<p>Correct calculation of the variation of free
energy upon base flipping is crucial in understanding the dynamics of DNA
systems. The free energy landscape along the flipping pathway gives the
thermodynamic stability and the flexibility of base-paired states. Although
numerous free energy simulations are performed in the base flipping cases, no
theoretically rigorous nonequilibrium techniques are devised and employed to
investigate the thermodynamics of base flipping. In the current work, we report
a general nonequilibrium stratification scheme for efficient calculation of the
free energy landscape of base flipping in DNA duplex. We carefully monitor the
convergence behavior of the equilibrium sampling based free energy simulation and
the nonequilibrium stratification and determine the empirical length of time
blocks required for converged sampling. Comparison between the performances of
equilibrium umbrella sampling and nonequilibrium stratification is given. The
results show that nonequilibrium free energy simulation is able to give similar
accuracy and efficiency compared with the equilibrium enhanced sampling technique
in the base flipping cases. We further test a convergence criterion we
previously proposed and it comes out that the convergence behavior determined
by this criterion agrees with those given by the time-invariant behavior of PMF
and the nonlinear dependence of standard deviation on the sample size. </p>
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