MSMBuilder: Statistical Models for Biomolecular Dynamics.

MSMBuilder is a software package for building statistical models of high-dimensional time-series data. It is designed with a particular focus on the analysis of atomistic simulations of biomolecular dynamics such as protein folding and conformational change. MSMBuilder is named for its ability to construct Markov state models (MSMs), a class of models that has gained favor among computational biophysicists. In addition to both well-established and newer MSM methods, the package includes complementary algorithms for understanding time-series data such as hidden Markov models and time-structure based independent component analysis. MSMBuilder boasts an easy to use command-line interface, as well as clear and consistent abstractions through its Python application programming interface. MSMBuilder was developed with careful consideration for compatibility with the broader machine learning community by following the design of scikit-learn. The package is used primarily by practitioners of molecular dynamics, but is just as applicable to other computational or experimental time-series measurements.

Markov State Models and tICA Reveal a Nonnative Folding Nucleus in Simulations of NuG2.

After reanalyzing simulations of NuG2-a designed mutant of protein G-generated by Lindorff-Larsen et al. with time structure-based independent components analysis and Markov state models as well as performing 1.5 ms of additional sampling on Folding@home, we found an intermediate with a register-shift in one of the ß-sheets that was visited along a minor folding pathway. The minor folding pathway was initiated by the register-shifted sheet, which is composed of solely nonnative contacts, suggesting that for some peptides, nonnative contacts can lead to productive folding events. To confirm this experimentally, we suggest a mutational strategy for stabilizing the register shift, as well as an infrared experiment that could observe the nonnative folding nucleus.

MDTraj: A Modern Open Library for the Analysis of Molecular Dynamics Trajectories.

As molecular dynamics (MD) simulations continue to evolve into powerful computational tools for studying complex biomolecular systems, the necessity of flexible and easy-to-use software tools for the analysis of these simulations is growing. We have developed MDTraj, a modern, lightweight, and fast software package for analyzing MD simulations. MDTraj reads and writes trajectory data in a wide variety of commonly used formats. It provides a large number of trajectory analysis capabilities including minimal root-mean-square-deviation calculations, secondary structure assignment, and the extraction of common order parameters. The package has a strong focus on interoperability with the wider scientific Python ecosystem, bridging the gap between MD data and the rapidly growing collection of industry-standard statistical analysis and visualization tools in Python. MDTraj is a powerful and user-friendly software package that simplifies the analysis of MD data and connects these datasets with the modern interactive data science software ecosystem in Python.

Dynamical phase transitions reveal amyloid-like states on protein folding landscapes.

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of ß-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein's dynamics, and we discuss the nonnative, ß-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.

Complex pathways in folding of protein G explored by simulation and experiment.

The B1 domain of protein G has been a classic model system of folding for decades, the subject of numerous experimental and computational studies. Most of the experimental work has focused on whether the protein folds via an intermediate, but the evidence is mostly limited to relatively slow kinetic observations with a few structural probes. In this work we observe folding on the submillisecond timescale with microfluidic mixers using a variety of probes including tryptophan fluorescence, circular dichroism, and photochemical oxidation. We find that each probe yields different kinetics and compare these observations with a Markov State Model constructed from large-scale molecular dynamics simulations and find a complex network of states that yield different kinetics for different observables. We conclude that there are many folding pathways before the final folding step and that these paths do not have large free energy barriers.

Probing the origins of two-state folding.

Many protein systems fold in a two-state manner. Random models, however, rarely display two-state kinetics and thus such behavior should not be accepted as a default. While theories for the prevalence of two-state kinetics have been presented, none sufficiently explain the breadth of experimental observations. A model, making minimal assumptions, is introduced that suggests two-state behavior is likely for any system with an overwhelmingly populated native state. We show two-state folding is a natural consequence of such two-state thermodynamics, and is strengthened by increasing the population of the native state. Further, the model exhibits hub-like behavior, with slow interconversions between unfolded states. Despite this, the unfolded state equilibrates quickly relative to the folding time. This apparent paradox is readily understood through this model. Finally, our results compare favorable with measurements of folding rates as a function of chain length and Keq, providing new insight into these relations.

The bacterially produced metabolite violacein is associated with survival of amphibians infected with a lethal fungus.

The disease chytridiomycosis, which is caused by the chytrid fungus Batrachochytrium dendrobatidis, is associated with recent declines in amphibian populations. Susceptibility to this disease varies among amphibian populations and species, and resistance appears to be attributable in part to the presence of antifungal microbial species associated with the skin of amphibians. The betaproteobacterium Janthinobacterium lividum has been isolated from the skins of several amphibian species and produces the antifungal metabolite violacein, which inhibits B. dendrobatidis. In this study, we added J. lividum to red-backed salamanders (Plethodon cinereus) to obtain an increased range of violacein concentrations on the skin. Adding J. lividum to the skin of the salamander increased the concentration of violacein on the skin, which was strongly associated with survival after experimental exposure to B. dendrobatidis. As expected from previous work, some individuals that did not receive J. lividum and were exposed to B. dendrobatidis survived. These individuals had concentrations of bacterially produced violacein on their skins that were predicted to kill B. dendrobatidis. Our study suggests that a threshold violacein concentration of about 18 microM on a salamander's skin prevents mortality and morbidity caused by B. dendrobatidis. In addition, we show that over one-half of individuals in nature support antifungal bacteria that produce violacein, which suggests that there is a mutualism between violacein-producing bacteria and P. cinereus and that adding J. lividum is effective for protecting individuals that lack violacein-producing skin bacteria.

Atomistic structural ensemble refinement reveals non-native structure stabilizes a sub-millisecond folding intermediate of CheY.

The dynamics of globular proteins can be described in terms of transitions between a folded native state and less-populated intermediates, or excited states, which can play critical roles in both protein folding and function. Excited states are by definition transient species, and therefore are difficult to characterize using current experimental techniques. Here, we report an atomistic model of the excited state ensemble of a stabilized mutant of an extensively studied flavodoxin fold protein CheY. We employed a hybrid simulation and experimental approach in which an aggregate 42 milliseconds of all-atom molecular dynamics were used as an informative prior for the structure of the excited state ensemble. This prior was then refined against small-angle X-ray scattering (SAXS) data employing an established method (EROS). The most striking feature of the resulting excited state ensemble was an unstructured N-terminus stabilized by non-native contacts in a conformation that is topologically simpler than the native state. Using these results, we then predict incisive single molecule FRET experiments as a means of model validation. This study demonstrates the paradigm of uniting simulation and experiment in a statistical model to study the structure of protein excited states and rationally design validating experiments.

Modeling molecular kinetics with tICA and the kernel trick.

The allure of a molecular dynamics simulation is that, given a sufficiently accurate force field, it can provide an atomic-level view of many interesting phenomena in biology. However, the result of a simulation is a large, high-dimensional time series that is difficult to interpret. Recent work has introduced the time-structure based Independent Components Analysis (tICA) method for analyzing MD, which attempts to find the slowest decorrelating linear functions of the molecular coordinates. This method has been used in conjunction with Markov State Models (MSMs) to provide estimates of the characteristic eigenprocesses contained in a simulation (e.g., protein folding, ligand binding). Here, we extend the tICA method using the kernel trick to arrive at nonlinear solutions. This is a substantial improvement as it allows for kernel-tICA (ktICA) to provide estimates of the characteristic eigenprocesses directly without building an MSM.

Statistical model selection for Markov models of biomolecular dynamics.

Markov state models provide a powerful framework for the analysis of biomolecular conformation dynamics in terms of their metastable states and transition rates. These models provide both a quantitative and comprehensible description of the long-time scale dynamics of large molecular dynamics with a Master equation and have been successfully used to study protein folding, protein conformational change, and protein-ligand binding. However, to achieve satisfactory performance, existing methodologies often require expert intervention when defining the model's discrete state space. While standard model selection methodologies focus on the minimization of systematic bias and disregard statistical error, we show that by consideration of the states' conditional distribution over conformations, both sources of error can be balanced evenhandedly. Application of techniques that consider both systematic bias and statistical error on two 100 µs molecular dynamics trajectories of the Fip35 WW domain shows agreement with existing techniques based on self-consistency of the model's relaxation time scales with more suitable results in regimes in which those time scale-based techniques encourage overfitting. By removing the need for expert tuning, these methods should reduce modeling bias and lower the barriers to entry in Markov state model construction.

Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9.

Markov State Models (MSMs) provide an automated framework to investigate the dynamical properties of high-dimensional molecular simulations. These models can provide a human-comprehensible picture of the underlying process, and have been successfully used to study protein folding, protein aggregation, protein ligand binding, and other biophysical systems. The MSM requires the construction of a discrete state-space such that two points are in the same state if they can interconvert rapidly. In the following, we suggest an improved method, which utilizes second order Independent Components Analysis (also known as time-structure based Independent Components Analysis, or tICA), to construct the state-space. We apply this method to simulations of NTL9 (provided by Lindorff-Larsen et al. Science2011), and show that the MSM is an improvement over previously built models using conventional distance metrics. Additionally, the resulting model provides insight into the role of non-native contacts by revealing many slow timescales associated with compact, non-native states.

Bicephalic amphiphile architecture affects antibacterial activity.

A series of cationic amphiphiles, each with an aromatic core, was prepared and investigated for antimicrobial properties. The synthesized amphiphiles in this study are bicephalic (double-headed) in that they each possess two trimethylammonium head groups and a single linear alkoxy tail. Minimum inhibitory and minimum bactericidal concentrations of these amphiphiles were in the low micromolar range. Antimicrobial activities are highly sensitive to the chain length of the hydrophobic region, and modestly reliant on the relative positioning of the head groups on the aromatic core. These trends were more pronounced in time kill assays, wherein longer chain compounds required significantly shorter times to completely kill bacteria. Microscopy suggested that the mode of cell death was lysis. Strong inhibition was observed with both biscationic compounds and monocationic comparisons against Gram-positive bacteria; only biscationic amphiphiles maintained good activity versus the Gram-negative bacteria tested. These observations provide direction for future antimicrobial structural investigations.

Towards a better understanding of the use of probiotics for preventing chytridiomycosis in Panamanian golden frogs.

Populations of native Panamanian golden frogs (Atelopus zeteki) have collapsed due to a recent chytridiomycosis epidemic. Reintroduction efforts from captive assurance colonies are unlikely to be successful without the development of methods to control chytridiomycosis in the wild. In an effort to develop a protective treatment regimen, we treated golden frogs with Janthinobacterium lividum, a skin bacterium that has been used to experimentally prevent chytridiomycosis in North American amphibians. Although J. lividum appeared to colonize A. zeteki skin temporarily, it did not prevent or delay mortality in A. zeteki exposed to Batrachochytrium dendrobatidis, the causative agent of chytridiomycosis. After introduction of J. lividum, average bacterial cell counts reached a peak of 1.7 × 10(6) cells per frog ~2 weeks after treatment but declined steadily after that. When J. lividum numbers declined to ~2.8 × 10(5) cells per frog, B. dendrobatidis infection intensity increased to greater than 13,000 zoospore equivalents per frog. At this point, frogs began to die of chytridiomycosis. Future research will concentrate on isolating and testing antifungal bacterial species from Panama that may be more compatible with Atelopus skin.

Skin microbes on frogs prevent morbidity and mortality caused by a lethal skin fungus.

Emerging infectious diseases threaten human and wildlife populations. Altered ecological interactions between mutualistic microbes and hosts can result in disease, but an understanding of interactions between host, microbes and disease-causing organisms may lead to management strategies to affect disease outcomes. Many amphibian species in relatively pristine habitats are experiencing dramatic population declines and extinctions due to the skin disease chytridiomycosis, which is caused by the chytrid fungus Batrachochytrium dendrobatidis. Using a randomized, replicated experiment, we show that adding an antifungal bacterial species, Janthinobacterium lividum, found on several species of amphibians to the skins of the frog Rana muscosa prevented morbidity and mortality caused by the pathogen. The bacterial species produces the anti-chytrid metabolite violacein, which was found in much higher concentrations on frog skins in the treatments where J. lividum was added. Our results show that cutaneous microbes are a part of amphibians' innate immune system, the microbial community structure on frog skins is a determinant of disease outcome and altering microbial interactions on frog skins can prevent a lethal disease outcome. A bioaugmentation strategy may be an effective management tool to control chytridiomycosis in amphibian survival assurance colonies and in nature.

Amphibian chemical defense: antifungal metabolites of the microsymbiont Janthinobacterium lividum on the salamander Plethodon cinereus.

Disease has spurred declines in global amphibian populations. In particular, the fungal pathogen Batrachochytrium dendrobatidis has decimated amphibian diversity in some areas unaffected by habitat loss. However, there is little evidence to explain how some amphibian species persist despite infection or even clear the pathogen beyond detection. One hypothesis is that certain bacterial symbionts on the skin of amphibians inhibit the growth of the pathogen. An antifungal strain of Janthinobacterium lividum, isolated from the skin of the red-backed salamander Plethodon cinereus, produces antifungal metabolites at concentrations lethal to B. dendrobatidis. Antifungal metabolites were identified by using reversed phase high performance liquid chromatography, high resolution mass spectrometry, nuclear magnetic resonance, and UV-Vis spectroscopy and tested for efficacy of inhibiting the pathogen. Two metabolites, indole-3-carboxaldehyde and violacein, inhibited the pathogen's growth at relatively low concentrations (68.9 and 1.82 microM, respectively). Analysis of fresh salamander skin confirmed the presence of J. lividum and its metabolites on the skin of host salamanders in concentrations high enough to hinder or kill the pathogen (51 and 207 microM, respectively). These results support the hypothesis that cutaneous, mutualistic bacteria play a role in amphibian resistance to fungal disease. Exploitation of this biological process may provide long-term resistance to B. dendrobatidis for vulnerable amphibians and serve as a model for managing future emerging diseases in wildlife populations.