Modeling Of Biomolecular Systems Research Articles

EzAlign: A Tool for Converting Coarse-Grained Molecular Dynamics Structures to Atomistic Resolution for Multiscale Modeling.

Soft condensed matter is challenging to study due to the vast time and length scales that are necessary to accurately represent complex systems and capture their underlying physics. Multiscale simulations are necessary to study processes that have disparate time and/or length scales, which abound throughout biology and other complex systems. Herein we present ezAlign, an open-source software for converting coarse-grained molecular dynamics structures to atomistic representation, allowing multiscale modeling of biomolecular systems. The ezAlign v1.1 software package is publicly available for download at github.com/LLNL/ezAlign. Its underlying methodology is based on a simple alignment of an atomistic template molecule, followed by position-restraint energy minimization, which forces the atomistic molecule to adopt a conformation consistent with the coarse-grained molecule. The molecules are then combined, solvated, minimized, and equilibrated with position restraints. Validation of the process was conducted on a pure POPC membrane and compared with other popular methods to construct atomistic membranes. Additional examples, including surfactant self-assembly, membrane proteins, and more complex bacterial and human plasma membrane models, are also presented. By providing these examples, parameter files, code, and an easy-to-follow recipe to add new molecules, this work will aid future multiscale modeling efforts.

OPLS/2020 Force Field for Unsaturated Hydrocarbons, Alcohols, and Ethers.

The OPLS all-atom force field was updated and applied to modeling unsaturated hydrocarbons, alcohols, and ethers. Testing has included gas-phase conformational energetics, properties of pure liquids, and free energies of hydration. Monte Carlo statistical mechanics (MC) calculations were used to model 60 liquids. In addition, a robust, automated procedure was devised to compute the free energies of hydration with high precision via free-energy perturbation (FEP) calculations using double annihilation. Testing has included larger molecules than in the past, and parameters are reported for the first time for some less common groups including alkynes, allenes, dienes, and acetals. The average errors in comparison with experimental data for the computed properties of the pure liquids were improved with the modified force field (OPLS/2020). For liquid densities and heats of vaporization, the average unsigned errors are 0.01 g/cm3 and 0.2 kcal/mol. The average error and signed error for free energies of hydration are both 1.2 kcal/mol. As noted before, this reflects a systematic overestimate of the hydrophobicity of organic molecules when the parametrization is done to minimize the errors for properties of pure liquids. Implications for the modeling of biomolecular systems with standard force fields are considered.

Integration of software tools for integrative modeling of biomolecular systems

Integrative modeling computes a model based on varied types of input information, be it from experiments or prior models. Often, a type of input information will be best handled by a specific modeling software package. In such a case, we desire to integrate our integrative modeling software package, Integrative Modeling Platform (IMP), with software specialized to the computational demands of the modeling problem at hand. After several attempts, however, we have concluded that even in collaboration with the software’s developers, integration is either impractical or impossible. The reasons for the intractability of integration include software incompatibilities, differing modeling logic, the costs of collaboration, and academic incentives. In the integrative modeling software ecosystem, several large modeling packages exist with often redundant tools. We reason, therefore, that the other development groups have similarly concluded that the benefit of integration does not justify the cost. As a result, modelers are often restricted to the set of tools within a single software package. The inability to integrate tools from distinct software negatively impacts the quality of the models and the efficiency of the modeling. As the complexity of modeling problems grows, we seek to galvanize developers and modelers to consider the long-term benefit that software interoperability yields. In this article, we formulate a demonstrative set of software standards for implementing a model search using tools from independent software packages and discuss our efforts to integrate IMP and the crystallography suite Phenix within the Bayesian modeling framework.

Integration of software tools for integrative modeling of biomolecular systems

Integrative modeling computes a model based on varied types of input information, be it from experiments, theory, or statistical analyses. Integrative modeling is used increasingly to compute structural models of complex biomolecular systems that are recalcitrant to traditional structural biology methods, from coarse-grained models of large biomolecular complexes to atomic models of single protein domains. Modeling requires a representation of a model (eg, atomic coordinates in high-resolution structure modeling), a scoring function that ranks alternative models given the input information (eg, the correlation coefficient between the density map and a model in electron microscopy), and a sampling scheme that finds good-scoring models (eg, a stochastic Monte Carlo search).

Modular dynamic biomolecular modelling with bond graphs: the unification of stoichiometry, thermodynamics, kinetics and data.

Renewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here, we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermodynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of Escherichia coli and published experimental data.

Domain-Specific Programming Languages for Computational Nucleic Acid Systems.

The construction of models of system behavior is of great importance throughout science and engineering. In bioengineering and bionanotechnology, these often take the form of dynamic models that specify the evolution of different species over time. To ensure that scientific observations and conclusions are consistent and that systems can be reliably engineered on the basis of model predictions, it is important that models of biomolecular systems can be constructed in a reliable, principled, and efficient manner. This review focuses on efforts to address this need by using domain-specific programming languages as the basis for custom design tools for researchers working on computational nucleic acid devices, where a domain-specific language is simply a programming language tailored to a particular application domain. The underlying thesis of our review is that there is a continuum of practical implementation strategies for computational nucleic acid systems, which can all benefit from appropriate domain-specific languages and software design tools. We emphasize the need for specialized yet flexible tools that can be realized using domain-specific languages that compile to more general-purpose representations.

Physically-plausible modelling of biomolecular systems: A simplified, energy-based model of the mitochondrial electron transport chain

Advances in systems biology and whole-cell modelling demand increasingly comprehensive mathematical models of cellular biochemistry. Such models require the development of simplified representations of specific processes which capture essential biophysical features but without unnecessarily complexity. Recently there has been renewed interest in thermodynamically-based modelling of cellular processes. Here we present an approach to developing of simplified yet thermodynamically consistent (hence physically plausible) models which can readily be incorporated into large scale biochemical descriptions but which do not require full mechanistic detail of the underlying processes. We illustrate the approach through development of a simplified, physically plausible model of the mitochondrial electron transport chain and show that the simplified model behaves like the full system.

Precision and accuracy of single-molecule FRET measurements\u2014a multi-laboratory benchmark study

Single-molecule Förster resonance energy transfer (smFRET) is increasingly being used to determine distances, structures, and dynamics of biomolecules in vitro and in vivo. However, generalized protocols and FRET standards to ensure the reproducibility and accuracy of measurements of FRET efficiencies are currently lacking. Here we report the results of a comparative blind study in which 20 labs determined the FRET efficiencies (E) of several dye-labeled DNA duplexes. Using a unified, straightforward method, we obtained FRET efficiencies with s.d. between ±0.02 and ±0.05. We suggest experimental and computational procedures for converting FRET efficiencies into accurate distances, and discuss potential uncertainties in the experiment and the modeling. Our quantitative assessment of the reproducibility of intensity-based smFRET measurements and a unified correction procedure represents an important step toward the validation of distance networks, with the ultimate aim of achieving reliable structural models of biomolecular systems by smFRET-based hybrid methods.

Polarizable Force Fields for Biomolecular Simulations: Recent Advances and Applications.

Realistic modeling of biomolecular systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in physical models, simulation algorithms, and computing hardware, biomolecular simulations with advanced force fields at biologically relevant timescales are becoming increasingly promising. These advancements have not only led to new biophysical insights but also afforded opportunities to advance our understanding of fundamental intermolecular forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomolecular simulations.

Molecular Surface Remeshing with Local Region Refinement.

Molecular surface mesh generation is a prerequisite for using the boundary element method (BEM) and finite element method (FEM) in implicit-solvent modeling. Molecular surface meshes typically have small angles, redundant vertices, and low-quality elements. In the implicit-solvent modeling of biomolecular systems it is usually required to improve the mesh quality and eliminate low-quality elements. Existing methods often fail to efficiently remove low-quality elements, especially in complex molecular meshes. In this paper, we propose a mesh refinement method that smooths the meshes, eliminates invalid regions in a cut-and-fill strategy, and improves the minimal angle. We compared our method with four different state-of-the-art methods and found that our method showed a significant improvement over state-of-the-art methods in minimal angle, aspect ratio, and other meshing quality measurements. In addition, our method showed satisfactory results in terms of the ratio of regular vertices and the preservation of area and volume.

MAMMOTh: A new database for curated mathematical models of biomolecular systems.

Living systems have a complex hierarchical organization that can be viewed as a set of dynamically interacting subsystems. Thus, to simulate the internal nature and dynamics of the entire biological system, we should use the iterative way for a model reconstruction, which is a consistent composition and combination of its elementary subsystems. In accordance with this bottom-up approach, we have developed the MAthematical Models of bioMOlecular sysTems (MAMMOTh) tool that consists of the database containing manually curated MAMMOTh fitted to the experimental data and a software tool that provides their further integration. The MAMMOTh database entries are organized as building blocks in a way that the model parts can be used in different combinations to describe systems with higher organizational level (metabolic pathways and/or transcription regulatory networks). The tool supports export of a single model or their combinations in SBML or Mathematica standards. The database currently contains 110 mathematical sub-models for Escherichia coli elementary subsystems (enzymatic reactions and gene expression regulatory processes) that can be combined in at least 5100 complex/sophisticated models concerning more complex biological processes as de novo nucleotide biosynthesis, aerobic/anaerobic respiration and nitrate/nitrite utilization in E. coli. All models are functionally interconnected and sufficiently complement public model resources. http://mammoth.biomodelsgroup.ru.

Bond graph modelling of chemoelectrical energy transduction

Energy-based bond graph modelling of biomolecular systems is extended to include chemoelectrical trans- duction thus enabling integrated thermodynamically-compliant modelling of chemoelectrical systems in general and excitable membranes in particular. Our general approach is illustrated by recreating a well-known model of an excitable membrane. This model is used to investigate the energy consumed during a membrane action potential thus contributing to the current debate on the trade-off between the speed of an action potential event and energy consumption. The influx of Na+ is often taken as a proxy for energy consumption; in contrast, this paper presents an energy based model of action potentials. As the energy based approach avoids the assumptions underlying the proxy approach it can be directly used to compute energy consumption in both healthy and diseased neurons. These results are illustrated by comparing the energy consumption of healthy and degenerative retinal ganglion cells using both simulated and in vitro data.

Modular bond-graph modelling and analysis of biomolecular systems.

Bond graphs can be used to build thermodynamically-compliant hierarchical models of biomolecular systems. As bond graphs have been widely used to model, analyse and synthesise engineering systems, this study suggests that they can play the same rôle in the modelling, analysis and synthesis of biomolecular systems. The particular structure of bond graphs arising from biomolecular systems is established and used to elucidate the relation between thermodynamically closed and open systems. Block diagram representations of the dynamics implied by these bond graphs are used to reveal implicit feedback structures and are linearised to allow the application of control-theoretical methods. Two concepts of modularity are examined: computational modularity where physical correctness is retained and behavioural modularity where module behaviour (such as ultrasensitivity) is retained. As well as providing computational modularity, bond graphs provide a natural formulation of behavioural modularity and reveal the sources of retroactivity. A bond graph approach to reducing retroactivity, and thus inter-module interaction, is shown to require a power supply such as that provided by the ATP ⇌ ADP + Pi reaction. The mitogen-activated protein kinase cascade (Raf-MEK-ERK pathway) is used as an illustrative example.

A Stochastic, Resonance-Free Multiple Time-Step Algorithm for Polarizable Models That Permits Very Large Time Steps.

Molecular dynamics remains one of the most widely used computational tools in the theoretical molecular sciences to sample an equilibrium ensemble distribution and/or to study the dynamical properties of a system. The efficiency of a molecular dynamics calculation is limited by the size of the time step that can be employed, which is dictated by the highest frequencies in the system. However, many properties of interest are connected to low-frequency, long time-scale phenomena, requiring many small time steps to capture. This ubiquitous problem can be ameliorated by employing multiple time-step algorithms, which assign different time steps to forces acting on different time scales. In such a scheme, fast forces are evaluated more frequently than slow forces, and as the former are often computationally much cheaper to evaluate, the savings can be significant. Standard multiple time-step approaches are limited, however, by resonance phenomena, wherein motion on the fastest time scales limits the step sizes that can be chosen for the slower time scales. In atomistic models of biomolecular systems, for example, the largest time step is typically limited to around 5 fs. Previously, we introduced an isokinetic extended phase-space algorithm (Minary et al. Phys. Rev. Lett. 2004, 93, 150201) and its stochastic analog (Leimkuhler et al. Mol. Phys. 2013, 111, 3579) that eliminate resonance phenomena through a set of kinetic energy constraints. In simulations of a fixed-charge flexible model of liquid water, for example, the time step that could be assigned to the slow forces approached 100 fs. In this paper, we develop a stochastic isokinetic algorithm for multiple time-step molecular dynamics calculations using a polarizable model based on fluctuating dipoles. The scheme developed here employs two sets of induced dipole moments, specifically, those associated with short-range interactions and those associated with a full set of interactions. The scheme is demonstrated on the polarizable AMOEBA water model. As was seen with fixed-charge models, we are able to obtain large time steps exceeding 100 fs, allowing calculations to be performed 10 to 20 times faster than standard thermostated molecular dynamics.

Theoretical modelling of biomolecular systems I. Large-scale QM/MM calculations of hydrogen-bonding networks of the oxygen evolving complex of photosystem II

Quantum mechanical (QM)/molecular mechanics (MM) calculations by the use of a large-scale QM model (QM Model V) have been performed to elucidate hydrogen-bonding networks and proton wires for proton release pathways (PRP) of water oxidation reaction in the oxygen evolving complex (OEC) of photosystem II (PSII). Full geometry optimisations of PRP by the QM/MM model have been carried out starting from the geometry of heavy atoms determined by the recent high-resolution X-ray diffraction (XRD) experiment of PSII refined to 1.9 Å resolution. Computational results by the QM/MM calculations have elucidated the hydrogen-bonding O···O(N) and O···H distances and O(N)–H···O angles in PRP, together with the Cl–O(N) and Cl···H distances and O(N)–H···Cl angles for chloride anions. The optimised hydrogen-bonding networks are well consistent with the XRD results and available experiments such as extended X-ray absorption fine structure, showing the reliability of channel structures of OEC of PSII revealed by the XRD experiment. The QM/MM computations have elucidated possible roles of chloride anions in the OEC of PSII. The QM/MM computational results have provided useful information for understanding and explanation of accumulated mutation experiments of key amino acid residues in the OEC of PSII. Implications of the present results are discussed in relation to three steps for theoretical modelling of water oxidation in the OEC of PSII and bio-inspired working hypotheses for developments of artificial water oxidation systems by use of 3d transition-metal complexes.

A software platform for continuum modeling of ion channels based on unstructured mesh

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson–Nernst–Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module

Stochastic, resonance-free multiple time-step algorithm for molecular dynamics with very large time steps

Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case, however, that the interparticle forces drive motion on many time scales, and the efficiency of a calculation is limited by the choice of time step, which must be sufficiently small that the fastest force components are accurately integrated. Multiple time-stepping algorithms partially alleviate this inefficiency by assigning to each time scale an appropriately chosen step-size. As the fast forces are often computationally cheaper to evaluate than the slow forces, this results in a significant gain in efficiency. However, such approaches are limited by resonance phenomena, wherein motion on the fastest time scales limits the step sizes associated with slower time scales. In atomistic models of biomolecular systems, for example, resonances limit the largest time step to around 5-6 fs. Stochastic processes promote mixing and ergodicity in dynamical systems and reduce the impact of resonant modes. In this paper, we introduce a set of stochastic isokinetic equations of motion that are shown to be rigorously ergodic, largely free of resonances, and can be integrated using a multiple time-stepping algorithm which is easily implemented in existing molecular dynamics codes. The technique is applied to a simple, illustrative problem and then to a more realistic system, namely, a flexible water model. Using this approach outer time steps as large as 100 fs are shown to be possible.

Coarse-Graining Methods for Computational Biology

Connecting the molecular world to biology requires understanding how molecular-scale dynamics propagate upward in scale to define the function of biological structures. To address this challenge, multiscale approaches, including coarse-graining methods, become necessary. We discuss here the theoretical underpinnings and history of coarse-graining and summarize the state of the field, organizing key methodologies based on an emerging paradigm for multiscale theory and modeling of biomolecular systems. This framework involves an integrated, iterative approach to couple information from different scales. The primary steps, which coincide with key areas of method development, include developing first-pass coarse-grained models guided by experimental results, performing numerous large-scale coarse-grained simulations, identifying important interactions that drive emergent behaviors, and finally reconnecting to the molecular scale by performing all-atom molecular dynamics simulations guided by the coarse-grained results. The coarse-grained modeling can then be extended and refined, with the entire loop repeated iteratively if necessary.

Coarse-graining of proteins based on elastic network models

To simulate molecular processes on biologically relevant length- and timescales, coarse-grained (CG) models of biomolecular systems with tens to even hundreds of residues per CG site are required. One possible way to build such models is explored in this article: an elastic network model (ENM) is employed to define the CG variables. Free energy surfaces are approximated by Taylor series, with the coefficients found by force-matching. CG potentials are shown to undergo renormalization due to roughness of the energy landscape and smoothing of it under coarse-graining. In the case study of hen egg-white lysozyme, the entropy factor is shown to be of critical importance for maintaining the native structure, and a relationship between the proposed ENM-mode-based CG models and traditional CG-bead-based models is discussed. The proposed approach uncovers the renormalizable character of CG models and offers new opportunities for automated and computationally efficient studies of complex free energy surfaces.

Between Algorithm and Model: Different Molecular Surface Definitions for the Poisson-Boltzmann Based Electrostatic Characterization of Biomolecules in Solution

The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well as in the molecular graphics field. In this work, two molecular surfaces are evaluated with respect to their suitability for electrostatic computation as alternatives to the widely used Connolly-Richards surface: the blobby surface, an implicit Gaussian atom centered surface, and the skin surface. As figures of merit, we considered surface differentiability and surface area continuity with respect to atom positions, and the agreement with explicit solvent simulations. Geometric analysis seems to privilege the skin to the blobby surface, and points to an unexpected relationship between the non connectedness of the surface, caused by interstices in the solute volume, and the surface area dependence on atomic centers. In order to assess the ability to reproduce explicit solvent results, specific software tools have been developed to enable the use of the skin surface in Poisson-Boltzmann calculations with the DelPhi solver. Results indicate that the skin and Connolly surfaces have a comparable performance from this last point of view.