arXiv subjects

Georg Diez

Publications and source records attributed to Georg Diez.

4 recordsLinked to original sources

arXiv2026

Lost in Projection? Gaussian Filtering Recovers Hidden Conformational States

To interpret molecular dynamics (MD) simulations, it is common practice to reduce the dimensionality of the molecular coordinates to a low-dimensional collective variable $x$. Projecting the high-dimensional MD data onto $x$ yields a free energy landscape $\Delta G(x)$, which highlights low-energy regions corresponding to conformational states. The accurate definition of these states, however, is often impeded by projection artifacts, resulting in artificially shortened state lifetimes or even the complete disappearance of states from the analysis. As demonstrated for a two-dimensional toy model, Gaussian low-pass filtering of the high-dimensional MD coordinates can restore the underlying free energy landscape, allowing to recover previously hidden states. When applied to an all-atom folding trajectory of HP35, the number of microstates increases by an order of magnitude, which leads to metastable states that are long-lived and much better defined structurally, even compared to dynamically cored state trajectories.

cond-mat.soft↗

arXiv2025

Recovering Hidden Degrees of Freedom Using Gaussian Processes

Dimensionality reduction represents a crucial step in extracting meaningful insights from Molecular Dynamics (MD) simulations. Conventional approaches, including linear methods such as principal component analysis as well as various autoencoder architectures, typically operate under the assumption of independent and identically distributed data, disregarding the sequential nature of MD simulations. Here, we introduce a physics-informed representation learning framework that leverages Gaussian Processes combined with variational autoencoders to exploit the temporal dependencies inherent in MD data. Time-dependent kernel functions--such as the Mat\'ern kernel--directly impose the temporal correlation structure of the input coordinates onto a low-dimensional space, preserving Markovianity in the reduced representation while faithfully capturing the essential dynamics. Using a three-dimensional toy model, we demonstrate that this approach can successfully identify and separate dynamically distinct states that are geometrically indistinguishable due to hidden degrees of freedom. Applying the framework to a $50\,\mu$s-long MD trajectory of T4 lysozyme, we uncover dynamically distinct conformational substates that previous analyses failed to resolve, revealing functional relationships that become apparent only when temporal correlations are taken into account. This time-aware perspective provides a promising framework for understanding complex biomolecular systems, in which conventional collective variables fail to capture the full dynamical picture.

cond-mat.soft↗

arXiv2024

Accurate estimation of the normalized mutual information of multidimensional data

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates. Avoiding any assumption about the underlying data, the mutual information $I(X, Y)$ does account for multidimensional correlations. However, unlike the normalized Pearson correlation, it has no upper bound ($I \in [0, \infty)$), i.e., it is not clear if say, $I = 0.4$ corresponds to a low or a high correlation. Moreover, the mutual information (MI) involves the estimation of high-dimensional probability densities (e.g., six-dimensional for Cartesian coordinates), which requires a k-nearest neighbor algorithm, such as the estimator by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)]. As existing methods to normalize the MI cannot be used in connection with this estimator, a new approach is presented, which uses an entropy estimation method that is invariant under variable transformations. The algorithm is numerically efficient and does not require more effort than the calculation of the (un-normalized) MI. After validating the method by applying it to various toy models, the normalized MI between the $C_{\alpha}$ -coordinates of T4 lysozyme is considered and compared to a correlation analysis of inter-residue contacts.

physics.data-an↗

arXiv2022

Correlation-based feature selection to identify functional dynamics in proteins

To interpret molecular dynamics simulations of biomolecular systems, systematic dimensionality reduction methods are commonly employed. Among others, this includes principal component analysis (PCA) and time-lagged independent component analysis (TICA), which aim to maximize the variance and the timescale of the first components, respectively. A crucial first step of such an analysis is the identification of suitable and relevant input coordinates (the so-called features), such as backbone dihedral angles and interresidue distances. As typically only a small subset of those coordinates is involved in a specific biomolecular process, it is important to discard the remaining uncorrelated motions or weakly correlated noise coordinates. This is because they may exhibit large amplitudes or long timescales and therefore will be erroneously be considered important by PCA and TICA, respectively. To discriminate collective motions underlying functional dynamics from uncorrelated motions, the correlation matrix of the input coordinates is block-diagonalized by a clustering method. This strategy avoids possible bias due to presumed functional observables and conformational states or variation principles that maximize variance or timescales. Considering several linear and nonlinear correlation measures and various clustering algorithms, it is shown that the combination of linear correlation and the Leiden community detection algorithm yields excellent results for all considered model systems. These include the functional motion of T4 lysozyme to demonstrate the successful identification of collective motion, as well as the folding of villin headpiece to highlight the physical interpretation of the correlated motions in terms of a functional mechanism.

q-bio.BM↗