Increasing number of biomolecular simulations provide sufficiently long simulations to predict equilibrium constants and associated free energies of simulated processes such as protein folding or protein-ligand binding. The equilibrium constant of a process of a transition from the state A to state B can be estimated as the fraction of times spent in B and A. Here we present a simple, yet exact, method to calculate the errors of the free energy estimations, which is based solely on temperature and the number of transitions from A to B and B to A. The 95% confidence interval of free energy calculated from a trajectory with one A to B and one B to A is the value ± 9.1 kJ/mol (2.2 kcal/mol) at 300 K. For two A to B and B to A transitions it is the value ± 5.7 kJ/mol (1.4 kcal/mol). Markovianity of the process is the prerequisite of the method. The error can be calculated online by our tool at jumpcount.cz.
The work was supported by Czech Science Foundation (22-29667S and 19-16857S) and the Ministry of Education, Youth and Sports of the Czech Republic (LM2018140, LM2018131).