Standard state free energies, not pKas, are ideal for describing small molecule protonation and tautomeric states

  • M. R. GunnerEmail author
  • Taichi Murakami
  • Ariën S. Rustenburg
  • Mehtap Işık
  • John D. Chodera


The pKa is the standard measure used to describe the aqueous proton affinity of a compound, indicating the proton concentration (pH) at which two protonation states (e.g. A and AH) have equal free energy. However, compounds can have additional protonation states (e.g. AH2+), and may assume multiple tautomeric forms, with the protons in different positions (microstates). Macroscopic pKas give the pH where the molecule changes its total number of protons, while microscopic pKas identify the tautomeric states involved. As tautomers have the same number of protons, the free energy difference between them and their relative probability is pH independent so there is no pKa connecting them. The question arises: What is the best way to describe protonation equilibria of a complex molecule in any pH range? Knowing the number of protons and the relative free energy of all microstates at a single pH, ∆G°, provides all the information needed to determine the free energy, and thus the probability of each microstate at each pH. Microstate probabilities as a function of pH generate titration curves that highlight the low energy, observable microstates, which can then be compared with experiment. A network description connecting microstates as nodes makes it straightforward to test thermodynamic consistency of microstate free energies. The utility of this analysis is illustrated by a description of one molecule from the SAMPL6 Blind pKa Prediction Challenge. Analysis of microstate ∆G°s also makes a more compact way to archive and compare the pH dependent behavior of compounds with multiple protonatable sites.


SAMPL6 pKa Tautomer Protonation state pH titration Multiprotic 



MRG and TM acknowledge the support of the National Science Foundation grant MCB-1519640. JDC acknowledges support of the National Cancer Institute of the National Institutes of Health under P30CA008748 and partial support from NIH grant P30 CA008748. MI, JDC, and ASR gratefully acknowledge support from NIH grant R01GM124270 supporting the SAMPL Blind Challenges. MI acknowledges support from a Doris J. Hutchinson Fellowship. MI and JDC acknowledge support from the Sloan Kettering Institute and are grateful to OpenEye Scientific for providing a free academic software license for use in this work.


A complete funding history for the Chodera lab can be found at

Compliance with ethical standards

Conflict of interest

JDC is a member of the Scientific Advisory Board of OpenEye Scientific Software. The Chodera laboratory receives or has received funding from multiple sources, including the National Institutes of Health, the National Science Foundation, the Parker Institute for Cancer Immunotherapy, Relay Therapeutics, Bayer, Entasis Therapeutics, Silicon Therapeutics, EMD Serono (Merck KGaA), AstraZeneca, XtalPi, the Molecular Sciences Software Institute, the Starr Cancer Consortium, the Open systematic Consortium, Cycle for Survival, a Louis V. Gerstner Young Investigator Award, and the Sloan Kettering Institute.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Physics City College of New YorkNew YorkUSA
  2. 2.Computational and Systems Biology ProgramSloan Kettering Institute, Memorial Sloan Kettering Cancer CenterNew YorkUSA
  3. 3.Graduate Program in Physiology, Biophysics and Systems BiologyWeill Cornell Medical CollegeNew YorkUSA
  4. 4.Tri-Institutional PhD Program in Chemical Biology, Weill Cornell Graduate School of Medical SciencesCornell UniversityNew YorkUSA
  5. 5.Tri-Institutional Training Program in Computational Biology and MedicineNew YorkUSA

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