511
15 (How to) Profit from Molecular Dynamics-based Ensemble Docking
Targeted MD can be used when two states of a given protein are known, e.g.,
the open and closed states of the binding pocket of serine racemase in a study of
Bruno et al [59]. An artificial force is applied during the MD to bias the transition
between the two states. The need of a reaction coordinate limits this application to
systems where a target structure is known beforehand. The trajectory of a targeted
MD simulation can be used in the same way as ensembles derived from unbiased
MD simulations [59].
Alternatively, biased simulations allow the reconstruction of the potential of
mean force or a free energy landscape [56]. If the reaction coordinates are selected
in a way that they cover the ligand binding or unbinding process, enhanced sampling methods allow an estimation of the free energy of binding. This was shown for
metadynamics simulations using an artificial potential which promotes the system
to leave conformational spaces already visited [62]. Such a “docking” strategy is
inherently considering the flexibility of both the ligand and the target, but is not
suitable for high-throughput screening due to the necessity of a defined reaction
coordinate and the exhaustive sampling for individual ligands.
Other sampling methods do not rely on the time-dependent evolution of a structure, but try to cover protein flexibility in collective variables. Collective variables
describe the global motions within a system and can be derived from an MD simulation or from network models. From an MD simulation a principal component analysis of the covariance matrix of the N atom positions yields a set of N eigenvectors.
The first ten to twenty eigenvectors contribute significantly to the overall atomic
fluctuations and are therefore called essential modes or soft modes [63].
Alternatively, collective variables can be obtained by normal mode analysis
(NMA) when diagonalizing the second derivative of the energy function with respect to the coordinates (the Hessian matrix) [24]. NMA is frequently applied on
network models of biomolecular systems where heavy atoms, C-α atoms or residue
representing beads (N) are connected with springs of an adapted force constant. The
various approaches suggested for subsequent docking have limited comparability
as they differ by the form of the network model, the underlying energy function
(origin of spring forces), the extraction of relevant normal modes and the weighting
of deformation along a normal mode. One of the models applied in the community
is the elastic network model (ENM) by Hinsen [64] on C-α atoms (N) with distancedependent force constants. NMA yields 3N-6 eigenvectors, which can be used as
coordinates for deformation of the protein and generation of an ensemble of alternative structures [24]. To limit the number of modes for subsequent structure generation, one can decide to focus on the first (up to 10) softest modes with the highest
eigenvalues [65, 66]. Alternative approaches to reduce dimensions are the identification of the relevant modes for loops in the binding site after NMA of an ENM [67]
or the limitation of the ENM on heavy atoms in the binding site region and analysis
of the first 100 modes [68]. Subsequently, normal modes can be used to generate
conformations, which are then used similarly as conformations generated during
an MD trajectory [66, 67, 68, 69]. Rueda et al. used a larger test set of targets and
could show that their approach could successfully reproduce a near-native ligand
pose in cross-docking for flexible targets [68]. Alternatively, collective variables
15 (How to) Profit from Molecular Dynamics-based Ensemble Docking
Targeted MD can be used when two states of a given protein are known, e.g.,
the open and closed states of the binding pocket of serine racemase in a study of
Bruno et al [59]. An artificial force is applied during the MD to bias the transition
between the two states. The need of a reaction coordinate limits this application to
systems where a target structure is known beforehand. The trajectory of a targeted
MD simulation can be used in the same way as ensembles derived from unbiased
MD simulations [59].
Alternatively, biased simulations allow the reconstruction of the potential of
mean force or a free energy landscape [56]. If the reaction coordinates are selected
in a way that they cover the ligand binding or unbinding process, enhanced sampling methods allow an estimation of the free energy of binding. This was shown for
metadynamics simulations using an artificial potential which promotes the system
to leave conformational spaces already visited [62]. Such a “docking” strategy is
inherently considering the flexibility of both the ligand and the target, but is not
suitable for high-throughput screening due to the necessity of a defined reaction
coordinate and the exhaustive sampling for individual ligands.
Other sampling methods do not rely on the time-dependent evolution of a structure, but try to cover protein flexibility in collective variables. Collective variables
describe the global motions within a system and can be derived from an MD simulation or from network models. From an MD simulation a principal component analysis of the covariance matrix of the N atom positions yields a set of N eigenvectors.
The first ten to twenty eigenvectors contribute significantly to the overall atomic
fluctuations and are therefore called essential modes or soft modes [63].
Alternatively, collective variables can be obtained by normal mode analysis
(NMA) when diagonalizing the second derivative of the energy function with respect to the coordinates (the Hessian matrix) [24]. NMA is frequently applied on
network models of biomolecular systems where heavy atoms, C-α atoms or residue
representing beads (N) are connected with springs of an adapted force constant. The
various approaches suggested for subsequent docking have limited comparability
as they differ by the form of the network model, the underlying energy function
(origin of spring forces), the extraction of relevant normal modes and the weighting
of deformation along a normal mode. One of the models applied in the community
is the elastic network model (ENM) by Hinsen [64] on C-α atoms (N) with distancedependent force constants. NMA yields 3N-6 eigenvectors, which can be used as
coordinates for deformation of the protein and generation of an ensemble of alternative structures [24]. To limit the number of modes for subsequent structure generation, one can decide to focus on the first (up to 10) softest modes with the highest
eigenvalues [65, 66]. Alternative approaches to reduce dimensions are the identification of the relevant modes for loops in the binding site after NMA of an ENM [67]
or the limitation of the ENM on heavy atoms in the binding site region and analysis
of the first 100 modes [68]. Subsequently, normal modes can be used to generate
conformations, which are then used similarly as conformations generated during
an MD trajectory [66, 67, 68, 69]. Rueda et al. used a larger test set of targets and
could show that their approach could successfully reproduce a near-native ligand
pose in cross-docking for flexible targets [68]. Alternatively, collective variables