Aug.  27,  2020  12  US 2020/0268679 Al  [APJ•]~[API+Jo-[API:IP],a,-[API:IPJ,1d  (9)  ([AP/]$_{0 }$ - [AP/:/P],m  - [AP/:/P],$_{1}$d)  ([/P]$_{0 }$ - [AP/:/P],m  - [AP/:/P],$_{1}$d)  -----------=Ks  [API:IP],m  (11)  [AP/:/P],zd  =  ~([AP/]$_{0 }$ +  [/P]$_{0 }$ -2[AP/:/P],m  - (12)  ✓  [AP/]5 +  [/P]6  - 2([API]o[/P]$_{0}$ )  +  4K,[API:IP],m  )  [API:IP]  ~  [APr-]  +  [IP-]  (3)  [APr-][W]  ----=Ks  [API:IP]  (4)  [API:IP]~[API:IP],a,  (5)  [APr-][W]  ----=Ks  [API:IP],m  (6)  [ APJ•J 0 ~[  API]o  (7)  P at or below 0.85, while IPs that have Log P at or above  1.86 successfully form precipitates.  [0087]  Ion pairs that are the least hydrophobic and least  acidic failed the first screening test, while ion pairs with  intermediate hydrophobicity and acidity failed during the  first and third screening tests (FIG.  4).  Successful IP agents  had hydrophobicities represented by log P>2.  [0088]  Increasing difficulty in deprotonation, represented  by increased pKa, requires greater hydrophobicity for suc› cessful NC formation. The first ionization of polymyxin  occurs at pH=l0.23. Therefore, the li.pKa gap between oleic  acid and polymyxin is over 5 units. In a previous study of  hydrophobic APis, li.pKa>2 values were required for stable  NC formation. For the very strongly basic polymyxin B and  gentamicin, that criteria li.pKa>2 is satisfied by all of the IP  counterions. These results provided general experimental  insight on candidate IP selection for hydrophobic ion pair› ing.  Model of IP Complex Equilibria  [0089]  Without being bound by theory, in order to gain  additional insight on IP selection and complexation forma› tion procedures, a quantitative model of complexation and  precipitation for basic and acidic APis and IPs was devel› oped and compared with experimental results. The goal was  to have rules that can predict the properties of successful IP  agents, and determine concentration ratios for successful  FNP NC formation. For the complexation of an ionized  basic API and acidic IP:  [0090]  Concentrations in square brackets are given in  equivalents of anionic or cationic charge, so [ API+] indicates  API in the units of molarity, with the compound having a  single cationic charge. At or above saturation of ion paired  complex, the concentration of aqueous API:IP is equal to the  aqueous saturation concentration of API:IP.  Correspondingly, at or above saturation, the concentrations  of aqueous API, IP, and API:IP complex are described by the  equilibrium relationship of Ks and that of [ API:IPL,. While  this equation is commonly reduced by combining the satu› ration concentrations and Ks terms to provide a solubility  product, it is useful to separate these terms when assessing  precipitation yields.  For strongly disassociating and fully ionizedAPI and IP, the  starting concentrations of ionized compounds would be  equal to the initial concentrations of the salt forms added.  After exceeding the solubility of the API:IP complex, pre› cipitates form. The amount of precipitate formed is denoted  as Vx[API:IPLM where Vis the volume of the system and  [API:IPJs$_{1}$ d  is the concentration of API:IP complex above its  saturation concentration prior to precipitation. This relation› ship would hold, if the volume of the precipitated solid  phase is much lower than that of the initial volume of  reaction such that the volume of the solution phase is  essentially constant. By mass balance and combining equa› tions (7-8), the concentration of aqueous soluble ionized API  and IP are as follows:  Substitution of (9-10) into (6), yields a general expression  that relates the starting concentrations of aqueous API and IP  with the moles of solid precipitated API:IP complex.  Solving for the precipitated API:IP complex, the expression  for the solid precipitate is obtained.  [0091]  This expression holds for concentrations above the  API:IP saturation concentrations. For the complexation of  the strongly basic polymyxin B and gentamicin at neutral pH  -7, and at concentrations where precipitates had formed,  these conditions are satisfied. Thus, under these assumptions  and conditions, the bulk concentration of precipitatedAPI:IP  is a function of the starting concentrations of API and IP, the  equilibrium constant K,, and aqueous saturation solubility  [API:IPLa,-all of which are readily determined. Whereas  the Ks [API:IPLa, term is typically simplified to a  Ksp  solubility product, separation of these two terms provides  mechanistic insight on precipitation yields.  Ksp  is a function  of complexation strength and molecular actions between the  API and IP (the charged groups between the API and IP),  while the [ API:IPLa, is a function of the hydrophobicity of  the IP complex, e.g., a function of the complex hydropho› bicity and interactions with water due to the hydrophobic tail  group on the IP.  [0092]  Inspection of Eq. 12 provides insight on how to  design precipitation reactions for NC processing, as shown  in FIGS.  SA  and  SB.  For a system with Ks and initialAPI and  IP concentrations, the fraction of initial API that precipitates  increases as the [API:IPLa, values decrease, as shown in  FIG.  SA.  The following conditions were used to generate  FIG.  SA:  [API]$_{0}$=l M; [IP]$_{0}$=l M; 10-$^{6 }$M<[API:IPLa,<l M;  and 10- 2  M-$^{1}$<Ks<l0 4  M- 1 . If the complex is below a  critical [ API:IPL, value, no solids are formed. Highly  hydrophobic IPs result in the formation of API:IP complexes  with lower saturation solubilities-which is in agreement  with our experiment results that higher Log P complexes are 