126
S. Alamdari et al.
with systems with markedly different CV fluctuations [65]. Readers are encouraged
to go through prior MetaD literature that details other variants [1, 5, 66, 70–73].
In the context of biomolecular applications, variants that couple MetaD with
replica exchange are perhaps the most widely employed MetaD methods and are
done so to explore more degrees of freedom [74]. Examples of these are parallel
tempering MetaD (PTMetaD), where temperature is used to increase sampling and
explore hidden degrees of freedom [75], parallel tempering MetaD in the welltempered ensemble (PTMetaD-WTE), which addressed the system size limitations
of PTMetaD [76], bias exchange MetaD (BEM) [54] which can increase dimensionality by biasing more than 2–3 CVs and collective variable tempering [77]. The
replica exchange methods above have the drawback of being computationally intensive, either requiring a careful, non-trivial choice of temperatures to generate replicas
or requiring an additional parameter (bias exchange stride in BEM) to sample the
CV space.
Traditionally, MetaD-based sampling has been limited to 1–2 CVs, because the
simulation time to converge a multi-CV system increases exponentially with the
number of CVs. In the case of BEM, each additional CV increases the number of
parallel replicas of the system, as serially biasing many CVs limits collective motion.
As an alternative that relies upon the basic premise of replica exchange with concurrent MetaD [77], Pfaendtner and Bonomi developed a scheme known as parallel bias
MetaD (PBMetaD). PBMetaD allows a single replica of the system to simultaneously apply 1-dimensional biases to many CVs, allowing for a highly parallelizable
simulation that can bias many more CVs when compared to other enhanced sampling
methods [78]. Recently, variations of PBMetaD have been proposed including metadynamic metainference (M and M) [64] and PBMetaD with partitioned families
(PBMetaD-PF) [79]. This review is a summary of methods and applications related
to the PBMetaD framework. Below, we discuss the theory behind PBMetaD and
its variants M and M and PBMetaD-PF. To illustrate the use of these methods, we
describe six examples that deal with: (1) sampling the structure of biomolecules at
interfaces, (2) elucidating chemical reaction pathways, or (3) guiding biomolecular
simulations toward experimentally observed structures. We briefly comment on the
power of this approach and further emphasize its potential to be incorporated in other
research areas.
2 Theory
The following section emphasizes how the bias potential calculation is uniquely
distributed in the PBMetaD method. In the original metadynamics method [52], a
single multi-dimensional bias potential is created, where the dimensionality of this
potential is equal to the number of CVs. In contrast, in the PBMetaD variant, several
single-dimensional bias potentials are constructed, and the number of potentials is
equal to the number of CVs. As shown empirically by Pfaendtner and Bonomi [78],
this method also converges to the correct free energy profile. This method permits the
S. Alamdari et al.
with systems with markedly different CV fluctuations [65]. Readers are encouraged
to go through prior MetaD literature that details other variants [1, 5, 66, 70–73].
In the context of biomolecular applications, variants that couple MetaD with
replica exchange are perhaps the most widely employed MetaD methods and are
done so to explore more degrees of freedom [74]. Examples of these are parallel
tempering MetaD (PTMetaD), where temperature is used to increase sampling and
explore hidden degrees of freedom [75], parallel tempering MetaD in the welltempered ensemble (PTMetaD-WTE), which addressed the system size limitations
of PTMetaD [76], bias exchange MetaD (BEM) [54] which can increase dimensionality by biasing more than 2–3 CVs and collective variable tempering [77]. The
replica exchange methods above have the drawback of being computationally intensive, either requiring a careful, non-trivial choice of temperatures to generate replicas
or requiring an additional parameter (bias exchange stride in BEM) to sample the
CV space.
Traditionally, MetaD-based sampling has been limited to 1–2 CVs, because the
simulation time to converge a multi-CV system increases exponentially with the
number of CVs. In the case of BEM, each additional CV increases the number of
parallel replicas of the system, as serially biasing many CVs limits collective motion.
As an alternative that relies upon the basic premise of replica exchange with concurrent MetaD [77], Pfaendtner and Bonomi developed a scheme known as parallel bias
MetaD (PBMetaD). PBMetaD allows a single replica of the system to simultaneously apply 1-dimensional biases to many CVs, allowing for a highly parallelizable
simulation that can bias many more CVs when compared to other enhanced sampling
methods [78]. Recently, variations of PBMetaD have been proposed including metadynamic metainference (M and M) [64] and PBMetaD with partitioned families
(PBMetaD-PF) [79]. This review is a summary of methods and applications related
to the PBMetaD framework. Below, we discuss the theory behind PBMetaD and
its variants M and M and PBMetaD-PF. To illustrate the use of these methods, we
describe six examples that deal with: (1) sampling the structure of biomolecules at
interfaces, (2) elucidating chemical reaction pathways, or (3) guiding biomolecular
simulations toward experimentally observed structures. We briefly comment on the
power of this approach and further emphasize its potential to be incorporated in other
research areas.
2 Theory
The following section emphasizes how the bias potential calculation is uniquely
distributed in the PBMetaD method. In the original metadynamics method [52], a
single multi-dimensional bias potential is created, where the dimensionality of this
potential is equal to the number of CVs. In contrast, in the PBMetaD variant, several
single-dimensional bias potentials are constructed, and the number of potentials is
equal to the number of CVs. As shown empirically by Pfaendtner and Bonomi [78],
this method also converges to the correct free energy profile. This method permits the