Stiff Spring Approximation Revisited: Inertial Effects in Nonequilibrium Trajectories.

Use of harmonic guiding potentials is the most commonly adopted method for implementing steered molecular dynamics (SMD) simulations, performed to obtain potentials of mean force (PMFs) using Jarzynski's equality and other nonequilibrium work (NEW) theorems. The stiff spring approximation (SSA) of Schulten and co-workers enables calculation of the PMF by using the work performed along many SMD trajectories in NEW theorems. We discuss and demonstrate how a high spring constant, k, required for the validity of the SSA can violate another requirement of SSA, the validity of Brownian dynamics in the system under study. These result in skewed work distributions with their width increasing with k. The skew and broadening of work distributions result in biased estimation (through invoking NEW theorems) of the PMF. Remarkably, the skewness and the broadening of work distributions are independent of the average drift velocity and physical asymmetries and can only be attributed to using too-stiff springs. We discuss the proper upper limit for k such that the inertial effects are minimized. In the presence of inertial effects, using the peak value (rather than the statistical mean) of the work distributions vastly reduces the bias in the calculated PMFs and improves the accuracy.

Implementation of the forward-reverse method for calculating the potential of mean force using a dynamic restraining protocol.

We present a new sampling and analysis scheme for calculating the potential of mean force (PMF) of systems studied by steered molecular dynamics simulations. This scheme, which we call the bin-passing method, is based on the forward-reverse (FR) method (due to I. Kosztin and co-workers, Kosztin et al. J. Chem. Phys. 2006, 124(6), 064106) and arguments based on the second law of thermodynamics. Applying the bin-passing method results in enhanced sampling, better separation of the reversible and irreversible work distributions, and faster convergence to the underlying PMF of the system under study. Post-simulation analysis is performed using a purpose-built software that we have made publicly available at https://github.com/1particle/bin-passing_analyzer under the terms of the GNU General Public License (version 3). Three examples are provided, for systems of varying sizes and complexities, to demonstrate the efficiency of this method and the quality of the results: for the dissociation PMF of NaCl in water, the bin-passing method obtains PMFs in excellent agreement with that obtained for the same system and using the same force-field through static (equilibrium) methods. The bin-passing method gives a very symmetric PMF for passage of a single water molecule through a DPPC bilayer, and the resultant PMF leads to permeability values in better agreement with experiments than those obtained through previous simulation studies. Finally, we consider the interaction of the antimicrobial peptide HHC-36 with two model membranes and employ the bin-passing method to obtain the PMFs for peptide adsorption to the membranes. The characteristics of these PMFs are consistent with the qualities established for the HHC-36 peptide through in vivo and in vitro experiments, as a non-toxic strong antimicrobial agent.

Dynamic turn conformation of a short tryptophan-rich cationic antimicrobial peptide and its interaction with phospholipid membranes.

Cationic antimicrobial peptides are promising sources for novel therapeutic agents against multi-drug-resistant bacteria. HHC-36 (KRWWKWWRR) is a simple but effective antimicrobial peptide with similar or superior activity compared with several conventional antibiotics. In this biophysical study, unique conformational properties of this peptide and some of its analogs as well as its interaction with lipid membranes are investigated in detail. Circular dichroism (CD) and molecular dynamics modeling studies of HHC-36 in different environments reveal a dynamic amphipathic structure composed of competing turn conformations with free energies lower than that of the unfolded state, implying a strong influence of tryptophan interactions in formation of the turns. CD spectra and gel electrophoresis also show strong evidence of self-association of this peptide in aqueous milieu and interaction with both neutrally and negatively charged lipid membrane systems. Isothermal titration calorimetry and acrylamide fluorescence quenching experiments emphasize the preference of HHC-36 for negatively charged vesicles. In addition, dye leakage experiments suggest that this peptide functions through a surface-associated mechanism with weak lytic activity against bacterial model membranes.

Drift-oscillatory steering with the forward-reverse method for calculating the potential of mean force.

We present a method that enables the use of the forward-reverse (FR) method of Kosztin et al. on a broader range of problems in soft matter physics. Our method, which we call the oscillating forward-reverse (OFR) method, adds an oscillatory steering potential to the constant velocity steering potential of the FR method. This enables the calculation of the potential of mean force (PMF) in a single unidirectional oscillatory drift, rather than multiple drifts in both directions as required by the FR method. By following small forward perturbations with small reverse perturbations, the OFR method is able to generate a piecewise reverse path that follows the piecewise forward path much more closely than any practical set of paths used in the FR method. We calculate the PMF for four different systems: a dragged Brownian oscillator, a pair of atoms in a Lennard-Jones liquid, a Na(+)-Cl⁻ ion pair in an aqueous solution, and a deca-alanine molecule being stretched in an implicit solvent. In all cases, the PMF results are in good agreement with those published previously using various other methods, and, to our knowledge, we give for the first time PMFs calculated by nonequilibrium methods for the Lennard-Jones and Na(+)-Cl⁻ systems.