Stefanie Muff

Wordom: A user-friendly program for the analysis of molecular structures, trajectories, and free energy surfaces

Wordom is a versatile, user‐friendly, and efficient program for manipulation and analysis of molecular structures and dynamics. The following new analysis modules have been added since the publication of the original Wordom paper in 2007: assignment of secondary structure, calculation of solvent accessible surfaces, elastic network model, motion cross correlations, protein structure network, shortest intra‐molecular and inter‐molecular communication paths, kinetic grouping analysis, and calculation of mincut‐based free energy profiles. In addition, an interface with the Python scripting language has been built and the overall performance and user accessibility enhanced. The source code of Wordom (in the C programming language) as well as documentation for usage and further development are available as an open source package under the GNU General Purpose License from http://wordom.sf.net.

Local modularity measure for network clusterizations.

Many complex networks have an underlying modular structure, i.e., structural subunits (communities or clusters) characterized by highly interconnected nodes. The modularity has been introduced as a measure to assess the quality of clusterizations. has a global view, while in many real-world networks clusters are linked mainly locally among each other (local cluster connectivity). Here we introduce a measure of localized modularity , which reflects local cluster structure. Optimization of and on the clusterization of two biological networks shows that the localized modularity identifies more cohesive clusters, yielding a complementary view of higher granularity.

α-Helix folding in the presence of structural constraints

We have investigated the site-specific folding kinetics of a photoswitchable cross-linked α-helical peptide by using single 13C = 18O isotope labeling together with time-resolved IR spectroscopy. We observe that the folding times differ from site to site by a factor of eight at low temperatures (6°C), whereas at high temperatures (45°C), the spread is considerably smaller. The trivial sum of the site signals coincides with the overall folding signal of the unlabeled peptide, and different sites fold in a noncooperative manner. Moreover, one of the sites exhibits a decrease of hydrogen bonding upon folding, implying that the unfolded state at low temperature is not unstructured. Molecular dynamics simulations at low temperature reveal a stretched-exponential behavior which originates from parallel folding routes that start from a kinetically partitioned unfolded ensemble. Different metastable structures (i.e., traps) in the unfolded ensemble have a different ratio of loop and helical content. Control simulations of the peptide at high temperature, as well as without the cross-linker at low temperature, show faster and simpler (i.e., single-exponential) folding kinetics. The experimental and simulation results together provide strong evidence that the rate-limiting step in formation of a structurally constrained α-helix is the escape from heterogeneous traps rather than the nucleation rate. This conclusion has important implications for an α-helical segment within a protein, rather than an isolated α-helix, because the cross-linker is a structural constraint similar to those present during the folding of a globular protein.

Kinetic analysis of molecular dynamics simulations reveals changes in the denatured state and switch of folding pathways upon single‐point mutation of a β‐sheet miniprotein

The effects of a single‐point mutation on folding thermodynamics and kinetics are usually interpreted by focusing on the native structure and the transition state. Here, the entire conformational spaces of a 20‐residue three‐stranded antiparallel β‐sheet peptide (double hairpin) and of its single‐point mutant W10V are sampled close to the melting temperature by equilibrium folding–unfolding molecular dynamics simulations for a total of 40 μs. The folded state as well as the most populated free energy basins in the denatured state are isolated by grouping conformations according to fast relaxation at equilibrium. Such kinetic analysis provides more detailed and useful information than a simple projection of the free energy. The W10V mutant has the same native structure as the wild type peptide, and similar folding rate and stability. In the denatured state, the N‐terminal hairpin is about 20% more structured in W10V than the wild type mainly because of van der Waals interactions. Notably, the W10V mutation influences also the van der Waals energy at the transition state ensemble causing a shift in the ratio of fluxes between two different transition state regions on parallel folding pathways corresponding to nucleation at either of the two β‐hairpins. Previous experimental studies have focused on the effects of denaturant‐dependent or temperature‐dependent changes in the structure of the denatured state. The atomistic simulations show that a single‐point mutation in the central strand of a β‐sheet peptide results in remarkable changes in the topography of the denatured state ensemble. These changes modulate the relative accessibility of parallel folding pathways because of kinetic partitioning of the denatured state. Therefore, the observed dependence of the folding process on the starting ensemble raises questions on the biological significance of in vitro folding studies under strongly denaturing conditions. Proteins 2008.

One-Dimensional Barrier-Preserving Free-Energy Projections of β-sheet Miniprotein: New Insights into the Folding Process

The conformational space of a 20-residue three-stranded antiparallel beta-sheet peptide (double hairpin) was sampled by equilibrium folding/unfolding molecular dynamics simulations for a total of 20 micros. The resulting one-dimensional free-energy profiles (FEPs) provide a detailed description of the free-energy basins and barriers for the folding reaction. The similarity of the FEPs obtained using the probability of folding before unfolding (pfold) or the mean first passage time supports the robustness of the procedure. The folded state and the most populated free-energy basins in the denatured state are described by the one-dimensional FEPs, which avoid the overlap of states present in the usual one- or two-dimensional projections. Within the denatured state, a basin with fluctuating helical conformations and a heterogeneous entropic state are populated near the melting temperature at about 11% and 33%, respectively. Folding pathways from the helical basin or enthalpic traps (with only one of the two hairpins formed) reach the native state through the entropic state, which is on-pathway and is separated by a low barrier from the folded state. A simplified equilibrium kinetic network based on the FEPs shows the complexity of the folding reaction and indicates, as augmented by additional analyses, that the basins in the denatured state are connected primarily by the native state. The overall folding kinetics shows single-exponential behavior because barriers between the non-native basins and the folded state have similar heights.

Identification of the protein folding transition state from molecular dynamics trajectories

The rate of protein folding is governed by the transition state so that a detailed characterization of its structure is essential for understanding the folding process. In vitro experiments have provided a coarse-grained description of the folding transition state ensemble (TSE) of small proteins. Atomistic details could be obtained by molecular dynamics (MD) simulations but it is not straightforward to extract the TSE directly from the MD trajectories, even for small peptides. Here, the structures in the TSE are isolated by the cut-based free-energy profile (cFEP) using the network whose nodes and links are configurations sampled by MD and direct transitions among them, respectively. The cFEP is a barrier-preserving projection that does not require arbitrarily chosen progress variables. First, a simple two-dimensional free-energy surface is used to illustrate the successful determination of the TSE by the cFEP approach and to explain the difficulty in defining boundary conditions of the Markov state model for an entropically stabilized free-energy minimum. The cFEP is then used to extract the TSE of a beta-sheet peptide with a complex free-energy surface containing multiple basins and an entropic region. In contrast, Markov state models with boundary conditions defined by projected variables and conventional histogram-based free-energy profiles are not able to identify the TSE of the beta-sheet peptide.

Correlates of preschool children’s objectively measured physical activity and sedentary behavior: a cross-sectional analysis of the SPLASHY study

BackgroundIdentifying ways to promote physical activity and decrease sedentary time during childhood is a key public health issue. Research on the putative influences on preschool children’s physical activity (PA) and sedentary behavior (SB) is limited and has yielded inconsistent results. Our aim was to identify correlates of PA and SB in preschool children.MethodsCross-sectional data were drawn from the Swiss Preschoolers’ Health Study (SPLASHY), a Swiss population-based cohort study. Of 476 two to six year old children, 394 (54% boys) had valid PA data assessed by accelerometry. Information on exposure data was directly measured or extracted from parental questionnaires. Multilevel linear regression modeling was used to separately assess associations between 35 potential correlates and total PA (TPA), moderate-to-vigorous PA (MVPA) and SB.ResultsIn total, 12 correlates from different domains were identified. TPA and MVPA were greater in boys than girls, increased with age and were positively associated with gross motor skills. Children from single parent families had a higher level of TPA and spent less time sedentary than those living with two parents. Time spent outdoors was positively associated with TPA and negatively with SB. The child’s activity temperament was related all three outcomes, whereas parental sports club membership, living area per person and neighborhood safety were associated with SB only. Fixed and random factors in the final models accounted for 28%, 32% and 22% of the total variance in TPA, MVPA and SB, respectively. Variance decomposition revealed that age, sex and activity temperament were the most influential correlates of both, TPA and MVPA, whereas the child’s activity temperament, time outdoors and neighborhood safety were identified as the most important correlates of SB.ConclusionsA multidimensional set of correlates of young children’s activity behavior has been identified. Personal factors had the greatest influence on PA, whereas environmental-level factors had the greatest influence on SB. Moreover, we identified a number of previously unreported, potentially modifiable correlates of young children’s PA and SB. These factors could serve to define target groups or become valuable targets for change in future interventions.Trial registrationCurrent Controlled Trials ISRCTN41045021 (date of registration: 21.03.14).

Extracting physically intuitive reaction coordinates from transition networks of a beta-sheet miniprotein.

Simulations are important for understanding complex reactions, but their interpretation is challenging owing to the large number of degrees of freedom typically involved. To address this issue, various means for relating the dynamics of a stochastic system to its structural and energetic features have been introduced. Here, we show how two leading approaches can be combined to advantage. We use the network of transitions observed in a reversible folding/unfolding simulation of a 20-residue three-stranded antiparallel beta-sheet peptide (beta3s) to estimate the probabilities of committing to stable states (the native state and major nonnative states), and these then serve as the basis for an efficient statistical procedure for identifying physical variables that describe the dynamics. We find that a single coordinate that jointly characterizes the formation of the two native turns of beta3s can adequately describe the overall folding process, despite its complex nature. Additional features associated with major pathways leading from individual nonnative states are resolved; indeed, a key result is an improved understanding of the unfolded state. Connections to other methods for analyzing complex reactions are discussed.

ETNA : Equilibrium Transitions Network and Arrhenius Equation for Extracting Folding Kinetics from REMD Simulations

It is difficult to investigate folding kinetics by conventional atomistic simulations of proteins. The replica exchange molecular dynamics (REMD) simulation technique enhances conformational sampling at the expenses of reduced kinetic information, which in REMD is directly available only for very short time scales. Here, we propose a procedure for obtaining kinetic data from REMD by making use of the equilibrium transitions network (ETN) sampled at the temperature of interest. This information is supplemented by mean folding times extracted from ETNs at higher REMD temperatures and scaled according to the Arrhenius equation. The procedure is applied to a three-stranded antiparallel beta-sheet peptide which has a very heterogeneous denatured state with a broad entropic basin and several enthalpic traps. Despite the complexity of the system and the REMD exchange time of only 0.1 ns, the procedure is able to estimate folding times (ranging from about 0.1 micros at the melting temperature of 330 K to about 8 micros at 286 K) as well as transition times from individual non-native basins to the native state.

Reverse attenuation in interaction terms due to covariate measurement error

Covariate measurement error may cause biases in parameters of regression coefficients in generalized linear models. The influence of measurement error on interaction parameters has, however, only rarely been investigated in depth, and if so, attenuation effects were reported. In this paper, we show that also reverse attenuation of interaction effects may emerge, namely when heteroscedastic measurement error or sampling variances of a mismeasured covariate are present, which are not unrealistic scenarios in practice. Theoretical findings are illustrated with simulations. A Bayesian approach employing integrated nested Laplace approximations is suggested to model the heteroscedastic measurement error and covariate variances, and an application shows that the method is able to reveal approximately correct parameter estimates.