Principal component analysis on a torus: Theory and application to protein dynamics

Sittel, Florian; Filk, Thomas; Stock, Gerhard

doi:10.1063/1.4998259

Cited by 60 publications

(81 citation statements)

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“…14,63,64 To take the periodicity of the dihedral angles into account, we shift the periodic boundary of the circular data to the region of the lowest point density. This "maximal gap shifting" approach was incorporated into the new version of the dihedral angle principal component analysis (dPCA+), 53 which represents a significant improvement to the previously advocated sine/cosine-transformed variables used in dPCA. 16,65 It avoids artificial doubling of coordinates and distortion errors due to the nonlinearity of the sine and cosine transformations.…”

Section: B Dimensionality Reductionmentioning

confidence: 99%

“…Selecting for principal components whose free energy projection reveals nontrivial structures (i. e., more than one single minimum), the six components x 1 to x 5 and x 7 were chosen here. 53 Using the maximal gap shifted data, we also performed time-lagged independent component analysis (TICA), which results in components that are linearly uncorre- lated (as in PCA) and at the same time show maximal autocovariances at a fixed lag time. 17,18 Using lag times τ TICA 10 ps, the resulting energy landscape of AD is almost identical to the PCA result in Fig.…”

Section: B Dimensionality Reductionmentioning

confidence: 99%

“…We use backbone dihedral angles (φ n , ψ n ) as MD input coordinates, which were maximal gap shifted (as introduced by the dimensionality reduction method dPCA+) to correctly account for the periodic nature of these variables. 53 Apart from PCA, we also considered TICA, which for AD and HP35, however, was found to emphasize irrelevant states and transitions. Next we perform density based clustering and explain the choice of parameters.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of HP35, on the other hand, we find that dynamical coring leads to a significant improvement of the Markovianity of the resulting microstates. In extension of previous studies using relatively few coarse-grained macrostates, 53 we construct an MSM of 57 structurally well-defined microstates of HP35. Apart from the main folding pathways, the model is shown to account for the dynamics within the unfolded energy basin of the protein.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical coring of Markov state models

Nagel

Weber

Lickert

et al. 2019

The Journal of Chemical Physics

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The accurate definition of suitable metastable conformational states is fundamental for the construction of a Markov state model describing biomolecular dynamics. Following the dimensionality reduction of a molecular dynamics trajectory, these microstates can be generated by a recently proposed density-based geometrical clustering algorithm [J. Chem. Theory Comput. 12, 2426 (2016)], which by design cuts the resulting clusters at the energy barriers and allows for a data-based identification of all parameters. Nevertheless, projection artifacts due to the inevitable restriction to a low-dimensional space combined with insufficient sampling often leads to a misclassification of sampled points in the transition regions. This typically causes intrastate fluctuations to be mistaken as interstate transitions, which leads to artificially short life time of the metastable states. As a simple but effective remedy, dynamical coring requires that the trajectory spends a minimum time in the new state for the transition to be counted. Adopting molecular dynamics simulations of two well-established biomolecular systems (alanine dipeptide and villin headpiece), dynamical coring is shown to considerably improve the Markovianity of the resulting metastable states, which is demonstrated by Chapman-Kolmogorov tests and increased implied timescales of the Markov model. Providing high structural and temporal resolution, the combination of density-based clustering and dynamical coring is particularly suited to describe the complex structural dynamics of unfolded biomolecules.

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Section: B Dimensionality Reductionmentioning

confidence: 99%

Section: B Dimensionality Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamical coring of Markov state models

Nagel

Weber

Lickert

et al. 2019

The Journal of Chemical Physics

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“…7,9,55,57 To take the periodicity of the dihedral angles into account, we shift the periodic boundary of the circular data to the region of the lowest point density. This "maximal gap shifting" approach was incorporated into the new version of the dihedral angle principal component analysis (dPCA+), 58 which represents a significant improvement to the previously advocated sine/cosine-transformed variables used in dPCA. 9,57 It avoids artificial doubling of coordinates and distortion errors due to the nonlinearity of the sine and cosine transformations.…”

Section: Dihedral Angle Principal Component Analysismentioning

confidence: 99%

Principal component analysis of nonequilibrium molecular dynamics simulations

Post

Wolf

Stock

2019

The Journal of Chemical Physics

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Principal component analysis (PCA) represents a standard approach to identify collective variables {x i } = x, which can be used to construct the free energy landscape ∆G(x) of a molecular system. While PCA is routinely applied to equilibrium molecular dynamics (MD) simulations, it is less obvious how to extend the approach to nonequilibrium simulation techniques. This includes, e.g., the definition of the statistical averages employed in PCA, as well as the relation between the equilibrium free energy landscape ∆G(x) and energy landscapes ∆G(x) obtained from nonequilibrium MD. As an example for a nonequilibrium method, "targeted MD" is considered which employs a moving distance constraint to enforce rare transitions along some biasing coordinate s. The introduced bias can be described by a weighting function P (s), which provides a direct relation between equilibrium and nonequilibrium data, and thus establishes a well-defined way to perform PCA on nonequilibrium data. While the resulting distribution P(x) and energy ∆G ∝ ln P will not reflect the equilibrium state of the system, the nonequilibrium energy landscape ∆G(x) may directly reveal the molecular reaction mechanism. Applied to targeted MD simulations of the unfolding of decaalanine, for example, a PCA performed on backbone dihedral angles is shown to discriminate several unfolding pathways. Although the formulation is in principle exact, its practical use depends critically on the choice of the biasing coordinate s, which should account for a naturally occurring motion between two well-defined end-states of the system.

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Measured Blood Pressure, Genetically Predicted Blood Pressure, and Cardiovascular Disease Risk in the UK Biobank

et al. 2022

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ImportanceHypertension remains the major cardiovascular disease risk factor globally, but variability in measured blood pressure may result in suboptimal management. Whether genetic contributors to elevated blood pressure may complementarily inform cardiovascular disease risk assessment is unknown.ObjectiveTo examine incident cardiovascular disease by blood pressure polygenic risk score independent of measured blood pressures and antihypertensive medication prescriptions.Design, Setting, and ParticipantsThe cohort study (UK Biobank) recruited UK residents aged 40 to 69 years between March 2006 and August 2010. Participants without a prior physician diagnosis of cardiovascular disease, including myocardial infarction, stroke, or heart failure, were included. Excluded were individuals with mismatch between self-reported and genotypically inferred sex, sex aneuploidy, missing genotype rates of 1% or greater, and excess genotypic heterozygosity. Data analyses were performed from September 25, 2021, to July 21, 2022.ExposuresMeasured blood pressure and externally derived blood pressure polygenic risk score stratified by hypertension diagnosis and management, which included normal blood pressure (&lt;130/80 mm Hg without antihypertensives), untreated hypertension (systolic blood pressure ≥130 mm Hg or diastolic blood pressure ≥80 mm Hg without antihypertensives), and treated hypertension (current antihypertensives prescriptions).Main Outcomes and MeasuresComposite of first incident myocardial infarction, stroke, heart failure, or cardiovascular-related death.ResultsOf the 331 078 study participants included (mean [SD] age at enrollment, 56.9 [8.1] years; 178 824 female [54.0%]), 83 094 (25.1%) had normal blood pressure, 197 597 (59.7%) had untreated hypertension, and 50 387 (15.2%) had treated hypertension. Over a median (IQR) follow-up of 11.1 (10.4-11.8) years, the primary outcome occurred in 15 293 participants. Among those with normal blood pressure, untreated hypertension, and treated hypertension, each SD increase in measured systolic blood pressure was associated with hazard ratios of 1.08 (95% CI, 0.93-1.25), 1.20 (95% CI, 1.16-1.23), and 1.16 (95% CI, 1.11-1.20), respectively, for the primary outcome. Among these same categories, each SD increase in genetically predicted systolic blood pressure was associated with increased hazard ratios of 1.13 (95% CI, 1.05-1.20), 1.04 (95% CI, 1.01-1.07), and 1.06 (95% CI, 1.02-1.10), respectively, for the primary outcome independent of measured blood pressures and other covariates. Findings were similar for measured and genetically predicted diastolic blood pressure.Conclusions and RelevanceBlood pressure polygenic risk score may augment identification of individuals at heightened cardiovascular risk, including those with both normal blood pressure and hypertension. Whether it may also guide antihypertensive initiation or intensification requires further study.

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Principal component analysis on a torus: Theory and application to protein dynamics

Cited by 60 publications

References 50 publications

Dynamical coring of Markov state models

Dynamical coring of Markov state models

Principal component analysis of nonequilibrium molecular dynamics simulations

Measured Blood Pressure, Genetically Predicted Blood Pressure, and Cardiovascular Disease Risk in the UK Biobank

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