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Stiff Spring Approximation Revisited: Inertial Effects in Nonequilibrium Trajectories
Mostafa Nategholeslam1, C G Gray2,3, Bruno Tomberli3,4
1Department of Physics, University of Guelph , Guelph, Ontario N1G 2W1, Canada.
The Journal of Physical Chemistry. B
|December 14, 2016
Summary
Steered molecular dynamics (SMD) simulations using stiff springs can skew results. Using the peak work distribution value, not the mean, improves accuracy for potentials of mean force (PMFs) calculations.
Area of Science:
- Computational Chemistry
- Biophysics
- Statistical Mechanics
Background:
- Harmonic guiding potentials are standard for steered molecular dynamics (SMD) simulations.
- Jarzynski's equality and nonequilibrium work (NEW) theorems are used with SMD to calculate potentials of mean force (PMFs).
- The stiff spring approximation (SSA) is commonly employed in these calculations.
Purpose of the Study:
- To investigate the impact of high spring constants (k) in SSA on the validity of Brownian dynamics.
- To identify the source of skewed work distributions in SMD simulations.
- To propose methods for improving the accuracy of PMF calculations.
Main Methods:
- Analysis of work distributions from SMD simulations with varying spring constants.
- Examination of the interplay between spring stiffness and Brownian dynamics.
- Comparison of PMF estimation using mean versus peak values of work distributions.
Main Results:
- High spring constants (k) required for SSA violate the validity of Brownian dynamics.
- This violation leads to skewed and broadened work distributions, independent of drift velocity or physical asymmetries.
- Skewness and broadening result in biased PMF estimations when using NEW theorems.
- Using the peak value of work distributions significantly reduces bias and improves accuracy in the presence of inertial effects.
Conclusions:
- The choice of spring constant in SMD simulations is critical for accurate PMF calculations.
- Excessively stiff springs introduce artifacts that bias results.
- Utilizing the peak work distribution value offers a more robust method for PMF estimation under certain conditions.
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