Discrete path sampling

Temperature- and field-induced structural transitions in magnetic colloidal clusters

Magnetic colloidal clusters can form chain, ring, and more compact structures depending on their size. In the present investigation we examine the combined effects of temperature and external magnetic field on these configurations by means of extensive Monte Carlo simulations and a dedicated analysis based on inherent structures. Various thermodynamical, geometric, and magnetic properties are calculated and altogether provide evidence for possibly multiple structural transitions at low external magnetic field. Temperature effects are found to overcome the ordering effect of the external field, the melted stated being associated with low magnetization and a greater compactness. Tentative phase diagrams are proposed for selected sizes.

Structure, thermodynamics, and rearrangement mechanisms in gold clusters-insights from the energy landscapes framework

We consider finite-size and temperature effects on the structure of model AuN clusters (30 ≤ N ≤ 147) bound by the Gupta potential. Equilibrium behaviour is examined in the harmonic superposition approximation, and the size-dependent melting temperature is also bracketed using molecular dynamics simulations. We identify structural transitions between distinctly different morphologies, characterised by various defect features. Reentrant behaviour and trends with respect to cluster size and temperature are discussed in detail. For N = 55, 85, and 147 we visualise the topography of the underlying potential energy landscape using disconnectivity graphs, colour-coded by the cluster morphology; and we use discrete path sampling to characterise the rearrangement mechanisms between competing structures separated by high energy barriers (up to 1 eV). The fastest transition pathways generally involve metastable states with multiple fivefold disclinations and/or a high degree of amorphisation, indicative of melting. For N = 55 we find that reoptimising low-lying minima using density functional theory (DFT) alters their energetic ordering and produces a new putative global minimum at the DFT level; however, the equilibrium structure predicted by the Gupta potential at room temperature is consistent with previous experiments.

Energy Landscape and Pathways for Transitions between Watson-Crick and Hoogsteen Base Pairing in DNA

The recent discovery that Hoogsteen (HG) base pairs are widespread in DNA across diverse sequences and positional contexts could have important implications for understanding DNA replication and DNA-protein recognition. While evidence is emerging that the Hoogsteen conformation could be a thermodynamically accessible conformation of the DNA duplex and provide a means to expand its functionality, relatively little is known about the molecular mechanism underlying the Watson-Crick (WC) to HG transition. In this Perspective, we describe pathways and kinetics for this transition at an atomic level of detail, using the energy landscape perspective. We show that competition between the duplex conformations results in a double funnel landscape, which explains some recent experimental observations. The interconversion pathways feature a number of intermediates, with a variable number of WC and HG base pairs. The relatively slow kinetics, with possible deviations from two-state behavior, suggest that this conformational switch is likely to be a challenging target for both simulation and experiment.

Implications of short time scale dynamics on long time processes

This review provides a comprehensive overview of the structural dynamics in topical gas- and condensed-phase systems on multiple length and time scales. Starting from vibrationally induced dissociation of small molecules in the gas phase, the question of vibrational and internal energy redistribution through conformational dynamics is further developed by considering coupled electron/proton transfer in a model peptide over many orders of magnitude. The influence of the surrounding solvent is probed for electron transfer to the solvent in hydrated I-. Next, the dynamics of a modified PDZ domain over many time scales is analyzed following activation of a photoswitch. The hydration dynamics around halogenated amino acid side chains and their structural dynamics in proteins are relevant for iodinated TyrB26 insulin. Binding of nitric oxide to myoglobin is a process for which experimental and computational analyses have converged to a common view which connects rebinding time scales and the underlying dynamics. Finally, rhodopsin is a paradigmatic system for multiple length- and time-scale processes for which experimental and computational methods provide valuable insights into the functional dynamics. The systems discussed here highlight that for a comprehensive understanding of how structure, flexibility, energetics, and dynamics contribute to functional dynamics, experimental studies in multiple wavelength regions and computational studies including quantum, classical, and more coarse grained levels are required.

Optimal Alignment of Structures for Finite and Periodic Systems

Finding the optimal alignment between two structures is important for identifying the minimum root-mean-square distance (RMSD) between them and as a starting point for calculating pathways. Most current algorithms for aligning structures are stochastic, scale exponentially with the size of structure, and the performance can be unreliable. We present two complementary methods for aligning structures corresponding to isolated clusters of atoms and to condensed matter described by a periodic cubic supercell. The first method (Go-PERMDIST), a branch and bound algorithm, locates the global minimum RMSD deterministically in polynomial time. The run time increases for larger RMSDs. The second method (FASTOVERLAP) is a heuristic algorithm that aligns structures by finding the global maximum kernel correlation between them using fast Fourier transforms (FFTs) and fast SO(3) transforms (SOFTs). For periodic systems, FASTOVERLAP scales with the square of the number of identical atoms in the system, reliably finds the best alignment between structures that are not too distant, and shows significantly better performance than existing algorithms. The expected run time for Go-PERMDIST is longer than FASTOVERLAP for periodic systems. For finite clusters, the FASTOVERLAP algorithm is competitive with existing algorithms. The expected run time for Go-PERMDIST to find the global RMSD between two structures deterministically is generally longer than for existing stochastic algorithms. However, with an earlier exit condition, Go-PERMDIST exhibits similar or better performance.

Structure and Dynamics of RNA Repeat Expansions That Cause Huntington's Disease and Myotonic Dystrophy Type 1

RNA repeat expansions cause a host of incurable, genetically defined diseases. The most common class of RNA repeats consists of trinucleotide repeats. These long, repeating transcripts fold into hairpins containing 1 × 1 internal loops that can mediate disease via a variety of mechanism(s) in which RNA is the central player. Two of these disorders are Huntington's disease and myotonic dystrophy type 1, which are caused by r(CAG) and r(CUG) repeats, respectively. We report the structures of two RNA constructs containing three copies of a r(CAG) [r(3×CAG)] or r(CUG) [r(3×CUG)] motif that were modeled with nuclear magnetic resonance spectroscopy and simulated annealing with restrained molecular dynamics. The 1 × 1 internal loops of r(3×CAG) are stabilized by one-hydrogen bond (cis Watson-Crick/Watson-Crick) AA pairs, while those of r(3×CUG) prefer one- or two-hydrogen bond (cis Watson-Crick/Watson-Crick) UU pairs. Assigned chemical shifts for the residues depended on the identity of neighbors or next nearest neighbors. Additional insights into the dynamics of these RNA constructs were gained by molecular dynamics simulations and a discrete path sampling method. Results indicate that the global structures of the RNA are A-form and that the loop regions are dynamic. The results will be useful for understanding the dynamic trajectory of these RNA repeats but also may aid in the development of therapeutics.

How geometric frustration shapes twisted fibres, inside and out: competing morphologies of chiral filament assembly

Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibres by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral filament bundle formation have shown that this frustration gives rise to several distinct morphological responses, including self-limiting bundle widths, anisotropic domain (tape-like) formation and topological defects in the lateral inter-filament order. In this paper, we employ a combination of continuum elasticity theory and discrete filament bundle simulations to explore how these distinct morphological responses compete in the broader phase diagram of chiral filament assembly. We show that the most generic model of bundle formation exhibits at least four classes of equilibrium structure-finite-width, twisted bundles with isotropic and anisotropic shapes, with and without topological defects, as well as bulk phases of untwisted, columnar assembly (i.e. 'frustration escape'). These competing equilibrium morphologies are selected by only a relatively small number of parameters describing filament assembly: bundle surface energy, preferred chiral twist and stiffness of chiral filament interactions, and mechanical stiffness of filaments and their lateral interactions. Discrete filament bundle simulations test and verify continuum theory predictions for dependence of bundle structure (shape, size and packing defects of two-dimensional cross section) on these key parameters.

Finding multiple reaction pathways via global optimization of action

Global searching for reaction pathways is a long-standing challenge in computational chemistry and biology. Most existing approaches perform only local searches due to computational complexity. Here we present a computational approach, Action-CSA, to find multiple diverse reaction pathways connecting fixed initial and final states through global optimization of the Onsager-Machlup action using the conformational space annealing (CSA) method. Action-CSA successfully overcomes large energy barriers via crossovers and mutations of pathways and finds all possible pathways of small systems without initial guesses on pathways. The rank order and the transition time distribution of multiple pathways are in good agreement with those of long Langevin dynamics simulations. The lowest action folding pathway of FSD-1 is consistent with recent experiments. The results show that Action-CSA is an efficient and robust computational approach to study the multiple pathways of complex reactions and large-scale conformational changes.

Improving Computational Predictions of Single-Stranded RNA Tetramers with Revised α/γ Torsional Parameters for the Amber Force Field

With current advancements in RNA based therapeutics, it is becoming crucial to utilize theoretical and computational methods to describe properly the physical properties of RNA molecules. NMR and X-ray crystallography are two powerful techniques for investigating structural properties. However, if the RNA molecules are complex or dynamic, these methods might not be adequate. For computational approaches, the quality of the force field will determine accuracy of our predictions. In this contribution, we revise the α/γ torsional parameters of RNA for amber force field using a model system representing an RNA dimer backbone. Combined with revised χ torsional parameters, previously shown to improve computational predictions, we benchmarked the revised force field on five single-stranded RNA (ssRNA) tetramers, three RNA dodecamer duplexes, and an RNA hairpin. A total of 60 μs of molecular dynamics (MD) simulations were run. We also employ the discrete path sampling (DPS) approach to compare the predictions for the revised amber force field with those for amber10. Our results indicate that the unphysical states observed with amber10 in ssRNA MD simulations are suppressed for the revised amber force field. In line with NMR experimental observations, incorporation of the revised α/γ and χ torsional parameters leads to A-form-like conformational states as the most favorable ssRNA tetramer conformations. Furthermore, the revised force field maintains the A-form geometry in regular RNA duplexes. Our revised amber force field for RNA should therefore improve structural and thermodynamic predictions for challenging RNA systems.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

Pressure-induced silica quartz amorphization studied by iterative stochastic surface walking reaction sampling

The origin of the pressure-induced amorphization of SiO₂ is resolved from theory based on pathways on the global potential energy surface.

Dynamics and thermodynamics of the coronene octamer described by coarse-grained potentials

Coarse-grained models developed for polycyclic aromatic hydrocarbons based on the Paramonov–Yaliraki potential have been employed to investigate the finite temperature thermodynamics, out-of-equilibrium dynamics, energy landscapes, and rearrangement pathways of the coronene octamer.

Path-sampling strategies for simulating rare events in biomolecular systems

Despite more than three decades of effort with molecular dynamics simulations, long-timescale (ms and beyond) biologically relevant phenomena remain out of reach in most systems of interest. This is largely because important transitions, such as conformational changes and (un)binding events, tend to be rare for conventional simulations (<10μs). That is, conventional simulations will predominantly dwell in metastable states instead of making large transitions in complex biomolecular energy landscapes. In contrast, path sampling approaches focus computing effort specifically on transitions of interest. Such approaches have been in use for nearly 20 years in biomolecular systems and enabled the generation of pathways and calculation of rate constants for ms processes, including large protein conformational changes, protein folding, and protein (un)binding.

Supracolloidal reconfigurable polyhedra via hierarchical self-assembly

Enclosed three-dimensional structures with hollow interiors have been attractive targets for the self-assembly of building blocks across different length scales. Colloidal self-assembly, in particular, has enormous potential as a bottom-up means of structure fabrication exploiting a priori designed building blocks because of the scope for tuning interparticle interactions. Here we use computer simulation study to demonstrate the self-assembly of designer charge-stabilised colloidal magnetic particles into a series of supracolloidal polyhedra, each displaying a remarkable two-level structural hierarchy. The parameter space for design supports thermodynamically stable polyhedra of very different morphologies, namely tubular and hollow spheroidal structures, involving the formation of subunits of four-fold and three-fold rotational symmetry, respectively. The spheroidal polyhedra are chiral, despite having a high degree of rotational symmetry. The dominant pathways for self-assembly into these polyhedra reveal two distinct mechanisms - a growth mechanism via sequential attachment of the subunits for a tubular structure and a staged or hierarchical pathway for a spheroidal polyhedron. These supracolloidal architectures open up in response to an external magnetic field. Our results suggest design rules for synthetic reconfigurable containers at the microscale exploiting a hierarchical self-assembly scheme.

Controlling Structural Transitions in AuAg Nanoparticles through Precise Compositional Design

We present a study of the transitional pathways between high-symmetry structural motifs for AgAu nanoparticles, with a specific focus on controlling the energetic barriers through chemical design. We show that the barriers can be altered by careful control of the elemental composition and chemical arrangement, with core@shell and vertex-decorated arrangements being specifically influential on the barrier heights. We also highlight the complexity of the potential and free energy landscapes for systems where there are low-symmetry geometric motifs that are energetically competitive to the high-symmetry arrangements. In particular, we highlight that some core@shell arrangements preferentially transition through multistep restructuring of low-symmetry truncated octahedra and rosette-icosahedra, instead of via the more straightforward square-diamond transformations, due to lower energy barriers and competitive energetic minima. Our results have promising implications for the continuing efforts in bespoke nanoparticle design for catalytic and plasmonic applications.

New Algorithms for Global Optimization and Reaction Path Determination

We present new schemes to improve the convergence of an important global optimization problem and to determine reaction pathways (RPs) between identified minima. Those methods have been implemented into the CAST program (Conformational Analysis and Search Tool). The first part of this chapter shows how to improve convergence of the Monte Carlo with minimization (MCM, also known as Basin Hopping) method when applied to optimize water clusters or aqueous solvation shells using a simple model. Since the random movement on the potential energy surface (PES) is an integral part of MCM, we propose to employ a hydrogen bonding-based algorithm for its improvement. We show comparisons of the results obtained for random dihedral and for the proposed random, rigid-body water molecule movement, giving evidence that a specific adaption of the distortion process greatly improves the convergence of the method. The second part is about the determination of RPs in clusters between conformational arrangements and for reactions. Besides standard approaches like the nudged elastic band method, we want to focus on a new algorithm developed especially for global reaction path search called Pathopt. We started with argon clusters, a typical benchmark system, which possess a flat PES, then stepwise increase the magnitude and directionality of interactions. Therefore, we calculated pathways for a water cluster and characterize them by frequency calculations. Within our calculations, we were able to show that beneath local pathways also additional pathways can be found which possess additional features.

Pathways to self-organization: Crystallization via nucleation and growth

Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In the initial stages of the transformation, a localized nucleus of the new phase forms in the old one due to a random fluctuation. Most of these nuclei disappear after a short time, but rarely a crystalline embryo may reach a critical size after which further growth becomes thermodynamically favorable and the entire system is converted into the new phase. In this article, we will discuss several theoretical concepts and computational methods to study crystallization. More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately. Particular attention is directed towards discussing statistical tools to analyze crystallization trajectories and identify the transition mechanism.

A Networks Approach to Modeling Enzymatic Reactions

Modeling enzymatic reactions is a demanding task due to the complexity of the system, the many degrees of freedom involved and the complex, chemical, and conformational transitions associated with the reaction. Consequently, enzymatic reactions are not determined by precisely one reaction pathway. Hence, it is beneficial to obtain a comprehensive picture of possible reaction paths and competing mechanisms. By combining individually generated intermediate states and chemical transition steps a network of such pathways can be constructed. Transition networks are a discretized representation of a potential energy landscape consisting of a multitude of reaction pathways connecting the end states of the reaction. The graph structure of the network allows an easy identification of the energetically most favorable pathways as well as a number of alternative routes.

Energy landscapes for a machine-learning prediction of patient discharge

The energy landscapes framework is applied to a configuration space generated by training the parameters of a neural network. In this study the input data consists of time series for a collection of vital signs monitored for hospital patients, and the outcomes are patient discharge or continued hospitalisation. Using machine learning as a predictive diagnostic tool to identify patterns in large quantities of electronic health record data in real time is a very attractive approach for supporting clinical decisions, which have the potential to improve patient outcomes and reduce waiting times for discharge. Here we report some preliminary analysis to show how machine learning might be applied. In particular, we visualize the fitting landscape in terms of locally optimal neural networks and the connections between them in parameter space. We anticipate that these results, and analogues of thermodynamic properties for molecular systems, may help in the future design of improved predictive tools.

Markov state modeling and dynamical coarse-graining via discrete relaxation path sampling

A method is derived to coarse-grain the dynamics of complex molecular systems to a Markov jump process (MJP) describing how the system jumps between cells that fully partition its state space. The main inputs are relaxation times for each pair of cells, which are shown to be robust with respect to positioning of the cell boundaries. These relaxation times can be calculated via molecular dynamics simulations performed in each cell separately and are used in an efficient estimator for the rate matrix of the MJP. The method is illustrated through applications to Sinai billiards and a cluster of Lennard-Jones discs.

Dynamical properties of two- and three-dimensional colloidal clusters of six particles

Colloidal clusters are important systems for studying self-assembly. Clusters of six colloidal particles attracting each other via short-ranged interactions have been recently studied both theoretically and experimentally. Here we present a computer modelling study of the thermodynamics and dynamics of these clusters using a short-ranged Morse potential in two and three dimensions. We combine energy landscape methods with comprehensive sampling, both of configurations using Markov chain Monte Carlo and also of trajectories using Langevin molecular dynamics propagation. We show that the interaction energies between the particles are probably greater than previously assumed. The rates predicted by transition state theory using harmonic vibrational densities of states are off by four orders of magnitude, since the effects of viscosity are not accounted for. In contrast, sampling short trajectories using an appropriate friction constant and discrete relaxation path sampling produces reasonable agreement with the experimental rates.

A Threshold-Minimization Scheme for Exploring the Energy Landscape of Biomolecules: Application to a Cyclic Peptide and a Disaccharide

We present a scheme, called the threshold-minimization method, for globally exploring the energy landscapes of small systems of biomolecular interest where typical exploration moves always require a certain degree of subsequent structural relaxation in order to be efficient, e.g., systems containing small or large circular carbon chains such as cyclic peptides or carbohydrates. We show that using this threshold-minimization method we can not only reproduce the global minimum and relevant local minima but also overcome energetic barriers associated with different types of isomerism for the example of a cyclic peptide, cyclo-(Gly)4. We then apply the new method to the disaccharide α-d-glucopyranose-1-2-β-d-fructofuranose, report energetically preferred configurations and barriers to boat-chair isomerization in the glucopyranosyl ring, and discuss the energy landscape.

Conformational Energy Landscape of the Ritonavir Molecule

Conformational polymorphism of ritonavir, a well-known pharmaceutical drug, is intricately linked to its efficacy in the treatment of acquired immunodeficiency syndrome (AIDS). Polymorphic transition from the crystalline form I to form II leads to the loss of bioactivity. The constituent ritonavir molecules adopt a trans configuration about the carbamate torsion angle in the form I crystal, and a cis configuration in the form II crystal. Investigating the energetics and mechanistic features of conformational transitions at the single molecule level is a key step toward decoding the complex features of the solid state polymorphism. In this work, we employ the energy landscape framework to investigate the conformational transitions of an isolated ritonavir molecule. The landscape is explored using discrete path sampling (DPS) and visualized in terms of disconnectivity graphs. We identify two distinct funnels corresponding to the two molecular forms that are identified by crystallography. The two regions can be reliably distinguished using the carbamate torsion angle, and the corresponding interconversion rates are predicted to follow Arrhenius behavior. The results provide mechanistic insight into pathways for cis ↔ trans interconversion at the molecular level and may also help in elucidating the polymorphic transitions in the crystal state.

Self-assembly of colloidal magnetic particles: energy landscapes and structural transitions

The self-assembly of colloidal magnetic particles is of particular interest for the rich variety of structures it produces and the potential for these systems to be reconfigurable.

Energy Landscapes and Global Optimization of Self-Assembling Cyclic Peptides

Self-assembled cyclic peptide nanotubes have attracted much attention because of their antimicrobial properties. Here, we present calculations on the formation of cyclic peptide dimers using basin-hopping and discrete path sampling. We present an analysis of the basin-hopping move sets that most efficiently explore the conformations of cyclic peptides. Group rotation moves, in which sections of the ring are rotated as a rigid body, are the most effective for cyclic peptides containing up to 20 residues. For cyclic peptide dimers, we find that a combination of group rotation intramolecular moves and rigid body intermolecular moves performs well. Discrete path sampling calculations on the cyclic peptide dimers show significant differences in the dimerization of hexa- and octapeptides.

Transition Networks for the Comprehensive Characterization of Complex Conformational Change in Proteins

Functionally relevant transitions between native conformations of a protein can be complex, involving, for example, the reorganization of parts of the backbone fold, and may occur via a multitude of pathways. Such transitions can be characterized by a transition network (TN), in which the experimentally determined end state structures are connected by a dense network of subtransitions via low-energy intermediates. We show here how the computation of a TN can be achieved for a complex protein transition. First, an efficient hierarchical procedure is used to uniformly sample the conformational subspace relevant to the transition. Then, the best path which connects the end states is determined as well as the rate-limiting ridge on the energy surface which separates them. Graph-theoretical algorithms permit this to be achived by computing the barriers of only a small number out of the many subtransitions in the TN. These barriers are computed using the Conjugate Peak Refinement method. The approach is illustrated on the conformational switch of Ras p21. The best and the 12 next-best transition pathways, having rate-limiting barriers within a range of 10 kcal/mol, were identified. Two main energy ridges, which respectively involve rearrangements of the switch I and switch II loops, show that switch I must rearrange by threading Tyr32 underneath the protein backbone before the rate-limiting switch II rearrangement can occur, while the details of the switch II rearrangement differ significantly among the low-energy pathways.

A chain-of-states acceleration method for the efficient location of minimum energy paths

We describe a robust and efficient chain-of-states method for computing Minimum Energy Paths (MEPs) associated to barrier-crossing events in poly-atomic systems, which we call the acceleration method. The path is parametrized in terms of a continuous variable t ∈ [0, 1] that plays the role of time. In contrast to previous chain-of-states algorithms such as the nudged elastic band or string methods, where the positions of the states in the chain are taken as variational parameters in the search for the MEP, our strategy is to formulate the problem in terms of the second derivatives of the coordinates with respect to t, i.e., the state accelerations. We show this to result in a very simple and efficient method for determining the MEP. We describe the application of the method to a series of test cases, including two low-dimensional problems and the Stone-Wales transformation in C60.

Computational investigation of RNA CUG repeats responsible for myotonic dystrophy 1

Despite the importance of the knowledge of molecular hydration entropy (ΔShyd) in chemical and biological processes, the exact calculation of ΔShyd is very difficult, because of the complexity in solute–water interactions. Although free-energy perturbation (FEP) methods have been employed quite widely in the literature, the poor convergent behavior of the van der Waals interaction term in the potential function limited the accuracy and robustness. In this study, we propose a new method for estimating ΔShyd by means of combining the FEP approach and the scaled particle theory (or information theory) to separately calculate the electrostatic solute–water interaction term (ΔSelec) and the hydrophobic contribution approximated by the cavity formation entropy (ΔScav), respectively. Decomposition of ΔShyd into ΔScav and ΔSelec terms is found to be very effective with a substantial accuracy enhancement in ΔShyd estimation, when compared to the conventional full FEP calculations. ΔScav appears to dominate over ΔSelec in magnitude, even in the case of polar solutes, implying that the major contribution to the entropic cost for hydration comes from the formation of a solvent-excluded volume. Our hybrid scaled particle theory and FEP method is thus found to enhance the accuracy of ΔShyd prediction by effectively complementing the conventional full FEP method.

A comparative analysis of clustering algorithms: O2 migration in truncated hemoglobin I from transition networks

The ligand migration network for O2-diffusion in truncated Hemoglobin N is analyzed based on three different clustering schemes. For coordinate-based clustering, the conventional k-means and the kinetics-based Markov Clustering (MCL) methods are employed, whereas the locally scaled diffusion map (LSDMap) method is a collective-variable-based approach. It is found that all three methods agree well in their geometrical definition of the most important docking site, and all experimentally known docking sites are recovered by all three methods. Also, for most of the states, their population coincides quite favourably, whereas the kinetics of and between the states differs. One of the major differences between k-means and MCL clustering on the one hand and LSDMap on the other is that the latter finds one large primary cluster containing the Xe1a, IS1, and ENT states. This is related to the fact that the motion within the state occurs on similar time scales, whereas structurally the state is found to be quite diverse. In agreement with previous explicit atomistic simulations, the Xe3 pocket is found to be a highly dynamical site which points to its potential role as a hub in the network. This is also highlighted in the fact that LSDMap cannot identify this state. First passage time distributions from MCL clusterings using a one- (ligand-position) and two-dimensional (ligand-position and protein-structure) descriptor suggest that ligand- and protein-motions are coupled. The benefits and drawbacks of the three methods are discussed in a comparative fashion and highlight that depending on the questions at hand the best-performing method for a particular data set may differ.

Membrane Protein Structure, Function, and Dynamics: a Perspective from Experiments and Theory

Membrane proteins mediate processes that are fundamental for the flourishing of biological cells. Membrane-embedded transporters move ions and larger solutes across membranes; receptors mediate communication between the cell and its environment and membrane-embedded enzymes catalyze chemical reactions. Understanding these mechanisms of action requires knowledge of how the proteins couple to their fluid, hydrated lipid membrane environment. We present here current studies in computational and experimental membrane protein biophysics, and show how they address outstanding challenges in understanding the complex environmental effects on the structure, function, and dynamics of membrane proteins.