Conformational analysis of lipid molecules by self-organizing maps

A Deep Graph Network-Enhanced Sampling Approach to Efficiently Explore the Space of Reduced Representations of Proteins

The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless development of computer architectures and algorithms. The consequent explosion in the number and extent of MD trajectories induces the need for automated methods to rationalize the raw data and make quantitative sense of them. Recently, an algorithmic approach was introduced by some of us to identify the subset of a protein's atoms, or mapping, that enables the most informative description of the system. This method relies on the computation, for a given reduced representation, of the associated mapping entropy, that is, a measure of the information loss due to such simplification; albeit relatively straightforward, this calculation can be time-consuming. Here, we describe the implementation of a deep learning approach aimed at accelerating the calculation of the mapping entropy. We rely on Deep Graph Networks, which provide extreme flexibility in handling structured input data and whose predictions prove to be accurate and-remarkably efficient. The trained network produces a speedup factor as large as 105 with respect to the algorithmic computation of the mapping entropy, enabling the reconstruction of its landscape by means of the Wang-Landau sampling scheme. Applications of this method reach much further than this, as the proposed pipeline is easily transferable to the computation of arbitrary properties of a molecular structure.

Interplay of lipid and surfactant: Impact on nanoparticle structure

Liquid lipid nanoparticles (LLN) are oil-in-water nanoemulsions of great interest in the delivery of hydrophobic drug molecules. They consist of a surfactant shell and a liquid lipid core. The small size of LLNs makes them difficult to study, yet a detailed understanding of their internal structure is vital in developing stable drug delivery vehicles (DDVs). Here, we implement machine learning techniques alongside small angle neutron scattering experiments and molecular dynamics simulations to provide critical insight into the conformations and distributions of the lipid and surfactant throughout the LLN. We simulate the assembly of a single LLN composed of the lipid, triolein (GTO), and the surfactant, Brij O10. Our work shows that the addition of surfactant is pivotal in the formation of a disordered lipid core; the even coverage of Brij O10 across the LLN shields the GTO from water and so the lipids adopt conformations that reduce crystallisation. We demonstrate the superior ability of unsupervised artificial neural networks in characterising the internal structure of DDVs, when compared to more conventional geometric methods. We have identified, clustered, classified and averaged the dominant conformations of lipid and surfactant molecules within the LLN, providing a multi-scale picture of the internal structure of LLNs.

Coarse-graining poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) block copolymers using the MARTINI force field

The MARTINI coarse-grain (CG) force field is extended for a class of triblock block copolymers known as Pluronics. Existing MARTINI bead types are used to model the non-bonded part of the potential while single chain properties for both homopolymers, poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO), are used to develop the bonded interactions. The new set of force field parameters reproduces structural and dynamical properties of high molecular weight homo- and copolymers. The CG model is moderately transferable in solvents of different polarity and concentration; however, the PEO homopolymer model presents a reduced thermodynamic transferability especially in water probably due to the lack of hydrogen bonds with the solvent. Our simulations of a monolayer of Pluronic L44 show polymer-brush-like characteristics for the PEO segments which protrude into the aqueous phase. Other membrane properties not easily accessible using experimental techniques such as its membrane thickness are also calculated.

Functional annotation of the mesophilic-like character of mutants in a cold-adapted enzyme by self-organising map analysis of their molecular dynamics

Multiple comparison of the Molecular Dynamics (MD) trajectories of mutants in a cold-adapted α-amylase (AHA) could be used to elucidate functional features required to restore mesophilic-like activity. Unfortunately it is challenging to identify the different dynamic behaviors and correctly relate them to functional activity by routine analysis. We here employed a previously developed and robust two-stage approach that combines Self-Organising Maps (SOMs) and hierarchical clustering to compare conformational ensembles of proteins. Moreover, we designed a novel strategy to identify the specific mutations that more efficiently convert the dynamic signature of the psychrophilic enzyme (AHA) to that of the mesophilic counterpart (PPA). The SOM trained on AHA and its variants was used to classify a PPA MD ensemble and successfully highlighted the relationships between the flexibilities of the target enzyme and of the different mutants. Moreover the local features of the mutants that mostly influence their global flexibility in a mesophilic-like direction were detected. It turns out that mutations of the cold-adapted enzyme to hydrophobic and aromatic residues are the most effective in restoring the PPA dynamic features and could guide the design of more mesophilic-like mutants. In conclusion, our strategy can efficiently extract specific dynamic signatures related to function from multiple comparisons of MD conformational ensembles. Therefore, it can be a promising tool for protein engineering.

Conformational and functional analysis of molecular dynamics trajectories by self-organising maps

BACKGROUND

Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.

RESULTS

The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.

CONCLUSIONS

The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.

Multiscale modeling of emergent materials: biological and soft matter

In this review, we focus on four current related issues in multiscale modeling of soft and biological matter. First, we discuss how to use structural information from detailed models (or experiments) to construct coarse-grained ones in a hierarchical and systematic way. This is discussed in the context of the so-called Henderson theorem and the inverse Monte Carlo method of Lyubartsev and Laaksonen. In the second part, we take a different look at coarse graining by analyzing conformations of molecules. This is done by the application of self-organizing maps, i.e., a neural network type approach. Such an approach can be used to guide the selection of the relevant degrees of freedom. Then, we discuss technical issues related to the popular dissipative particle dynamics (DPD) method. Importantly, the potentials derived using the inverse Monte Carlo method can be used together with the DPD thermostat. In the final part we focus on solvent-free modeling which offers a different route to coarse graining by integrating out the degrees of freedom associated with solvent.

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.

Representability problems for coarse-grained water potentials

The use of an effective intermolecular potential often involves a compromise between more accurate, complex functional forms and more tractable simple representations. To study this choice in detail, we systematically derive coarse-grained isotropic pair potentials that accurately reproduce the oxygen-oxygen radial distribution function of the TIP4P-Ew water model at state points over density ranges from 0.88 to 1.30 g/cm3 and temperature ranges from 235 to 310 K. Although by construction these effective potentials correctly represent the isothermal compressibility of TIP4P-Ew water, they do not accurately resolve other thermodynamic properties such as the virial pressure, the internal energy, or thermodynamic anomalies. Because at a given state point the pair potential that reproduces the pair structure is unique, we have therefore explicitly demonstrated that it is impossible to simultaneously represent the pair structure and several key equilibrium thermodynamic properties of water with state-point dependent radially symmetric pair potentials. We argue that such representability problems are related to, but different from, more widely acknowledged transferability problems and discuss in detail the implications this has for the modeling of water and other liquids by coarse-grained potentials. Nevertheless, regardless of thermodynamic inconsistencies, the state-point dependent effective potentials for water do generate structural and dynamical anomalies.

Coarse-grained model for phospholipid/cholesterol bilayer employing inverse Monte Carlo with thermodynamic constraints

The authors introduce a coarse-grained (CG) model for a lipid membrane comprised of phospholipids and cholesterol at different molar concentrations, which allows them to study systems that are approximately 100 nm in linear size. The systems are studied in the fluid phase above the main transition temperature. The effective interactions for the CG model are extracted from atomic-scale molecular dynamics simulations using the inverse Monte Carlo (IMC) technique, an approach similar to the one the authors used earlier to construct another CG bilayer model [T. Murtola et al., J. Chem. Phys. 121, 9156 (2004)]. Here, the authors improve their original CG model by employing a more accurate description of the molecular structure for the phospholipid molecules. Further, they include a thermodynamic constraint in the IMC procedure to yield area compressibilities in line with experimental data. The more realistic description of the molecular structure of phospholipids and a more accurate representation of the interaction between cholesterols and phospholipid tails are shown to improve the behavior of the model significantly. In particular, the new model predicts the formation of denser transient regions in a pure phospholipid system, a finding that the authors have verified through large scale atomistic simulations. They also find that the model predicts the formation of cholesterol-rich and cholesterol-poor domains at intermediate cholesterol concentrations, in agreement with the original model and the experimental phase diagram. However, the domains observed here are much more distinct compared to the previous model. Finally, the authors also explore the limitations of the model, discussing its advantages and disadvantages.