How does a simplified-sequence protein fold?

Self-assembly of emulsion droplets through programmable folding

In the realm of particle self-assembly, it is possible to reliably construct nearly arbitrary structures if all the pieces are distinct^1-3, but systems with fewer flavours of building blocks have so far been limited to the assembly of exotic crystals^4-6. Here we introduce a minimal model system of colloidal droplet chains⁷, with programmable DNA interactions that guide their downhill folding into specific geometries. Droplets are observed in real space and time, unravelling the rules of folding. Combining experiments, simulations and theory, we show that controlling the order in which interactions are switched on directs folding into unique structures, which we call colloidal foldamers⁸. The simplest alternating sequences (ABAB...) of up to 13 droplets yield 11 foldamers in two dimensions and one in three dimensions. Optimizing the droplet sequence and adding an extra flavour uniquely encodes more than half of the 619 possible two-dimensional geometries. Foldamers consisting of at least 13 droplets exhibit open structures with holes, offering porous design. Numerical simulations show that foldamers can further interact to make complex supracolloidal architectures, such as dimers, ribbons and mosaics. Our results are independent of the dynamics and therefore apply to polymeric materials with hierarchical interactions on all length scales, from organic molecules all the way to Rubik's Snakes. This toolbox enables the encoding of large-scale design into sequences of short polymers, placing folding at the forefront of materials self-assembly.

Unsupervised Learning Methods for Molecular Simulation Data

Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.

quicksom: Self-Organizing Maps on GPUs for clustering of molecular dynamics trajectories

Summary

We implemented the Self-Organizing Maps algorithm running efficiently on GPUs, and also provide several clustering methods of the resulting maps. We provide scripts and a use case to cluster macro-molecular conformations generated by molecular dynamics simulations.

Availability and implementation

The method is available on GitHub and distributed as a pip package.

The Misfolding of Proteins

Protein folding is considered strongly linked with genetics. The deeper understanding of the mechanisms that allow the folding of proteins is expected to lead to advances in the pharmaceutical sector. The shape of a protein dictates its biological activity, and any exceptions from its natural form can lead to diseases such as Alzheimer's, Parkinson's, and many others. The recent advances in the research of protein folding include computational models for the prediction of protein folding with enough accuracy. In order to understand the process of protein misfolding, a synopsis of the properties of protein molecules is required.

Basic units of protein structure, folding, and function

Study of the hierarchy of domain structure with alternative sets of domains and analysis of discontinuous domains, consisting of remote segments of the polypeptide chain, raised a question about the minimal structural unit of the protein domain. The hypothesis on the decisive role of the polypeptide backbone in determining the elementary units of globular proteins have led to the discovery of closed loops. It is reviewed here how closed loops form the loop-n-lock structure of proteins, providing the foundation for stability and designability of protein folds/domain and underlying their co-translational folding. Simplified protein sequences are considered here with the aim to explore the basic principles that presumably dominated the folding and stability of proteins in the early stages of structural evolution. Elementary functional loops (EFLs), closed loops with one or few catalytic residues, are, in turn, units of the protein function. They are apparent descendants of the prebiotic ring-like peptides, which gave rise to the first functional folds/domains being fused in the beginning of the evolution of protein structure. It is also shown how evolutionary relations between protein functional superfamilies and folds delineated with the help of EFLs can contribute to establishing the rules for design of desired enzymatic functions. Generalized descriptors of the elementary functions are proposed to be used as basic units in the future computational design.

An automatic tool to analyze and cluster macromolecular conformations based on self-organizing maps

MOTIVATION

Sampling the conformational space of biological macromolecules generates large sets of data with considerable complexity. Data-mining techniques, such as clustering, can extract meaningful information. Among them, the self-organizing maps (SOMs) algorithm has shown great promise; in particular since its computation time rises only linearly with the size of the data set. Whereas SOMs are generally used with few neurons, we investigate here their behavior with large numbers of neurons.

RESULTS

We present here a python library implementing the full SOM analysis workflow. Large SOMs can readily be applied on heavy data sets. Coupled with visualization tools they have very interesting properties. Descriptors for each conformation of a trajectory are calculated and mapped onto a 3D landscape, the U-matrix, reporting the distance between neighboring neurons. To delineate clusters, we developed the flooding algorithm, which hierarchically identifies local basins of the U-matrix from the global minimum to the maximum.

AVAILABILITY AND IMPLEMENTATION

The python implementation of the SOM library is freely available on github: https://github.com/bougui505/SOM.

CONTACT

michael.nilges@pasteur.fr or guillaume.bouvier@pasteur.fr

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Protein conformational disorder and enzyme catalysis

Though lacking a well-defined three-dimensional structure, intrinsically unstructured proteins are ubiquitous in nature. These molecules play crucial roles in many cellular processes, especially signaling and regulation. Surprisingly, even enzyme catalysis can tolerate substantial disorder. This observation contravenes conventional wisdom but is relevant to an understanding of how protein dynamics modulates enzyme function. This chapter reviews properties and characteristics of disordered proteins, emphasizing examples of enzymes that lack defined structures, and considers implications of structural disorder for catalytic efficiency and evolution.

Free Energy Guided Sampling

A free energy-guided sampling (FEGS) method is proposed for accelerating exploration of conformational space in unbiased molecular dynamics. Using the cut-based free energy profile and Markov state models, FEGS speeds up sampling of the canonical ensemble by iteratively restarting multiple short simulations in parallel from regions of the free energy surface visited rarely. This exploration stage is followed by a refinement stage in which multiple independent runs are initiated from Boltzmann distributed conformations. Notably, FEGS does not require either collective variables or reaction coordinates and can control the kinetic distance from the starting conformation. We applied FEGS to the alanine dipeptide, which has a human-comprehensible two-dimensional free energy landscape, and a three-stranded antiparallel β-sheet peptide of 20 residues whose folding/unfolding process is governed by a delicate interplay of enthalpy and entropy. For these two systems, FEGS speeds up the exploration of conformational space by 1 to 2 orders of magnitude with respect to conventional sampling and preserves the basins and barriers on the free energy profile.

Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

The coarse-graining of data from molecular simulations yields conformational space networks that may be used for predicting the system's long time scale behavior, to discover structural pathways connecting free energy basins in the system, or simply to represent accessible phase space regions of interest and their connectivities in a two-dimensional plot. In this contribution, we present a tree-based algorithm to partition conformations of biomolecules into sets of similar microstates, i.e., to coarse-grain trajectory data into mesostates. On account of utilizing an architecture similar to that of established tree-based algorithms, the proposed scheme operates in near-linear time with data set size. We derive expressions needed for the fast evaluation of mesostate properties and distances when employing typical choices for measures of similarity between microstates. Using both a pedagogically useful and a real-word application, the algorithm is shown to be robust with respect to tree height, which in addition to mesostate threshold size is the main adjustable parameter. It is demonstrated that the derived mesostate networks can preserve information regarding the free energy basins and barriers by which the system is characterized.

Delineation of folding pathways of a β-sheet miniprotein

Several methods have been developed in the past few years for the analysis of molecular dynamics simulations of biological (macro)molecules whose complexity is difficult to capture by simple projections of the free-energy surface onto one or two geometric variables. The locally scaled diffusion map (LSDMap) method is a nonlinear dimensionality reduction technique for describing the dynamics of complex systems in terms of a few collective coordinates. Here, we compare LSDMap to two previously developed approaches for the characterization of the configurational landscape associated with the folding dynamics of a three-stranded antiparallel β-sheet peptide, termed Beta3s. The analysis is aided by an improved procedure for extracting pathways from the equilibrium transition network, which enables calculation of pathway-specific cut-based free energy profiles. We find that the results from LSDMap are consistent with analysis based on transition networks and allow a coherent interpretation of metastable states and folding pathways in terms of different time scales of transitions between minima on the free energy projections.

What determines the activity of antimicrobial and cytolytic peptides in model membranes

We previously proposed three hypotheses relating the mechanism of antimicrobial and cytolytic peptides in model membranes to the Gibbs free energies of binding and insertion into the membrane [Almeida, P. F., and Pokorny, A. (2009) Biochemistry 48, 8083-8093]. Two sets of peptides were designed to test those hypotheses, by mutating of the sequences of δ-lysin, cecropin A, and magainin 2. Peptide binding and activity were measured on phosphatidylcholine membranes. In the first set, the peptide charge was changed by mutating basic to acidic residues or vice versa, but the amino acid sequence was not altered much otherwise. The type of dye release changed from graded to all-or-none according to prediction. However, location of charged residues in the sequence with the correct spacing to form salt bridges failed to improve binding. In the second set, the charged and other key residues were kept in the same positions, whereas most of the sequence was significantly but conservatively simplified, maintaining the same hydrophobicity and amphipathicity. This set behaved completely different from predicted. The type of release, which was expected to be maintained, changed dramatically from all-or-none to graded in the mutants of cecropin and magainin. Finally, contrary to the hypotheses, the results indicate that the Gibbs energy of binding to the membrane, not the Gibbs energy of insertion, is the primary determinant of peptide activity.

The free energy landscape of small molecule unbinding

The spontaneous dissociation of six small ligands from the active site of FKBP (the FK506 binding protein) is investigated by explicit water molecular dynamics simulations and network analysis. The ligands have between four (dimethylsulphoxide) and eleven (5-diethylamino-2-pentanone) non-hydrogen atoms, and an affinity for FKBP ranging from 20 to 0.2 mM. The conformations of the FKBP/ligand complex saved along multiple trajectories (50 runs at 310 K for each ligand) are grouped according to a set of intermolecular distances into nodes of a network, and the direct transitions between them are the links. The network analysis reveals that the bound state consists of several subbasins, i.e., binding modes characterized by distinct intermolecular hydrogen bonds and hydrophobic contacts. The dissociation kinetics show a simple (i.e., single-exponential) time dependence because the unbinding barrier is much higher than the barriers between subbasins in the bound state. The unbinding transition state is made up of heterogeneous positions and orientations of the ligand in the FKBP active site, which correspond to multiple pathways of dissociation. For the six small ligands of FKBP, the weaker the binding affinity the closer to the bound state (along the intermolecular distance) are the transition state structures, which is a new manifestation of Hammond behavior. Experimental approaches to the study of fragment binding to proteins have limitations in temporal and spatial resolution. Our network analysis of the unbinding simulations of small inhibitors from an enzyme paints a clear picture of the free energy landscape (both thermodynamics and kinetics) of ligand unbinding.

Distance-dependent classification of amino acids by information theory

Reduced amino acid alphabets are useful to understand molecular evolution as they reveal basal, shared properties of amino acids, which the structures and functions of proteins rely on. Several previous studies derived such reduced alphabets and linked them to the origin of life and biotechnological applications. However, all this previous work presupposes that only direct contacts of amino acids in native protein structures are relevant. We show in this work, using information-theoretical measures, that an appropriate alphabet reduction scheme is in fact a function of the maximum distance amino acids interact at. Although for small distances our results agree with previous ones, we show how long-range interactions change the overall picture and prompt for a revised understanding of the protein design process.

Protein dynamics investigated by inherent structure analysis

Molecular dynamics (MD) simulations provide essential information about the thermodynamics and dynamics of proteins. To construct the free-energy surface from equilibrium trajectories, it is necessary to group the individual snapshots in a meaningful way. The inherent structures (IS) are shown to provide an appropriate discretization of the trajectory and to avoid problems that can arise in clustering algorithms that have been employed previously. The IS-based approach is illustrated with a 30-ns room temperature "native" state MD simulation of a 10-residue peptide in a beta-hairpin conformation. The transitions between the IS are used to construct a configuration space network from which a one-dimensional free-energy profile is obtained with the mincut method. The results demonstrate that the IS approach is useful and that even for this simple system, there exists a nontrivial organization of the native state into several valleys separated by barriers as high as 3 kcal/mol. Further, by introducing a coarse-grained network, it is demonstrated that there are multiple pathways connecting the valleys. This scenario is hidden when the snapshots of the trajectory are used directly with rmsd clustering to compute the free-energy profile. Application of the IS approach to the native state of the PDZ2 signaling domain indicates its utility for the study of biologically relevant systems.