A goal in the kinetic characterization of a macromolecular system is the description of its slow relaxation processes, involving (i) identification of the structural changes involved in these processes, and (ii) estimation of the rates or timescales at which these slow processes occur. Most of the approaches to this task, including Markov models, Master-equation models, and kinetic network models, start by discretizing the high-dimensional state space and then characterize relaxation processes in terms of the eigenvectors and eigenvalues of a discrete transition matrix. The practical success of such an approach depends very much on the ability to finely discretize the slow order parameters. How can this task be achieved in a high-dimensional configuration space without relying on subjective guesses of the slow order parameters? In this paper, we use the variational principle of conformation dynamics to derive an optimal way of identifying the "slow subspace" of a large set of prior order parameters -either generic internal coordinates (distances and dihedral angles), or a user-defined set of parameters. It is shown that a method to identify this slow subspace exists in statistics: the time-lagged independent component analysis (TICA). Furthermore, optimal indicators-order parameters indicating the progress of the slow transitions and thus may serve as reaction coordinates-are readily identified. We demonstrate that the slow subspace is well suited to construct accurate kinetic models of two sets of molecular dynamics simulations, the 6-residue fluorescent peptide MR121-GSGSW and the 30-residue natively disordered peptide KID. The identified optimal indicators reveal the structural changes associated with the slow processes of the molecular system under analysis.

Markov (state) models (MSMs) and related models of molecular kinetics have recently received a surge of interest as they can systematically reconcile simulation data from either a few long or many short simulations and allow us to analyze the essential metastable structures, thermodynamics, and kinetics of the molecular system under investigation. However, the estimation, validation, and analysis of such models is far from trivial and involves sophisticated and often numerically sensitive methods. In this work we present the open-source Python package PyEMMA ( http://pyemma.org ) that provides accurate and efficient algorithms for kinetic model construction. PyEMMA can read all common molecular dynamics data formats, helps in the selection of input features, provides easy access to dimension reduction algorithms such as principal component analysis (PCA) and time-lagged independent component analysis (TICA) and clustering algorithms such as k-means, and contains estimators for MSMs, hidden Markov models, and several other models. Systematic model validation and error calculation methods are provided. PyEMMA offers a wealth of analysis functions such that the user can conveniently compute molecular observables of interest. We have derived a systematic and accurate way to coarse-grain MSMs to few states and to illustrate the structures of the metastable states of the system. Plotting functions to produce a manuscript-ready presentation of the results are available. In this work, we demonstrate the features of the software and show new methodological concepts and results produced by PyEMMA.

The eigenvalues and eigenvectors of the molecular dynamics propagator (or transfer operator) contain the essential information about the molecular thermodynamics and kinetics. This includes the stationary distribution, the metastable states, and state-to-state transition rates. Here, we present a variational approach for computing these dominant eigenvalues and eigenvectors. This approach is analogous to the variational approach used for computing stationary states in quantum mechanics. A corresponding method of linear variation is formulated. It is shown that the matrices needed for the linear variation method are correlation matrices that can be estimated from simple MD simulations for a given basis set. The method proposed here is thus to first define a basis set able to capture the relevant conformational transitions, then compute the respective correlation matrices, and then to compute their dominant eigenvalues and eigenvectors, thus obtaining the key ingredients of the slow kinetics.

We have carried out a series of extended unbiased molecular dynamics (MD) simulations (up to 10 μs long, ∼162 μs in total) complemented by replica-exchange with the collective variable tempering (RECT) approach for several human telomeric DNA G-quadruplex (GQ) topologies with TTA propeller loops. We used different AMBER DNA force-field variants and also processed simulations by Markov State Model (MSM) analysis. The slow conformational transitions in the propeller loops took place on a scale of a few μs, emphasizing the need for long simulations in studies of GQ dynamics. The propeller loops sampled similar ensembles for all GQ topologies and for all force-field dihedral-potential variants. The outcomes of standard and RECT simulations were consistent and captured similar spectrum of loop conformations. However, the most common crystallographic loop conformation was very unstable with all force-field versions. Although the loss of canonical γ-trans state of the first propeller loop nucleotide could be related to the indispensable bsc0 α/γ dihedral potential, even supporting this particular dihedral by a bias was insufficient to populate the experimentally dominant loop conformation. In conclusion, while our simulations were capable of providing a reasonable albeit not converged sampling of the TTA propeller loop conformational space, the force-field description still remained far from satisfactory.

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The rise of multi-drug resistance in bacterial pathogens is one of the grand challenges facing medical science. A major concern is the speed of development of β-lactamase-mediated resistance in Gram-negative species, thus putting at risk the efficacy of the most recently approved antibiotics and inhibitors, including carbapenems and avibactam, respectively. New strategies to overcome resistance are urgently required, which will ultimately be facilitated by a deeper understanding of the mechanisms that regulate the function of β-lactamases such as the Klebsiella Pneumoniae carbapenemases (KPCs). Using enhanced sampling computational methods together with site-directed mutagenesis, we report the identification of two “hydrophobic networks” in the KPC-2 enzyme, the integrity of which has been found to be essential for protein stability and corresponding resistance. Present throughout the structure, these networks are responsible for the structural integrity and allosteric signaling. Disruption of the networks leads to a loss of the KPC-2 mediated resistance phenotype, resulting in restored susceptibility to different classes of β-lactam antibiotics including carbapenems and cephalosporins. The ”hydrophobic networks” were found to be highly conserved among class-A β-lactamases, which implies their suitability for exploitation as a potential target for therapeutic intervention.

Effective Lennard-Jones models for the water-carbon interaction are derived from existing high-level ab initio calculations of water adsorbed on graphene models. The resulting potential energy well (εCO + 2εCH ≈ 1 kJ mol(-1)) is deeper than most of the previously used values in the literature on water in carbon nanotubes (CNTs). Moreover, a substantial anisotropy of the water-carbon interaction (εCO ≈ 2εCH) is obtained, which is neglected in most of the literature. We systematically investigate the effect of this anisotropy on structure and dynamics of TIP5P water confined in narrow, single-walled CNTs by means of molecular dynamics simulations for T = 300 K. While for isotropic models water usually forms one-dimensional, ordered chains inside (6,6) CNTs, we find frequent chain ruptures in simulations with medium to strongly anisotropic potentials. Here, the water molecules tend to form denser clusters displaying a liquid-like behaviour, allowing for self-diffusion along the CNT axis, in contrast to all previous simulations employing spherical (εCH = 0) interaction models. For (7,7) CNTs we observe structures close to trigonal, helical ice nanotubes which exhibit a non-monotonous dependence on the anisotropy of the water-carbon interaction. Both for vanishing and for large values of εCH we find increased fluctuations leading to a more liquid-like behaviour, with enhanced axial diffusion. In contrast, structure and dynamics of water inside (8,8) CNTs are found to be almost independent of the anisotropy of the underlying potential, which is attributed to the higher stability of the non-helical fivefold water prisms. We predict this situation to also prevail for larger CNTs, as the influence of the water-water interaction dominates over that of the water-carbon interaction.

The UV-vis absorption spectra of the photoreceptor chromophores biliverdin (BV) in the ZZZssa conformation and the phycocyanobilin (PCB) with conformations ZZZssa and ZZZasa have been investigated by means of time-dependent density functional theory (TD-DFT) with a polarized continuum model. The three systems are studied in different conditions to include protonation, solvation- and protein-environmental effects on gas phase and available X-ray structures. The crystal structures of BV in bacteriophytochrome of Deinococcus radiodurans and PCB in C-Phycocyanin serve to calibrate the performance of the TD-DFT method and allow estimating the spectral shifts created when gas phase structures instead of a proper environment are used. In contrast, the structure of PCB in the cyanobacterial phytochrome Cphl is unknown. The excellent agreement of the theoretical spectrum with experimentally recorded data for the PCB in the cyanobacterial phytochrome Cph1 strongly supports a semicyclic ZZZssa structure, similar to that found for the BV chromophore.