ray scattering patterns of enzymatic breakdown of colistin (3.4 mg/mL) versus colistin C3Ms (total concentration 5.0 mg/mL) in the presence of trypsin.Theoretical SAXS patterns were calculated based on either the added scattering from C3Ms and enzymes (0% enzyme breakdown, orange squares) or colistin, polymer, and enzyme separately summed up (100% break down, blue circles).The effect of enzymatic degradation after 24 hours at 37°C was measured by either adding Trypsin to colistin followed by complexation with polymer (indicated by green triangles) or the addition of enzyme to C3Ms (indicated by grey diamonds).The SAXS patterns were fitted by using the fuzzy-surface complex coacervate model for complex coacervates with added Debye scattering of the corresponding enzymes.It can be observed that trypsin does not seem to break down colistin.

Figure S10 .
Figure S10.Cell morphologies of MSC (A), HGK (B), and HUVEC (C) after exposure to treatments of colistin, PEO-b-PMAA, and Colistin-C3Ms.Pictures are taken at 1, 2, and 3 days.Lower densities in images can be attributed to cell death, causing cell detachment.The scale bar is 200 µm.

Table S2 .
Ratio experiment fitting values for P1-colistin coacervate complexes at 2.5 mg/mL a .It was not possible to fit SAXS curves at this concentration at f+ < 0.33 and f+ > 0.91. a

Table S4 .
Model parameters for the ionic strength dependency in mixing for P1-colistin coacervate complexes at 5.0 mg/mL, using a stopped-flow device at a mixing rate of 6.7 mL/s.

Table S5 .
Model parameters for the ionic strength dependency after mixing (salt annihilation) for P1-colistin coacervate complexes at 5.0 mg/mL.