Shedding Light on the Dock-Lock Mechanism in Amyloid Fibril Growth Using Markov State Models

EGCG-Mediated Protection of Transthyretin Amyloidosis by Stabilizing Transthyretin Tetramers and Disrupting Transthyretin Aggregates

Transthyretin amyloidosis (ATTR) is a progressive and systemic disease caused by the misfolding and amyloid aggregation of transthyretin (TTR). Stabilizing the TTR tetramers and disrupting the formed TTR aggregation are treated as a promising strategy for the treatment of ATTR. Previous studies have reported that epigallocatechin gallate (EGCG) can participate in the whole process of TTR aggregation to prevent ATTR. However, the interaction mechanism of EGCG in this process is still obscure. In this work, we performed molecular dynamics simulations to investigate the interactions between EGCG and TTR tetramers, and between EGCG and TTR aggregates formed by the V30M mutation. The obtained results suggest that EGCG at the binding site of the V30M TTR tetramer can form stable hydrogen bonds with residues in the flexible AB-loop and EF-helix-loop, which reduces the structural mobility of these regions significantly. Additionally, the polyaromatic property of EGCG contributes to the increasement of hydrophobicity at the binding site and thus makes the tetramer difficult to be solvated and dissociated. For V30M-TTR-generated aggregates, EGCG can promote the dissociation of boundary β-strands by destroying key residue interactions of TTR aggregates. Moreover, EGCG is capable of inserting into the side-chain of residues of neighboring β-strands and disrupting the highly structured aggregates. Taken together, this study elucidates the role of EGCG in preventing TTR amyloidosis, which can provide important theoretical support for the future of drug design for ATTR.

Aggregation of an Amyloidogenic Peptide on Gold Surfaces

Solid surfaces have been shown to affect the aggregation and assembly of many biomolecular systems. One important example is the formation of protein fibrils, which can occur on a range of biological and synthetic surfaces. The rate of fibrillation depends on both the protein structure and the surface chemistry, with the different molecular and oligomer structures adopted by proteins on surfaces likely to be crucial. In this paper, the aggregation of the model amyloidogenic peptide, Aβ(16-22), corresponding to a hydrophobic segment of the amyloid beta protein on a gold surface is studied using molecular dynamics simulation. Previous simulations of this peptide on gold surfaces have shown that it adopts conformations on surfaces that are quite different from those in bulk solution. These simulations show that this then leads to significant differences in the oligomer structures formed in solution and on gold surfaces. In particular, oligomers formed on the surface are low in beta-strands so are unlike the structures formed in bulk solution. When oligomers formed in solution adsorb onto gold surfaces they can then restructure themselves. This can then help explain the inhibition of Aβ(16-22) fibrillation by gold surfaces and nanoparticles seen experimentally.

Amyloidogenesis: What Do We Know So Far?

The study of protein aggregation, and amyloidosis in particular, has gained considerable interest in recent times. Several neurodegenerative diseases, such as Alzheimer's (AD) and Parkinson's (PD) show a characteristic buildup of proteinaceous aggregates in several organs, especially the brain. Despite the enormous upsurge in research articles in this arena, it would not be incorrect to say that we still lack a crystal-clear idea surrounding these notorious aggregates. In this review, we attempt to present a holistic picture on protein aggregation and amyloids in particular. Using a chronological order of discoveries, we present the case of amyloids right from the onset of their discovery, various biophysical techniques, including analysis of the structure, the mechanisms and kinetics of the formation of amyloids. We have discussed important questions on whether aggregation and amyloidosis are restricted to a subset of specific proteins or more broadly influenced by the biophysiochemical and cellular environment. The therapeutic strategies and the significant failure rate of drugs in clinical trials pertaining to these neurodegenerative diseases have been also discussed at length. At a time when the COVID-19 pandemic has hit the globe hard, the review also discusses the plausibility of the far-reaching consequences posed by the virus, such as triggering early onset of amyloidosis. Finally, the application(s) of amyloids as useful biomaterials has also been discussed briefly in this review.

Markov state models elucidate the stability of DNA influenced by the chiral 5S-Tg base

The static and dynamic structures of DNA duplexes affected by 5S-Tg (Tg, Thymine glycol) epimers were studied using MD simulations and Markov State Models (MSMs) analysis. The results show that the 5S,6S-Tg base caused little perturbation to the helix, and the base-flipping barrier was determined to be 4.4 kcal mol-1 through the use of enhanced sampling meta-eABF calculations, comparable to 5.4 kcal mol-1 of the corresponding thymine flipping. Two conformations with the different hydrogen bond structures between 5S,6R-Tg and A19 were identified in several independent MD trajectories. The 5S,6R-Tg:O6HO6•••N1:A19 hydrogen bond is present in the high-energy conformation displaying a clear helical distortion, and near barrier-free Tg base flipping. The low-energy conformation always maintains Watson-Crick base pairing between 5S,6R-Tg and A19, and 5S-Tg base flipping is accompanied by a small barrier of ca. 2.0 KBT (T = 298 K). The same conformations are observed in the MSMs analysis. Moreover, the transition path and metastable structures of the damaged base flipping are for the first time verified through MSMs analysis. The data clearly show that the epimers have completely different influence on the stability of the DNA duplex, thus implying different enzymatic mechanisms for DNA repair.

Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances

Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.

Amyloid-Like Peptide Aggregates

Self-assembly of proteins and peptides into the amyloid fold is a widespread phenomenon in the natural world. The structural hallmark of self-assembly into amyloid fibrillar assemblies is the cross-beta motif, which conveys distinct morphological and mechanical properties. The amyloid fibril formation has contrasting results depending on the organism, in the sense that it can bestow an organism with the advantages of mechanical strength and improved functionality or, on the contrary, could give rise to pathological states. In this chapter we review the existing information on amyloid-like peptide aggregates, which could either be derived from protein sequences, but also could be rationally or de novo designed in order to self-assemble into amyloid fibrils under physiological conditions. Moreover, the development of self-assembled fibrillar biomaterials that are tailored for the desired properties towards applications in biomedical or environmental areas is extensively analyzed. We also review computational studies predicting the amyloid propensity of the natural amino acid sequences and the structure of amyloids, as well as designing novel functional amyloid materials.

Structural Characteristics of Monomeric Aβ42 on Fibril in the Early Stage of Secondary Nucleation Process

Amyloid-β (Aβ) aggregates are believed to be one of the main causes of Alzheimer's disease. Aβ peptides form fibrils having cross β-sheet structures mainly through primary nucleation, secondary nucleation, and elongation. In particular, self-catalyzed secondary nucleation is of great interest. Here, we investigate the adsorption of Aβ42 peptides to the Aβ42 fibril to reveal a role of adsorption as a part of secondary nucleation. We performed extensive molecular dynamics simulations based on replica exchange with solute tempering 2 (REST2) to two systems: a monomeric Aβ42 in solution and a complex of an Aβ42 peptide and Aβ42 fibril. Results of our simulations show that the Aβ42 monomer is extended on the fibril. Furthermore, we find that the hairpin structure of the Aβ42 monomer decreases but the helix structure increases by adsorption to the fibril surface. These structural changes are preferable for forming fibril-like aggregates, suggesting that the fibril surface serves as a catalyst in the secondary nucleation process. In addition, the stabilization of the helix structure of the Aβ42 monomer on the fibril indicates that the strategy of a secondary nucleation inhibitor design for Aβ40 can also be used for Aβ42.

Amyloid assembly is dominated by misregistered kinetic traps on an unbiased energy landscape

Atomistic description of protein fibril formation has been elusive due to the complexity and long time scales of the conformational search. Here, we develop a multiscale approach combining numerous atomistic simulations in explicit solvent to construct Markov State Models (MSMs) of fibril growth. The search for the in-register fully bound fibril state is modeled as a random walk on a rugged two-dimensional energy landscape defined by β-sheet alignment and hydrogen-bonding states, whereas transitions involving states without hydrogen bonds are derived from kinetic clustering. The reversible association/dissociation of an incoming peptide and overall growth kinetics are then computed from MSM simulations. This approach is applied to derive a parameter-free, comprehensive description of fibril elongation of Aβ_16-22 and how it is modulated by phenylalanine-to-cyclohexylalanine (CHA) mutations. The trajectories show an aggregation mechanism in which the peptide spends most of its time trapped in misregistered β-sheet states connected by weakly bound states twith short lifetimes. Our results recapitulate the experimental observation that mutants CHA19 and CHA1920 accelerate fibril elongation but have a relatively minor effect on the critical concentration for fibril growth. Importantly, the kinetic consequences of mutations arise from cumulative effects of perturbing the network of productive and nonproductive pathways of fibril growth. This is consistent with the expectation that nonfunctional states will not have evolved efficient folding pathways and, therefore, will require a random search of configuration space. This study highlights the importance of describing the complete energy landscape when studying the elongation mechanism and kinetics of protein fibrils.

The misfolding mechanism of the key fragment R3 of tau protein: a combined molecular dynamics simulation and Markov state model study

All-atom molecular dynamics (MD) simulation combined with Markov state model (MSM) were used to uncover the structural characteristics and misfolding mechanism of the key R3 fragment of tau protein at the atomic level.

Exploration of the Misfolding Mechanism of Transthyretin Monomer: Insights from Hybrid-Resolution Simulations and Markov State Model Analysis

Misfolding and aggregation of transthyretin (TTR) is widely known to be responsible for a progressive systemic disorder called amyloid transthyretin (ATTR) amyloidosis. Studies suggest that TTR aggregation is initiated by a rate-limiting dissociation of the homo-tetramer into its monomers, which can rapidly misfold and self-assemble into amyloid fibril. Thus, exploring conformational change involved in TTR monomer misfolding is of vital importance for understanding the pathogenesis of ATTR amyloidosis. In this work, microsecond timescale hybrid-resolution molecular dynamics (MD) simulations combined with Markov state model (MSM) analysis were performed to investigate the misfolding mechanism of the TTR monomer. The results indicate that a macrostate with partially unfolded conformations may serve as the misfolded state of the TTR monomer. This misfolded state was extremely stable with a very large equilibrium probability of about 85.28%. With secondary structure analysis, we found the DAGH sheet in this state to be significantly destroyed. The CBEF sheet was relatively stable and sheet structure was maintained. However, the F-strand in this sheet was likely to move away from E-strand and reform a new β-sheet with the H-strand. This observation is consistent with experimental finding that F and H strands in the outer edge drive the misfolding of TTR. Finally, transition pathways from a near native state to this misfolded macrostate showed that the conformational transition can occur either through a native-like β-sheet intermediates or through partially unfolded intermediates, while the later appears to be the main pathway. As a whole, we identified a potential misfolded state of the TTR monomer and elucidated the misfolding pathway for its conformational transition. This work can provide a valuable theoretical basis for understanding of TTR aggregation and the pathogenesis of ATTR amyloidosis at the atomic level.

Probing transient non-native states in amyloid beta fiber elongation by NMR

Using NMR to probe transient binding of Aβ1-40 monomers to fibers, we find partially bound conformations with the highest degree of interaction near F19-K28 and a lesser degree of interaction near the C-terminus (L34-G37). This represents a shift away from the KLVFFA recognition sequence (residues 16-21) currently used for inhibitor design.

Formation of functional, non-amyloidogenic fibres by recombinant Bacillus subtilis TasA

Bacterial biofilms are communities of microbial cells encased within a self-produced polymeric matrix. In the Bacillus subtilis biofilm matrix, the extracellular fibres of TasA are essential. Here, a recombinant expression system allows interrogation of TasA, revealing that monomeric and fibre forms of TasA have identical secondary structure, suggesting that fibrous TasA is a linear assembly of globular units. Recombinant TasA fibres form spontaneously, and share the biological activity of TasA fibres extracted from B. subtilis, whereas a TasA variant restricted to a monomeric form is inactive and subjected to extracellular proteolysis. The biophysical properties of both native and recombinant TasA fibres indicate that they are not functional amyloid-like fibres. A gel formed by TasA fibres can recover after physical shear force, suggesting that the biofilm matrix is not static and that these properties may enable B. subtilis to remodel its local environment in response to external cues. Using recombinant fibres formed by TasA orthologues we uncover species variability in the ability of heterologous fibres to cross-complement the B. subtilis tasA deletion. These findings are indicative of specificity in the biophysical requirements of the TasA fibres across different species and/or reflect the precise molecular interactions needed for biofilm matrix assembly.

Nonproductive Binding Modes as a Prominent Feature of Aβ40 Fiber Elongation: Insights from Molecular Dynamics Simulation

The formation of amyloid fibers has been implicated in a number of neurodegenerative diseases. The growth of amyloid fibers is strongly thermodynamically favorable, but kinetic traps exist where the incoming monomer binds in an incompatible conformation that blocks further elongation. Unfortunately, this process is difficult to follow experimentally at the atomic level. It is also too complex to simulate in full detail and to date has been explored either through coarse-grained simulations, which may miss many important interactions, or full atomic simulations, in which the incoming peptide is constrained to be near the ideal fiber geometry. Here we use an alternate approach starting from a docked complex in which the monomer is from an experimental NMR structure of one of the major conformations in the unbound ensemble, a largely unstructured peptide with the central hydrophobic region in a 3₁₀ helix. A 1000 ns full atomic simulation in explicit solvent shows the formation of a metastable intermediate by sequential, concerted movements of both the fiber and the monomer. A Markov state model shows that the unfolded monomer is trapped at the end of the fiber in a set of interconverting antiparallel β-hairpin conformations. The simulation here may serve as a model for the binding of other non-β-sheet conformations to amyloid fibers.

The attachment of α-synuclein to a fiber: A coarse-grain approach

We present simulations of the amyloidogenic core of α-synuclein, the protein causing Parkinson's disease, as a short chain of coarse-grain patchy particles. Each particle represents a sequence of about a dozen amino acids. The fluctuating secondary structure of this intrinsically disordered protein is modelled by dynamic variations of the shape and interaction characteristics of the patchy particles, ranging from spherical with weak isotropic attractions for the disordered state to spherocylindrical with strong directional interactions for a β-sheet. Flexible linkers between the particles enable sampling of the tertiary structure. This novel model is applied here to study the growth of an amyloid fibril, by calculating the free energy profile of a protein attaching to the end of a fibril. The simulation results suggest that the attaching protein readily becomes trapped in a mis-folded state, thereby inhibiting further growth of the fibril until the protein has readjusted to conform to the fibril structure, in line with experimental findings and previous simulations on small fragments of other proteins.

Intrinsic Conformational Preferences and Interactions in α-Synuclein Fibrils: Insights from Molecular Dynamics Simulations

Amyloid formation by the intrinsically disordered α-synuclein protein is the hallmark of Parkinson's disease. We present atomistic Molecular Dynamics simulations of the core of α-synuclein using enhanced sampling techniques to describe the conformational and binding free energy landscapes of fragments implicated in fibril stabilization. The theoretical framework is derived to combine the free energy profiles of the fragments into the reaction free energy of a protein binding to a fibril. Our study shows that individual fragments in solution have a propensity toward attaining non-β conformations, indicating that in a fibril β-strands are stabilized by interactions with other strands. We show that most dimers of hydrogen-bonded fragments are unstable in solution, while hydrogen bonding stabilizes the collective binding of five fragments to the end of a fibril. Hydrophobic effects make further contributions to the stability of fibrils. This study is the first of its kind where structural and binding preferences of the five major fragments of the hydrophobic core of α-synuclein have been investigated. This approach improves sampling of intrinsically disordered proteins, provides information on the binding mechanism between the core sequences of α-synuclein, and enables the parametrization of coarse grained models.

An adaptive bias - hybrid MD/kMC algorithm for protein folding and aggregation

In this paper, we present a novel hybrid Molecular Dynamics/kinetic Monte Carlo (MD/kMC) algorithm and apply it to protein folding and aggregation in explicit solvent. The new algorithm uses a dynamical definition of biases throughout the MD component of the simulation, normalized in relation to the unbiased forces. The algorithm guarantees sampling of the underlying ensemble in dependency of one average linear coupling factor 〈α〉_τ. We test the validity of the kinetics in simulations of dialanine and compare dihedral transition kinetics with long-time MD-simulations. We find that for low 〈α〉_τ values, kinetics are in good quantitative agreement. In folding simulations of TrpCage and TrpZip4 in explicit solvent, we also find good quantitative agreement with experimental results and prior MD/kMC simulations. Finally, we apply our algorithm to study growth of the Alzheimer Amyloid Aβ 16-22 fibril by monomer addition. We observe two possible binding modes, one at the extremity of the fibril (elongation) and one on the surface of the fibril (lateral growth), on timescales ranging from ns to 8 μs.

Elucidation of the conformational dynamics of multi-body systems by construction of Markov state models

Constructing Markov State Models (MSMs) based on short molecular dynamics simulations is a powerful computational technique to complement experiments in predicting long-time kinetics of biomolecular processes at atomic resolution. Even though the MSM approach has been widely applied to study one-body processes such as protein folding and enzyme conformational changes, the majority of biological processes, e.g. protein-ligand recognition, signal transduction, and protein aggregation, essentially involve multiple entities. Here we review the attempts at constructing MSMs for multi-body systems, point out the challenges therein and discuss recent algorithmic progresses that alleviate these challenges. In particular, we describe an automatic kinetics based partitioning method that achieves optimal definition of the conformational states in a multi-body system, and discuss a novel maximum-likelihood approach that efficiently estimates the slow uphill kinetics utilizing pre-computed equilibrium populations of all states. We expect that these new algorithms and their combinations may boost investigations of important multi-body biological processes via the efficient construction of MSMs.

The Levinthal Problem in Amyloid Aggregation: Sampling of a Flat Reaction Space

The formation of amyloid fibrils has been associated with many neurodegenerative disorders, yet the mechanism of aggregation remains elusive, partly because aggregation time scales are too long to probe with atomistic simulations. A microscopic theory of fibril elongation was recently developed that could recapitulate experimental results with respect to the effects of temperature, denaturants, and protein concentration on fibril growth kinetics (Schmit, J. D. J. Chem. Phys. 2013, 138 (18), 185102). The theory identifies the conformational search over H-bonding states as the slowest step in the aggregation process and suggests that this search can be efficiently modeled as a random walk on a rugged one-dimensional energy landscape. This insight motivated the multiscale computational algorithm for simulating fibril growth presented in this paper. Briefly, a large number of short atomistic simulations are performed to compute the system diffusion tensor in the reaction coordinate space predicted by the analytic theory. Ensemble aggregation pathways and growth kinetics are then computed from Markov state model (MSM) trajectories. The algorithm is deployed here to understand the fibril growth mechanism and kinetics of Aβ_16-22 and three of its mutants. The order of growth rates of the wild-type and two single mutation peptides (CHA19 and CHA20) predicted by the MSM trajectories is consistent with experimental results. The simulation also correctly predicts that the double mutation (CHA19/CHA20) would reduce the fibril growth rate, even though the degree of rate reduction with respect to either single mutation is overestimated. This artifact may be attributed to the simplistic implicit solvent model. These trends in the growth rate are not apparent from inspection of the rate constants of individual bonds or the lifetimes of the mis-registered states that are the primary kinetic traps but only emerge in the ensemble of trajectories generated by the MSM.

Simulations of disordered proteins and systems with conformational heterogeneity

Intrinsically disordered proteins (IDPs) and protein regions can facilitate a wide variety of complex physiological processes such as binding, signaling, and formation of membraneless organelles. They can however also play pathological roles by aggregating into cytotoxic oligomers and fibrils. Characterizing the structure and function of disordered proteins is an onerous task, primarily because these proteins adopt transient structures, which are difficult to capture in experiments. Simulations have emerged as a powerful tool for interpreting and augmenting experimental measurements of IDPs. In this review we focus on computer simulations of disordered protein structures, functions, assemblies, and emerging questions that, taken together, give an overview of the field as it exists today.

Analytical methods for structural ensembles and dynamics of intrinsically disordered proteins

Intrinsically disordered proteins, proteins that do not have a well-defined three-dimensional structure, make up a significant proportion of our proteome and are particularly prevalent in signaling and regulation. Although their importance has been realized for two decades, there is a lack of high-resolution experimental data. Molecular dynamics simulations have been crucial in reaching our current understanding of the dynamical structural ensemble sampled by intrinsically disordered proteins. In this review, we discuss enhanced sampling simulation methods that are particularly suitable to characterize the structural ensemble, along with examples of applications and limitations. The dynamics within the ensemble can be rigorously analyzed using Markov state models. We discuss recent developments that make Markov state modeling a viable approach for studying intrinsically disordered proteins. Finally, we briefly discuss challenges and future directions when applying molecular dynamics simulations to study intrinsically disordered proteins.

Emerging Computational Methods for the Rational Discovery of Allosteric Drugs

Allosteric drug development holds promise for delivering medicines that are more selective and less toxic than those that target orthosteric sites. To date, the discovery of allosteric binding sites and lead compounds has been mostly serendipitous, achieved through high-throughput screening. Over the past decade, structural data has become more readily available for larger protein systems and more membrane protein classes (e.g., GPCRs and ion channels), which are common allosteric drug targets. In parallel, improved simulation methods now provide better atomistic understanding of the protein dynamics and cooperative motions that are critical to allosteric mechanisms. As a result of these advances, the field of predictive allosteric drug development is now on the cusp of a new era of rational structure-based computational methods. Here, we review algorithms that predict allosteric sites based on sequence data and molecular dynamics simulations, describe tools that assess the druggability of these pockets, and discuss how Markov state models and topology analyses provide insight into the relationship between protein dynamics and allosteric drug binding. In each section, we first provide an overview of the various method classes before describing relevant algorithms and software packages.

Advances in the Simulation of Protein Aggregation at the Atomistic Scale

Protein aggregation into highly structured amyloid fibrils is associated with various diseases including Alzheimer's disease, Parkinson's disease, and type II diabetes. Amyloids can also have normal biological functions and, in the future, could be used as the basis for novel nanoscale materials. However, a full understanding of the physicochemical forces that drive protein aggregation is still lacking. Such understanding is crucial for the development of drugs that can effectively inhibit aberrant amyloid aggregation and for the directed design of functional amyloids. Atomistic simulations can help understand protein aggregation. In particular, atomistic simulations can be used to study the initial formation of toxic oligomers which are hard to characterize experimentally and to understand the difference in aggregation behavior between different amyloidogenic peptides. Here, we review the latest atomistic simulations of protein aggregation, concentrating on amyloidogenic protein fragments, and provide an outlook for the future in this field.

Dynamics of the conformational transitions during the dimerization of an intrinsically disordered peptide: a case study on the human islet amyloid polypeptide fragment

Dimerization pathways of the human islet amyloid polypeptide fragment are elucidated from extensive molecular dynamics simulations.

PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models

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.