120 research outputs found
Exploring the Free Energy Landscape: From Dynamics to Networks and Back
The knowledge of the Free Energy Landscape topology is the essential key to
understand many biochemical processes. The determination of the conformers of a
protein and their basins of attraction takes a central role for studying
molecular isomerization reactions. In this work, we present a novel framework
to unveil the features of a Free Energy Landscape answering questions such as
how many meta-stable conformers are, how the hierarchical relationship among
them is, or what the structure and kinetics of the transition paths are.
Exploring the landscape by molecular dynamics simulations, the microscopic data
of the trajectory are encoded into a Conformational Markov Network. The
structure of this graph reveals the regions of the conformational space
corresponding to the basins of attraction. In addition, handling the
Conformational Markov Network, relevant kinetic magnitudes as dwell times or
rate constants, and the hierarchical relationship among basins, complete the
global picture of the landscape. We show the power of the analysis studying a
toy model of a funnel-like potential and computing efficiently the conformers
of a short peptide, the dialanine, paving the way to a systematic study of the
Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press
Why are MD simulated protein folding times wrong?
The question of significant deviations of protein folding times simulated using molecular dynamics from experimental values is investigated. It is shown that in the framework of Markov State Model (MSM) describing the conformational dynamics of peptides and proteins, the folding time is very sensitive to the simulation model parameters, such as forcefield and temperature. Using two peptides as examples, we show that the deviations in the folding times can reach an order of magnitude for modest variations of the molecular model. We, therefore, conclude that the folding rate values obtained in molecular dynamics simulations have to be treated with care
A weak characterization of slow variables in stochastic dynamical systems
We present a novel characterization of slow variables for continuous Markov
processes that provably preserve the slow timescales. These slow variables are
known as reaction coordinates in molecular dynamical applications, where they
play a key role in system analysis and coarse graining. The defining
characteristics of these slow variables is that they parametrize a so-called
transition manifold, a low-dimensional manifold in a certain density function
space that emerges with progressive equilibration of the system's fast
variables. The existence of said manifold was previously predicted for certain
classes of metastable and slow-fast systems. However, in the original work, the
existence of the manifold hinges on the pointwise convergence of the system's
transition density functions towards it. We show in this work that a
convergence in average with respect to the system's stationary measure is
sufficient to yield reaction coordinates with the same key qualities. This
allows one to accurately predict the timescale preservation in systems where
the old theory is not applicable or would give overly pessimistic results.
Moreover, the new characterization is still constructive, in that it allows for
the algorithmic identification of a good slow variable. The improved
characterization, the error prediction and the variable construction are
demonstrated by a small metastable system
Molecular dynamics simulations and drug discovery
This review discusses the many roles atomistic computer simulations of macromolecular (for example, protein) receptors and their associated small-molecule ligands can play in drug discovery, including the identification of cryptic or allosteric binding sites, the enhancement of traditional virtual-screening methodologies, and the direct prediction of small-molecule binding energies. The limitations of current simulation methodologies, including the high computational costs and approximations of molecular forces required, are also discussed. With constant improvements in both computer power and algorithm design, the future of computer-aided drug design is promising; molecular dynamics simulations are likely to play an increasingly important role
Minimum Free Energy Path of Ligand-Induced Transition in Adenylate Kinase
Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme
CACHE (Critical Assessment of Computational Hit-finding Experiments): A public–private partnership benchmarking initiative to enable the development of computational methods for hit-finding
One aspirational goal of computational chemistry is to predict potent and drug-like binders for any protein, such that only those that bind are synthesized. In this Roadmap, we describe the launch of Critical Assessment of Computational Hit-finding Experiments (CACHE), a public benchmarking project to compare and improve small-molecule hit-finding algorithms through cycles of prediction and experimental testing. Participants will predict small-molecule binders for new and biologically relevant protein targets representing different prediction scenarios. Predicted compounds will be tested rigorously in an experimental hub, and all predicted binders as well as all experimental screening data, including the chemical structures of experimentally tested compounds, will be made publicly available and not subject to any intellectual property restrictions. The ability of a range of computational approaches to find novel binders will be evaluated, compared and openly published. CACHE will launch three new benchmarking exercises every year. The outcomes will be better prediction methods, new small-molecule binders for target proteins of importance for fundamental biology or drug discovery and a major technological step towards achieving the goal of Target 2035, a global initiative to identify pharmacological probes for all human proteins. [Figure not available: see fulltext.
Modeling Conformational Ensembles of Slow Functional Motions in Pin1-WW
Protein-protein interactions are often mediated by flexible loops that experience conformational dynamics on the microsecond to millisecond time scales. NMR relaxation studies can map these dynamics. However, defining the network of inter-converting conformers that underlie the relaxation data remains generally challenging. Here, we combine NMR relaxation experiments with simulation to visualize networks of inter-converting conformers. We demonstrate our approach with the apo Pin1-WW domain, for which NMR has revealed conformational dynamics of a flexible loop in the millisecond range. We sample and cluster the free energy landscape using Markov State Models (MSM) with major and minor exchange states with high correlation with the NMR relaxation data and low NOE violations. These MSM are hierarchical ensembles of slowly interconverting, metastable macrostates and rapidly interconverting microstates. We found a low population state that consists primarily of holo-like conformations and is a “hub” visited by most pathways between macrostates. These results suggest that conformational equilibria between holo-like and alternative conformers pre-exist in the intrinsic dynamics of apo Pin1-WW. Analysis using MutInf, a mutual information method for quantifying correlated motions, reveals that WW dynamics not only play a role in substrate recognition, but also may help couple the substrate binding site on the WW domain to the one on the catalytic domain. Our work represents an important step towards building networks of inter-converting conformational states and is generally applicable
A Kinetic Model of Trp-Cage Folding from Multiple Biased Molecular Dynamics Simulations
Trp-cage is a designed 20-residue polypeptide that, in spite of its size, shares several features with larger globular proteins. Although the system has been intensively investigated experimentally and theoretically, its folding mechanism is not yet fully understood. Indeed, some experiments suggest a two-state behavior, while others point to the presence of intermediates. In this work we show that the results of a bias-exchange metadynamics simulation can be used for constructing a detailed thermodynamic and kinetic model of the system. The model, although constructed from a biased simulation, has a quality similar to those extracted from the analysis of long unbiased molecular dynamics trajectories. This is demonstrated by a careful benchmark of the approach on a smaller system, the solvated Ace-Ala3-Nme peptide. For the Trp-cage folding, the model predicts that the relaxation time of 3100 ns observed experimentally is due to the presence of a compact molten globule-like conformation. This state has an occupancy of only 3% at 300 K, but acts as a kinetic trap. Instead, non-compact structures relax to the folded state on the sub-microsecond timescale. The model also predicts the presence of a state at of 4.4 Å from the NMR structure in which the Trp strongly interacts with Pro12. This state can explain the abnormal temperature dependence of the and chemical shifts. The structures of the two most stable misfolded intermediates are in agreement with NMR experiments on the unfolded protein. Our work shows that, using biased molecular dynamics trajectories, it is possible to construct a model describing in detail the Trp-cage folding kinetics and thermodynamics in agreement with experimental data
The Free Energy Landscape of Small Molecule Unbinding
The spontaneous dissociation of six small ligands from the active site of FKBP
(the FK506 binding protein) is investigated by explicit water molecular dynamics
simulations and network analysis. The ligands have between four
(dimethylsulphoxide) and eleven (5-diethylamino-2-pentanone) non-hydrogen atoms,
and an affinity for FKBP ranging from 20 to 0.2 mM. The conformations of the
FKBP/ligand complex saved along multiple trajectories (50 runs at 310 K for each
ligand) are grouped according to a set of intermolecular distances into nodes of
a network, and the direct transitions between them are the links. The network
analysis reveals that the bound state consists of several subbasins, i.e.,
binding modes characterized by distinct intermolecular hydrogen bonds and
hydrophobic contacts. The dissociation kinetics show a simple (i.e.,
single-exponential) time dependence because the unbinding barrier is much higher
than the barriers between subbasins in the bound state. The unbinding transition
state is made up of heterogeneous positions and orientations of the ligand in
the FKBP active site, which correspond to multiple pathways of dissociation. For
the six small ligands of FKBP, the weaker the binding affinity the closer to the
bound state (along the intermolecular distance) are the transition state
structures, which is a new manifestation of Hammond behavior. Experimental
approaches to the study of fragment binding to proteins have limitations in
temporal and spatial resolution. Our network analysis of the unbinding
simulations of small inhibitors from an enzyme paints a clear picture of the
free energy landscape (both thermodynamics and kinetics) of ligand
unbinding
The Effect of Macromolecular Crowding, Ionic Strength and Calcium Binding on Calmodulin Dynamics
The flexibility in the structure of calmodulin (CaM) allows its binding to
over 300 target proteins in the cell. To investigate the structure-function
relationship of CaM, we combined methods of computer simulation and experiments
based on circular dichroism (CD) to investigate the structural characteristics
of CaM that influence its target recognition in crowded cell-like conditions.
We developed a unique multiscale solution of charges computed from quantum
chemistry, together with protein reconstruction, coarse-grained molecular
simulations, and statistical physics, to represent the charge distribution in
the transition from apoCaM to holoCaM upon calcium binding. Computationally, we
found that increased levels of macromolecular crowding, in addition to calcium
binding and ionic strength typical of that found inside cells, can impact the
conformation, helicity and the EF hand orientation of CaM. Because EF hand
orientation impacts the affinity of calcium binding and the specificity of
CaM's target selection, our results may provide unique insight into
understanding the promiscuous behavior of calmodulin in target selection inside
cells.Comment: Accepted to PLoS Comp Biol, 201
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