Uncertainties of Predictions from Temperature Replica Exchange Simulations

Pavel Kříž - Faculty of Mathematics and Physics, Charles University,
             Prague, Czech Republic
             Department of Mathematics, Informatics and Cybernetics,
             University of Chemistry and Technology, Prague, Czech
             Republic
Jan Beránek - Department of Biochemistry and Microbiology, 
              University of Chemistry and Technology, Prague, Czech
              Republic
Vojtěch Spiwok - Department of Biochemistry and Microbiology, University
                 of Chemistry and Technology, Prague, Czech Republic
e-mail - spiwokv@vscht.cz

Parallel tempering molecular dynamics simulation, also known as temperature
replica exchange simulation, is a popular enhanced sampling method used to study
biomolecular systems. This method makes it possible to calculate the free energy
differences between states of the system for a series of temperatures. We
developed a method to easily calculate errors (standard errors or confidence
intervals) of these predictions using a modified version of our recently
introduced JumpCount method. The number of transitions between states (e.g.
protein folding events) is counted for each temperature. This number of
transitions, together with the temperature, fully determines the value of
standard error or the confidence interval of the free energy difference. We also
address the issue of convergence in the situation where all replicas start from
one state by developing an estimator of the equilibrium constant from
simulations that are not fully equilibrated. The prerequisite of the method is
the Markovianity of the process studied.

Software:
GROMACS 2022.31
R 3.6.3.
Python 3.6.9

Content:
figure1 - R script used to produce Figure 1 with the resulting images

figure2 - R script used to produce Figure 2 with the resulting image

figure3 - R scripts used to produce Figure 3 with the resulting images

figure4 - R script used to produce Figure 4 with the resulting images

figure5 - Python scripts used to perform simulations on a model energy
          profiles with output data, R script used to produce Figure 5,
          and the resulting images

figure6 - data and R script used to produce Figure 6 with the resulting
          images

figure7 - simulation data (Gromacs inputs, script, output etc.) and
          R script used to produce Figure 7 with the resulting images

figure8 - simulation data (Gromacs inputs, script, output etc.) and
          R script used to produce Figure 8 with the resulting images

figureS1 - R script used to produce Figure S1 with the resulting images

figureS2 - data and R script used to produce Figure S2 with the
          resulting images

figureS3 - data and R script used to produce Figure S3 with the
          resulting images

figureS4 - data and R script used to produce Figure S4 with the
          resulting images

