Estimating Absolute Configurational Entropies of Macromolecules: The Minimally Coupled Subspace Approach

Hensen, Ulf; Lange, Oliver; Grubmüller, Helmut

doi:10.1371/journal.pone.0009179

Cited by 66 publications

(102 citation statements)

References 49 publications

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“…To do this, we only take into account the change in interface configurational entropy, Factor (2a) above, when an inter-atomic interaction is removed. Moreover, we use a coarse approximation of the full-blown entropy computation which is a notoriously difficult problem in general with a vast literature [15,34,2,13,14,12,16,11,27,17]. Yet our ranking tallied remarkably well with the mutagenesis results obtained at the Agbandje-Mckenna lab as described in the previous section.…”

Section: Contribution and Organizationsupporting

confidence: 57%

Robustness measure for an adeno-associated viral shell self-assembly is accurately predicted by configuration space atlasing using EASAL

Ozkan

Bennett

et al. 2012

Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine

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Viral shell assembly occurs spontaneously in solution, caused by weak inter-atomic interactions between the identical coatprotein monomers that constitute the shell. A sound measure of robustness of the assembly process is therefore based on determining the weak interactions whose disruption significantly disrupts successful assembly.We used data isolated from the X-ray structure of a T=1, Adeno-Associated Virus as input to a new software suite of algorithms, EASAL, (Efficient Atlasing and Search of Assembly Landscapes, developed by 3 of the authors). Since assembly is entropically driven, we predicted and ranked the crucial interactions for assembly, purely by focusing on key changes in the geometry of the assembly configuration space when specific interactions are dropped. Using the same data for mutagenesis experiments towards assembly disruption, the 2 other authors experimentally verified these predictions successfully.This paper briefly describes the problem background for supramolecular assembly, the key features and novelty of EASAL, the geometric features of the configuration space chosen to measure robustness of assembly, the process by which the input data for EASAL is extracted from X-ray crystallography viral structure data, and a validation of EASAL's robustness predictions with mutagenesis results for *

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Section: Contribution and Organizationsupporting

confidence: 57%

Robustness measure for an adeno-associated viral shell self-assembly is accurately predicted by configuration space atlasing using EASAL

Ozkan

Bennett

et al. 2012

Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine

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“…5 and 6), has remained prohibitive a priori. Alternatively, model calculations have been useful for identifying key qualitative features (7)(8)(9)(10)(11), whereas some full molecular dynamics simulations of the free energy using empirical force fields have been revealing for SAMs (12)(13)(14)(15) and also for macromolecules (16), and DFT molecular dynamics approaches are appearing (17). A priori computational methods have significant advantages in that they do not require parameterization, they treat interactions both generally and accurately, and, through use of implicit solvation models, they can avoid extensive liquid structure simulations.…”

mentioning

confidence: 99%

A priori calculations of the free energy of formation from solution of polymorphic self-assembled monolayers

Reimers

Panduwinata

Visser

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

110

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Modern quantum chemical electronic structure methods typically applied to localized chemical bonding are developed to predict atomic structures and free energies for meso-tetraalkylporphyrin self-assembled monolayer (SAM) polymorph formation from organic solution on highly ordered pyrolytic graphite surfaces. Large polymorphdependent dispersion-induced substrate−molecule interactions (e.g., −100 kcal mol −1 to −150 kcal mol −1 for tetratrisdecylporphyrin) are found to drive SAM formation, opposed nearly completely by large polymorph-dependent dispersion-induced solvent interactions (70-110 kcal mol −1 ) and entropy effects (25-40 kcal mol −1 at 298 K) favoring dissolution. Dielectric continuum models of the solvent are used, facilitating consideration of many possible SAM polymorphs, along with quantum mechanical/molecular mechanical and dispersion-corrected density functional theory calculations. These predict and interpret newly measured and existing high-resolution scanning tunnelling microscopy images of SAM structure, rationalizing polymorph formation conditions. A wide range of molecular condensed matter properties at room temperature now appear suitable for prediction and analysis using electronic structure calculations.self-assembled monolayers | density functional theory | dispersion | free energy | polymorphism A priori calculations of the free energies of chemical reactions using density functional theory (DFT) and/or ab initio methods are now well established for gas-phase processes (1, 2), gas surface reactions (3), and, using continuum self-consistent reaction field (SCRF) methods, for condensed phase processes also (4). Over the last few years, a major advance in computational methods has occurred, however, allowing for rapid and accurate evaluation of intermolecular dispersion interactions. This makes feasible similar SCRF calculations for physisorption, macromolecule structuring, and other self-assembly processes in condensed phases. We present the first application of this type, to our knowledge, considering the free energy of formation of various polymorphs of tetraalkylporphyrin self-assembled monolayers (SAMs) at solid/liquid interfaces on highly ordered pyrolytic graphite (HOPG) surfaces. Calculated structures and free energies are used to interpret new and existing high-resolution scanning tunneling microscopy (STM) images, focusing on the critical roles played by the dispersion interaction in driving SAM formation and by entropy and dispersion-based desolvation effects that oppose it.Calculating a priori free energies for SAM formation from solution is a significant challenge. Accurate representations of the substrate−molecule energies, the intermolecular energies, the solvent interaction energies, and the effects of solvent structure are required, a set of tasks that, with a few exceptions (see e.g., refs. 5 and 6), has remained prohibitive a priori. Alternatively, model calculations have been useful for identifying key qualitative features (7-11), whereas some full molecular dynamics si...

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“…There has been a long and distinguished history of configurational entropy and free energy computation methods [18,2,14,15,13,19,12,33,20], many of which use as input the configuration trajectories of Molecular Dynamics or Monte Carlo simulations.…”

Section: Traditional Methods For Configurational Entropy and Free Energymentioning

confidence: 99%

“…This also causes problems for many entropy computation methods that rely on principal component analyses of the covariance matrices from a trajectory of samples in internal coordinates, followed by a quasiharmonic [2] or nonparametric (such as nearestneighbor-based) [14] estimates. Such methods generally overestimate the volumes of configuration space regions with high geometric or topological complexity, even when hybridized with higher order mutual information [15], and nonlinear kernel methods, such as the Minimally Coupled Subspace approach of [13]. Ab initio methods such as [33] based on geometric algebras (Lie algebra, Grassman-Cayley algebra etc.…”

Section: Traditional Methods For Configurational Entropy and Free Energymentioning

confidence: 99%

Modeling Autonomous Supramolecular Assembly

Sitharam

2013

Discrete and Topological Models in Molecular Biology

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Supramolecular assembly is often a remarkably robust, rapid and spontaneous process, starting from a small number of monomeric types. Although, the process occurs widely in nature and is increasingly important in healthcare and engineering, it is poorly understood. Icosahedral viral shell assembly is one such outstanding example. We sketch the experimental roadblocks that necessitate mathematical and computational modeling of assembly, and list the types of experimental data available for model validation, thereby defining the models' input and output, and framing the scope of model predictions. We isolate the various factors, specifically configurational and combinatorial entropy that influence spontaneous supramolecular assembly, pinpointing the modeling challenges and motivating the use of multiscale models. We then survey existing modeling paradigms for the modeling different scales, emphasizing the newest models and paradigms developed by the author's group, geared towards not only predicting, but also intuitively explaining, analyzing and engineering assembly processes. The models leverage geometric and algebraic characteristics unique to molecular assembly (as opposed to folding), and permit provable performance guarantees together with some level of forward and backward analysis as well as a desired level of precision and refinability of prediction.

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Estimating Absolute Configurational Entropies of Macromolecules: The Minimally Coupled Subspace Approach

Cited by 66 publications

References 49 publications

Robustness measure for an adeno-associated viral shell self-assembly is accurately predicted by configuration space atlasing using EASAL

Robustness measure for an adeno-associated viral shell self-assembly is accurately predicted by configuration space atlasing using EASAL

A priori calculations of the free energy of formation from solution of polymorphic self-assembled monolayers

Modeling Autonomous Supramolecular Assembly

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