able to make large ligand displacements and protein collective
motions enabling very efficient ligand migration and protein con-
formational sampling [23, 24]. PELE is being used in the pharma-
ceutical industry for highly flexible docking [25]. It is also clear that
having some knowledge of important motions can help the ENM
capture the correct motions [26].
Natural move Monte-Carlo (NMMC) is another interesting
basin-hopping approach utilizing collective motions. The philoso-
phy of NMMC is to produce very large-scale simulations with
detailed models (e.g., atomistic or three-particle per residue CG).
This is achieved by customizing Monte-Carlo moves such that
natural collective motions are made and any backbone breakage is
fixed with a clever closure algorithm [27, 28]. A recent study shows
how NMMC can be applied to a protein system with customized
hierarchical moves [29].
Like PELE, NMMC sampling does not adhere to the condition
of detailed balance and therefore does not strictly speaking sample
the canonical distribution, although in both cases it could be
argued that they are in a regime which is close to the correct
distribution. Hence, these basin-hopping approaches attempt to
overcome the fundamental limitations of atomistic protein simula-
tions by optimally localizing sampling and approximating the sta-
tistical mechanical rules.3.3 Current
Important Classes
of Molecular Dynamics
Exploration
For exploring protein conformational transitions there are cur-
rently two major groups of approaches: biased potential methods
like umbrella-sampling, meta-dynamics, or replica-exchange
[30–32] and celling approaches like Markov state models
[33]. These two groups of approaches can in theory be used for
the same problems but in practice tend to be used in different cases.
This difference between these two approaches is rooted in the
fundamental sampling problem of large energy barriers and large
entropic conformational spaces. Biased potential methods are good
at scaling large energy barrier while celling approaches struggle as
these events happen so rarely. Celling approaches are good at
exploring large conformational spaces as they are systematic.3.3.1 Biased Potential
Methods
Umbrella sampling adds a biasing potential (often harmonic) with
respect to a predefined collective variable to the Hamiltonian.
These calculations are usually broken up into a series of overlapping
simulation windows such that simple biases can be used to achieve
intensive sampling. The unbiased free-energy profile is then recov-
ered by removing the previously added bias. The most common
method for this reweighting is the weighted histogram
analysis [34].
Metadynamics conceptually fills a system’s energy surface with
computational sand. In similarity to umbrella sampling, metady-
namics biases a simulation with respect to carefully chosen344 Benjamin P. Cossins et al.