Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

Vitalis, Andreas; Caflisch, Amedeo

doi:10.1021/ct200801b

Cited by 40 publications

(50 citation statements)

References 68 publications

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“…To construct a one‐dimensional free energy profile, the MD trajectory has to be further processed. Here, the total of 655,000 snapshots was binned along a reaction coordinate (RC), another common method would be grouping the snapshots with a clustering algorithm (e.g., using a tree‐based algorithm30). The binning suggests the conventional way of projecting the free energy as F H ( i ) = − kTlnZ H ( i ) where Z H ( i ) denotes the partition function which is equal to the density of bin i , that is, Z H ( i ) = ${\#{\rm frames\;in\;bin}\;i \over {\rm bin\;size}}$ and F H is short for histogram‐based free energy.…”

Section: Methodsmentioning

confidence: 99%

Peptide binding to the PDZ3 domain by conformational selection

Steiner

Caflisch

2012

Proteins

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The PDZ domains, a large family of peptide recognition proteins, bind to the C-terminal segment of membrane ion channels and receptors thereby mediating their localization. The peptide binding process is not known in detail and seems to differ among different PDZ domains. For the third PDZ domain of the synaptic protein PSD-95 (PDZ3), a lock-and-key mechanism was postulated on the basis of the almost perfect overlap of the crystal structures in the presence and absence of its peptide ligand. Here, peptide binding to PDZ3 is investigated by explicit solvent molecular dynamics (MD) simulations (for a total of 1.3 μs) and the cut-based free energy profile method for determining free energy barriers and basins. The free energy landscape of apo PDZ3 indicates that there are multiple basins within the native state. These basins differ by the relative orientation of the α2 helix and β2 strand, the two secondary structure elements that make up the peptide binding site. Only the structure with the smallest aperture of the binding site is populated in the MD simulations of the complex whose analysis reveals that the peptide ligand binds to PDZ3 by selecting one of three conformations. Thus, the dynamical information obtained by the atomistic simulations increment the static, that is, partial, picture of the PDZ3 binding mechanism based on the X-ray crystallography data. Importantly, the simulation results show for the first time that conformational selection is a possible mechanism of peptide binding by PDZ domains in general.

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Section: Methodsmentioning

confidence: 99%

Peptide binding to the PDZ3 domain by conformational selection

Steiner

Caflisch

2012

Proteins

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“…49 has been used in a slightly modified form. That is, a tree with total six layers was constructed with decreasing RMSD cut-offs.…”

Section: Building Microstatesmentioning

confidence: 99%

“…Otherwise, the snapshot structure was added to the node with the smallest RMSD, whose centroid structure was shifted so that it becomes the average over all snapshot structures within that node (in contrast to Ref. 49, a centroid structure has also been calculated for the lowest tree level). In the second scan of the MD data, the tree as well as the centroid structures were taken from the first scan and kept fixed.…”

Section: Building Microstatesmentioning

confidence: 99%

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Markov state model of the two-state behaviour of water

Hamm

2016

The Journal of Chemical Physics

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With the help of a Markov State Model (MSM), two-state behaviour is resolved for two computer models of water in a temperature range from 255 K to room temperature (295 K). The method is first validated for ST2 water, for which the so far strongest evidence for a liquid-liquid phase transition exists. In that case, the results from the MSM can be cross-checked against the radial distribution function g(5)(r) of the 5th-closest water molecule around a given reference water molecule. The latter is a commonly used local order parameter, which exhibits a bimodal distribution just above the liquidliquid critical point that represents the low-density form of the liquid (LDL) and the high density liquid. The correlation times and correlation lengths of the corresponding spatial domains are calculated and it is shown that they are connected via a simple diffusion model. Once the approach is established, TIP4P/2005 will be considered, which is the much more realistic representation of real water. The MSM can resolve two-state behavior also in that case, albeit with significantly smaller correlation times and lengths. The population of LDL-like water increases with decreasing temperature, thereby explaining the density maximum at 4 degrees C along the lines of the two-state model of water. Published by AIP Publishing. With the help of a Markov State Model (MSM), two-state behaviour is resolved for two computer models of water in a temperature range from 255 K to room temperature (295 K). The method is first validated for ST2 water, for which the so far strongest evidence for a liquid-liquid phase transition exists. In that case, the results from the MSM can be cross-checked against the radial distribution function g 5 (r) of the 5th-closest water molecule around a given reference water molecule. The latter is a commonly used local order parameter, which exhibits a bimodal distribution just above the liquid-liquid critical point that represents the low-density form of the liquid (LDL) and the high density liquid. The correlation times and correlation lengths of the corresponding spatial domains are calculated and it is shown that they are connected via a simple diffusion model. Once the approach is established, TIP4P/2005 will be considered, which is the much more realistic representation of real water. The MSM can resolve two-state behavior also in that case, albeit with significantly smaller correlation times and lengths. The population of LDL-like water increases with decreasing temperature, thereby explaining the density maximum at 4• C along the lines of the two-state model of water. Published by AIP Publishing. [http://dx

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“…Here, we apply the cut-based analysis on the MSM describing the reversible folding of the 20-residue three-stranded antiparallel β-sheet peptide studied in ref 22. The molecular dynamics sampling has been clustered according to backbone dihedral angles values, by means of a hierarchical algorithm 36 implemented in the molecular modeling package CAMPARI. 37 The resulting network has V = 157 380 nodes and E = 329 011 edges; it has been analyzed with PYKOV (a Markov chain Python module).…”

Section: ■ Examplesmentioning

confidence: 99%

Ultrametricity in Protein Folding Dynamics

Scalco

Caflisch

2012

J. Chem. Theory Comput.

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The free energy of the transition state (TS) between two nodes of an ergodic Markov state model (MSM) can be obtained from the minimum cut, which is the set of edges that has the smallest sum of the flow capacities among all the possible cuts separating the two nodes. Here, we first show that the free energy of the TS is an ultrametric distance. The ultrametric property offers a way to simplify the MSM in a small number of states and, as a consequence, meaningful rate constants (free energy barriers) for the simplified MSM can be defined. We also present a new definition of the cut-based free energy profile (cbFEP), which is useful to check for the existence of a state for which the equilibration is much faster than the time to escape from it. From our analysis, a parallelism emerges between the minimum cut (maximum flow), and transition state theory (TST) or Kramers' theory.

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Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

Cited by 40 publications

References 68 publications

Peptide binding to the PDZ3 domain by conformational selection

Peptide binding to the PDZ3 domain by conformational selection

Markov state model of the two-state behaviour of water

Ultrametricity in Protein Folding Dynamics

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