Thermodynamic Correlation between Liquid–Liquid Phase Separation and Crystalline Solubility of Drug-Like Molecules

The purpose of the present study was to experimentally confirm the thermodynamic correlation between the intrinsic liquid–liquid phase separation (LLPS) concentration (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>S</mi><mn>0</mn><mrow><mi>L</mi><mi>L</mi><mi>P</mi><mi>S</mi></mrow></msubsup></mrow></semantics></math></inline-formula>) and crystalline solubility (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>S</mi><mn>0</mn><mi>c</mi></msubsup></mrow></semantics></math></inline-formula>) of drug-like molecules. Based on the thermodynamic principles, the crystalline solubility LLPS concentration melting point (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub></mrow></semantics></math></inline-formula>) equation (CLME) was derived (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mi>o</mi><msub><mi>g</mi><mrow><mn>10</mn></mrow></msub><msubsup><mi>S</mi><mn>0</mn><mi>C</mi></msubsup><mo>=</mo><mi>l</mi><mi>o</mi><msub><mi>g</mi><mrow><mn>10</mn></mrow></msub><msubsup><mi>S</mi><mn>0</mn><mrow><mi>L</mi><mi>L</mi><mi>P</mi><mi>S</mi></mrow></msubsup><mo>−</mo><mn>0.0095</mn><mfenced><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>−</mo><mn>310</mn></mrow></mfenced></mrow></semantics></math></inline-formula> for 310 K). The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>S</mi><mn>0</mn><mrow><mi>L</mi><mi>L</mi><mi>P</mi><mi>S</mi></mrow></msubsup></mrow></semantics></math></inline-formula> values of 31 drugs were newly measured by simple bulk phase pH-shift or solvent-shift precipitation tests coupled with laser-assisted visual turbidity detection. To ensure the precipitant was not made crystalline at <10 s, the precipitation tests were also performed under the polarized light microscope. The calculated and observed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>log</mi></mrow><mrow><mn>10</mn></mrow></msub><msubsup><mi>S</mi><mn>0</mn><mi>C</mi></msubsup></mrow></semantics></math></inline-formula> values showed a good correlation (root mean squared error: 0.40 log unit, absolute average error: 0.32 log unit).