Implementation of the Forward–Reverse Method for Calculating the Potential of Mean Force Using a Dynamic Restraining Protocol

Nategholeslam, Mostafa; Gray, C.G.; Tomberli, Bruno

doi:10.1021/jp504942t

Cited by 10 publications

(14 citation statements)

References 70 publications

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“…This event is rare, and so potentials of mean force calculations were implemented using steered molecular dynamics (SMD) (26,27). We wished to eliminate the effects of water friction from this calculation, and so a previously described, bidirectional algorithm was used (28). The water molecules and ions in the solution add resistance and drag on the Ca 2+ , in the form of dissipative work in both the forward and reverse directions (28).…”

Section: +mentioning

confidence: 99%

Atomic resolution probe for allostery in the regulatory thin filament

Williams

Lehman

Tardiff

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Calcium binding and dissociation within the cardiac thin filament (CTF) is a fundamental regulator of normal contraction and relaxation. Although the disruption of this complex, allosterically mediated process has long been implicated in human disease, the precise atomiclevel mechanisms remain opaque, greatly hampering the development of novel targeted therapies. To address this question, we used a fully atomistic CTF model to test both Ca 2+ binding strength and the energy required to remove Ca 2+ from the N-lobe binding site in WT and mutant troponin complexes that have been linked to genetic cardiomyopathies. This computational approach is combined with measurements of in vitro Ca 2+ dissociation rates in fully reconstituted WT and cardiac troponin T R92L and R92W thin filaments. These human disease mutations represent known substitutions at the same residue, reside at a significant distance from the calcium binding site in cardiac troponin C, and do not affect either the binding pocket affinity or EF-hand structure of the binding domain. Both have been shown to have significantly different effects on cardiac function in vivo. We now show that these mutations independently alter the interaction between the Ca 2+ ion and cardiac troponin I subunit. This interaction is a previously unidentified mechanism, in which mutations in one protein of a complex indirectly affect a third via structural and dynamic changes in a second to yield a pathogenic change in thin filament function that results in mutation-specific disease states. We can now provide atom-level insight that is potentially highly actionable in drug design.cardiac thin filament | hypertrophic cardiomyopathy | calcium homeostasis | molecular modeling | steered molecular dynamics C ardiac contraction is regulated by the binding of Ca 2+ to cardiac troponin C (cTnC) (1, 2) ( Fig. 1). The Ca 2+ binds in an EF-hand motif, consisting of two α-helices separated by a loop region containing seven coordinating oxygens that interact with the Ca 2+ , as seen in Fig. 2. Once Ca 2+ is bound, interactions between cTnC and the switch peptide domain of cardiac troponin I (cTnI) cause conformational changes that reduce the ability of cTnI to bind to actin (3). When bound to actin, cTnI shifts the equilibrium location of cardiac tropomyosin (cTM) to a position that prevents the interaction of actin with myosin, thereby inhibiting the power stroke that drives contraction of cardiac muscle (4, 5). Thus, Ca 2+ binding can be viewed as the initial step in a process that results in the eventual hydrolysis of ATP, with the sliding of the thin filament over the thick filament and the generation of mechanical work (5, 6). In disease states, changes in the ability of the cardiac muscle to be properly regulated by and to regulate Ca 2+ are often observed and play a central role in pathogenic remodeling and sudden cardiac death (SCD) (7). What is not well understood is the proximal biophysical cause by which mutation affects function at the molecular level.Due to both the size (ove...

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Section: +mentioning

confidence: 99%

Atomic resolution probe for allostery in the regulatory thin filament

Williams

Lehman

Tardiff

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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“…Methods based on bi-directional pulling have complemented these efforts in an attempt to increase the applicability of the non-equilibrium methods to free energy calculations. [69] A renormalization approach has been proposed to permit application of SMD to long-time dynamics on the microsecond time scale, which would increase the sampling and therefore the accuracy of thermodynamic averages. [70] The use of local sampling implemented using conformational freezing has been considered as a method to enhance the accuracy of the calculated PMF.…”

Section: Introductionmentioning

confidence: 99%

Steered molecular dynamics study of inhibitor binding in the internal binding site in dehaloperoxidase-hemoglobin

Zhang

Santos

Zhou

et al. 2016

Biophysical Chemistry

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The binding free energy of 4-bromophenol (4-BP), an inhibitor that binds in the internal binding site in dehaloperoxidase-hemoglobin (DHP) was calculated using Molecular Dynamics (MD) methods combined with pulling or umbrella sampling. The effects of systematic changes in the pulling speed, pulling force constant and restraint force constant on the calculated potential of mean force (PMF) are presented in this study. The PMFs calculated using steered molecular dynamics (SMD) were validated by umbrella sampling (US) in the strongly restrained regime. A series of restraint force constants ranging from 1000 down to 5 kJ/(mol nm(2)) were used in SMD simulations. This range was validated using US, however noting that weaker restraints give rise to a broader sampling of configurations. This comparison was further tested by a pulling simulation conducted without any restraints, which was observed to have a value closest to the experimentally measured free energy for binding of 4-BP to DHP based on ultraviolet-visible (UV-vis) and resonance Raman spectroscopies. The protein-inhibitor system is well suited for fundamental study of free energy calculations because the DHP protein is relatively small and the inhibitor is quite rigid. Simulation configuration structures are compared to the X-ray crystallography structures of the binding site of 4-BP in the distal pocket above the heme.

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“…For each series of simulations (with a given mass and spring constant), PMFs calculated using both the bin-passing (averaging) [31] and peak-finding methods are shown. 2 ).…”

Section: 6mentioning

confidence: 99%

“…Such a bias has been reported by other authors [29,30], and its relation to the underlying work distributions is investigated in the following sections. In a recent publication [31] we have presented an efficient method for implementing the FR method, in the absence of these inertial effects. In the following, we first demonstrate the outcome of the inertial effects just described on the characteristics of non-equilibrium work distributions and then on the PMF estimations obtained using (the average of) those work distributions.…”

Section: Introductionmentioning

confidence: 99%

Stiff Spring Approximation Revisited: Inertial Effects in Nonequilibrium Trajectories

2017

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Use of harmonic guiding potentials is perhaps the most commonly adopted method for implementing steered molecular dynamics (SMD) simulations, performed to obtain potentials of mean force (PMFs) of molecular systems using Jarzynski's equality and other non-equilibrium work (NEW) theorems. Harmonic guiding potentials are also the natural choice in single molecule force spectroscopy experiments such as optical tweezers and atomic force microscopy, performed to find the potential of mean force using NEW theorems. The stiff spring approximation (SSA) of Schulten and coworkers enables to use the work performed along many SMD trajectories in Jarzynski's equality to obtain the PMF.We discuss and demonstrate how a high spring constant, k, required for the validity of the SSA can violate another requirement of this theory, i.e., the validity of Brownian dynamics of the system under study, if the value of k is too high. Violation of the Brownian condition results in the introduction of kinetic energy contributions to the external work, performed during SMD simulations.These inertial effects result in skewed work distributions, rather than the Gaussian distributions predicted by SSA. The inertial effects also result in broader work distributions, which in turn worsen the effect of the skewness when one tries to calculate reliable work averages. Remarkably, neither the skewness nor the broadening of work distributions can be attributed to factors other than using too-stiff springs. In particular, our results strongly suggest that the skew and width of work distributions are independent of the average drift velocity and the asymmetries of the physical systems studied, at least for the range of systems and velocities we examined.The skew and broadening of work distributions result in biased estimation of the underlying PMF, using Jarzynski's equality or the more efficient forward-reverse (FR) method of Kosztin and coworkers. This pathology is more pronounced in larger biomolecular simulations, where longer samplings are required to achieve convergence. The bias manifests in such simulations in the form of a systematic error that increases with simulation time. We discuss the proper upper limit for k, such that the inertial effects are practically avoided. Used together with the relation for the lower limit of k (which follows naturally from considering thermal fluctuations per degree of freedom of the system), the practitioner of SMD can then conduct accurate steering, while satisfying the Brownian dynamics requirements of SSA. Even in cases where inertial effects (due to high k) result in biased estimations of the PMF, we argue and demonstrate that using the peak-value (rather than the statistical mean) of the work distributions vastly reduces the bias in the calculated PMFs 2 and improves the accuracy.

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Implementation of the Forward–Reverse Method for Calculating the Potential of Mean Force Using a Dynamic Restraining Protocol

Cited by 10 publications

References 70 publications

Atomic resolution probe for allostery in the regulatory thin filament

Atomic resolution probe for allostery in the regulatory thin filament

Steered molecular dynamics study of inhibitor binding in the internal binding site in dehaloperoxidase-hemoglobin

Stiff Spring Approximation Revisited: Inertial Effects in Nonequilibrium Trajectories

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