Unsupervised Machine Learning for Analysis of Phase Separation in Ternary Lipid Mixture

Building complex membranes with Martini 3

The Martini model is a popular force field for coarse-grained simulations. Membranes have always been at the center of its development, with the latest version, Martini 3, showing great promise in capturing more and more realistic behavior. In this chapter we provide a step-by-step tutorial on how to construct starting configurations, run initial simulations and perform dedicated analysis for membrane-based systems of increasing complexity, including leaflet asymmetry, curvature gradients and embedding of membrane proteins.

Characterization of domain formation in complex membranes

A widely known property of lipid membranes is their tendency to undergo a separation into disordered (Ld) and ordered (Lo) domains. This impacts the local structure of the membrane relevant for the physical (e.g., enhanced electroporation) and biological (e.g., protein sorting) significance of these regions. The increase in computing power, advancements in simulation software, and more detailed information about the composition of biological membranes shifts the study of these domains into the focus of classical molecular dynamics simulations. In this chapter, we present a versatile yet robust analysis pipeline that can be easily implemented and adapted for a wide range of lipid compositions. It employs Gaussian-based Hidden Markov Models to predict the hidden order states of individual lipids by describing their structure through the area per lipid and the average SCC order parameters per acyl chain. Regions of the membrane with a high correlation between ordered lipids are identified by employing the Getis-Ord local spatial autocorrelation statistic on a Voronoi tessellation of the lipids. As an example, the approach is applied to two distinct systems at a coarse-grained resolution, demonstrating either a strong tendency towards phase separation (1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dilinoleoyl-sn-glycero-3-phosphocholine (DIPC), cholesterol) or a weak tendency toward phase separation (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-docosahexaenoyl-sn-glycero-3-phosphocholine (PUPC), cholesterol). Explanations of the steps are complemented by coding examples written in Python, providing both a comprehensive understanding and practical guidance for a seamless integration of the workflow into individual projects.

Anomalous lateral diffusion of lipids during the fluid/gel phase transition of a lipid membrane

A lipid membrane undergoes a phase transition from fluid to gel phase upon changing external thermodynamic conditions, such as decreasing temperature and increasing pressure. Extremophilic organisms face the challenge of preventing this deleterious phase transition. The main focus of their adaptive strategy is to facilitate effective temperature sensing through sensor proteins, relying on the drastic changes in packing density and membrane fluidity during the phase transition. Although the changes in packing density parameters due to the fluid/gel phase transition are studied in detail, the impact on membrane fluidity is less explored in the literature. Understanding the lateral diffusive dynamics of lipids in response to temperature, particularly during the fluid/gel phase transition, is albeit crucial. Here we have simulated the phase transition of a single component lipid membrane composed of dipalmitoylphosphatidylcholine (DPPC) lipids using a coarse-grained (CG) model and studied the changes of the structural and dynamical properties. It is observed that near the phase transition point, both fluid and gel phase domains coexist together. The dynamics remains highly non-Gaussian for a long time even when the mean square displacement reaches the Fickian regime at a much earlier time. This Fickian yet non-Gaussian diffusion (FnGD) is a characteristic of a highly heterogeneous system, previously observed for the lateral diffusion of lipids in raft mimetic membranes having liquid-ordered and liquid-disordered phases co-existing together. We have analyzed the molecular trajectories and calculated the jump-diffusion of the lipids, stemming from sudden jump translations, using a translational jump-diffusion (TJD) approach. An overwhelming contribution of the jump-diffusion of the lipids is observed suggesting anomalous diffusion of lipids during fluid/gel phase transition of the membrane. These results are important in unravelling the intricate nature of lipid diffusion during the phase transition of the membrane and open up a new possibility of investigating the most significant change of membrane properties during phase transition, which can be effectively sensed by proteins.

The roles of artificial intelligence techniques for increasing the prediction performance of important parameters and their optimization in membrane processes: A systematic review

Membrane-based separation processes has been recently of significant global interest compared to other conventional separation approaches due to possessing undeniable advantages like superior performance, environmentally-benign nature and simplicity of application. Computational simulation of fluids has shown its undeniable role in modeling and simulation of numerous physical/chemical phenomena including chemical engineering, chemical reaction, aerodynamics, drug delivery and plasma physics. Definition of fluids can be occurred using the Navier-Stokes equations, but solving the equations remains an important challenge. In membrane-based separation processes, true perception of fluid's manner through disparate membrane modules is an important concern, which has been significantly limited applying numerical/computational procedures such s computational fluid dynamics (CFD). Despite this noteworthy advantage, the optimization of membrane processes using CFD is time-consuming and expensive. Therefore, combination of artificial intelligence (AI) and CFD can result in the creation of a promising hybrid model to accurately predict the model results and appropriately optimize membrane processes and phase separation. This paper aims to provide a comprehensive overview about the advantages of commonly-employed ML-based techniques in combination with the CFD to intelligently increase the optimization accuracy and predict mass transfer and the unfavorable events (i.e., fouling) in various membrane processes. To reach this objective, four principal strategies of AI including SL, USL, SSL and ANN were explained and their advantages/disadvantages were discussed. Then after, prevalent ML-based algorithm for membrane-based separation processes. Finally, the application potential of AI techniques in different membrane processes (i.e., fouling control, desalination and wastewater treatment) were presented.

Relationships between Molecular Structural Order Parameters and Equilibrium Water Dynamics in Aqueous Mixtures

Water's unique thermophysical properties and how it mediates aqueous interactions between solutes have long been interpreted in terms of its collective molecular structure. The seminal work of Errington and Debenedetti [Nature 2001, 409, 318-321] revealed a striking hierarchy of relationships among the thermodynamic, dynamic, and structural properties of water, motivating many efforts to understand (1) what measures of water structure are connected to different experimentally accessible macroscopic responses and (2) how many such structural metrics are adequate to describe the collective structural behavior of water. Diffusivity constitutes a particularly interesting experimentally accessible equilibrium property to investigate such relationships because advanced NMR techniques allow the measurement of bulk and local water dynamics in nanometer proximity to molecules and interfaces, suggesting the enticing possibility of measuring local diffusivities that report on water structure. Here, we apply statistical learning methods to discover persistent structure-dynamic correlations across a variety of simulated aqueous mixtures, from alcohol-water to polypeptoid-water systems. We investigate a variety of molecular water structure metrics and find that an unsupervised statistical learning algorithm (namely, sequential feature selection) identifies only two or three independent structural metrics that are sufficient to predict water self-diffusivity accurately. Surprisingly, the translational diffusivity of water across all mixed systems studied here is strongly correlated with a measure of tetrahedral order given by water's triplet angle distribution. We also identify a separate small number of structural metrics that well predict an important thermodynamic property, the excess chemical potential of an idealized methane-sized hydrophobe in water. Ultimately, we offer a Bayesian method of inferring water structure by using only structure-dynamics linear regression models with experimental Overhauser dynamic nuclear polarization (ODNP) measurements of water self-diffusivity. This study thus quantifies the relationships among several distinct structural order parameters in water and, through statistical learning, reveals the potential to leverage molecular structure to predict fundamental thermophysical properties. In turn, these findings suggest a framework for solving the inverse problem of inferring water's molecular structure using experimental measurements such as ODNP studies that probe local water properties.

Homeoviscous Adaptation of the Lipid Membrane of a Soil Bacterium Surviving under Diurnal Temperature Variation: A Molecular Simulation Perspective

A recent experiment has reported the lipidome remodeling of a soil-based plant-associated bacterium Methylobacterium extorquens due to diurnal temperature variations. The key adaptation strategy is the headgroup-specific remodeling of the acyl chain. To understand the idiosyncratic adaptation at the molecular level, we simulate the model membrane of the same bacterium using the reported lipidome compositions at four different experimental temperatures. We investigate the temperature-dependent packing density and fluidity of the membrane, the constancy of which is key to the homeoviscous adaptation. The results show that complex lipidome remodeling approximately preserves membrane properties under heat and cold stress. The headgroup-specific remodeling of the acyl chain serves to fine-tune the packing density and fluidity of the membrane at different temperatures. While lipids with strongly interacting headgroups are more abundant at higher temperatures, the lipidome is more dominated by lipids with weaker interacting headgroups at lower temperatures. This adaptation alleviates lipid membrane disruption caused by heat and cold stress. This study provides a molecular picture of the homeoviscous adaptation of the realistic lipid membrane of a soil-based bacterium.

Phase Separation in Liposomes Determined by Ergosterol and Classified Using Machine Learning

Recent studies indicated that ergosterol (Erg) helps form strongly ordered lipid domains in membranes that depend on their chemical characters. However, direct evidence of concentration-dependent interaction of Erg with lipid membranes has not been reported. We studied the Erg concentration-dependent changes in the phase behaviors of membranes using cell-sized liposomes containing 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC)/1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). We observed the concentration range of phase separation in ternary membranes was significantly wider when Erg rather than cholesterol (Chol) was used as the sterol component. We used machine learning for the first time to analyze microscopic images of cell-sized liposomes and identify phase-separated structures. The automated method was successful in identifying homogeneous membranes but performance remained data-limited for the identification of phase separation domains characterized by more complex features.

Importance of feature construction in machine learning for phase transitions

Machine learning is an important tool in the study of the phase behavior from molecular simulations. In this work we use un-supervised machine learning methods to study the phase behavior of two off-lattice models, a binary Lennard-Jones (LJ) mixture and the Widom-Rowlinson (WR) mixture. We find that the choice of the feature vector is crucial to the ability of the algorithm to predict a phase transition. We consider two feature vectors, one where the elements are distances of the particles of a given species from a probe (distance-based feature) and one where the elements are +1 if there is an excess of particles of the same species within a cut-off distance and -1 otherwise (affinity-based feature). We use principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) methods to investigate the phase behavior at a critical composition. We find that the choice of the feature vector is key to the success of unsupervised machine learning algorithm in predicting the phase behavior, and the sophistication of the machine learning algorithm is of secondary importance. In the case of the LJ mixture both feature vectors are adequate to accurately predict the critical point, but in the case of the WR mixture the affinity-based feature vector provides accurate estimates of the critical point, but the distance-based feature vector does not provide a clear signature of the phase transition. The study suggests that physical insight in choice of input features is an important aspect of implementing machine learning methods.

Intelligent fluorescence image analysis of giant unilamellar vesicles using convolutional neural network

Background

Fluorescence image analysis in biochemical science often involves the complex tasks of identifying samples for analysis and calculating the desired information from the intensity traces. Analyzing giant unilamellar vesicles (GUVs) is one of these tasks. Researchers need to identify many vesicles to statistically analyze the degree of molecular interaction or state of molecular organization on the membranes. This analysis is complicated, requiring a careful manual examination by researchers, so automating the analysis can significantly aid in improving its efficiency and reliability.

Results

We developed a convolutional neural network (CNN) assisted intelligent analysis routine based on the whole 3D z-stack images. The programs identify the vesicles with desired morphology and analyzes the data automatically. The programs can perform protein binding analysis on the membranes or state decision analysis of domain phase separation. We also show that the method can easily be applied to similar problems, such as intensity analysis of phase-separated protein droplets. CNN-based classification approach enables the identification of vesicles even from relatively complex samples. We demonstrate that the proposed artificial intelligence-assisted classification can further enhance the accuracy of the analysis close to the performance of manual examination in vesicle selection and vesicle state determination analysis.

Conclusions

We developed a MATLAB based software capable of efficiently analyzing confocal fluorescence image data of giant unilamellar vesicles. The program can automatically identify GUVs with desired morphology and perform intensity-based calculation and state decision for each vesicle. We expect our method of CNN implementation can be expanded and applied to many similar problems in image data analysis.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04577-2.

Molecular Organization of a Raft-like Domain in a Polyunsaturated Phospholipid Bilayer: A Supervised Machine Learning Analysis of Molecular Dynamics Simulations

Numerous health benefits are associated with omega-3 polyunsaturated fatty acids (n-3 PUFA) consumed in fish oils. An understanding of the mechanism remains elusive. The plasma membrane as a site of action is the focus in this study. With large-scale all-atom MD simulations run on a model membrane (1050 lipid molecules), we observed the evolution over time (6 μs) of a circular (raft-like) domain composed of N-palmitoylsphingomyelin (PSM) and cholesterol embedded into a surrounding (non-raft) patch composed of polyunsaturated 1-palmitoyl-2-docosahexaenoylphosphatylcholine (PDPC) (1:1:1 mol). A supervised machine learning algorithm was developed to characterize the migration of each lipid based on molecular conformation and the local environment. PDPC molecules were seen to infiltrate the ordered raft-like domain in a small amount, while a small concentration of PSM and cholesterol molecules was seen to migrate into the disordered non-raft region. Enclosing the raft-like domain, a narrow (∼2 nm in width) interfacial zone composed of PDPC, PSM, and cholesterol that buffers the substantial difference in order (ΔS_CD ≈ 0.12) between raft-like and non-raft environments was seen to form. Our results suggest that n-3 PUFA regulate the architecture of lipid rafts enriched in sphingolipids and cholesterol with a minimal effect on order within their interior in membranes.

MLLPA: A Machine Learning-assisted Python module to study phase-specific events in lipid membranes

Machine Learning-assisted Lipid Phase Analysis (MLLPA) is a new Python 3 module developed to analyze phase domains in a lipid membrane based on lipid molecular states. Reading standard simulation coordinate and trajectory files, the software first analyze the phase composition of the lipid membrane by using machine learning tools to label each individual molecules with respect to their state, and then decompose the simulation box using Voronoi tessellations to analyze the local environment of all the molecules of interest. MLLPA is versatile as it can read from multiple format (e.g., GROMACS, LAMMPS) and from either all-atom (e.g., CHARMM36) or coarse-grain models (e.g., Martini). It can also analyze multiple geometries of membranes (e.g., bilayers, vesicles). Finally, the software allows for training with more than two phases, allowing for multiple phase coexistence analysis.

Effect of alcohol on the phase separation in model membranes

The discovery of coexisting liquid-ordered and liquid-disordered phases in multicomponent lipid bilayers has received widespread attention due to its potential relevance for biological systems. One of the many open questions is how the presence of additional components affects the nature of the coexisting phases. Of particular interest is the addition of alcohols because their anesthetic properties may arise from modulating bilayer behavior. We use coarse-grained Molecular Dynamics simulations to gain insight into the partitioning preferences of linear n-alcohols into ordered and disordered bilayers alongside their effects on local membrane structure. We find that alcohols cause only small changes to membrane composition alongside a lack of significant effects on membrane thickness and lipid tail order. Cholesterol and n-alcohol trans-bilayer motion is measured and found to be near or within the range of previous atomistic results. The cholesterol flip-flop rates increase with both n-alcohol length and concentration for octanol, dodecanol, and hexadecanol, indicating a decrease in lipid order. Umbrella sampling simulations of removing cholesterol from tertiary membranes find no significant difference with or without n-alcohols at various concentrations. Simulations of a phase-separated bilayer show that octanol preferentially partitions into the liquid-disordered phase in a ratio of approximately 3:1 over the liquid-ordered phase. Furthermore, partition coefficients of alcohol in single-phase membranes show a preference for longer alcohols (dodecanol and hexadecanol) to partition preferentially into the liquid-ordered phase, while decreasing the length of the alcohol reverses this trend. Our work tests experimental results while also investigating the ability for coarse-grained MARTINI simulations to capture minute differences in model membrane spatial arrangements on the nanoscale level.

A machine learning approach to estimation of phase diagrams for three-component lipid mixtures

The plasma membrane of eukaryotic cells is commonly believed to contain ordered lipid domains. The interest in understanding the origin of such domains has led to extensive studies on the phase behavior of mixed lipid systems. Three-component phase diagrams, composed of a high melting temperature (Tm) lipid, cholesterol, and a low Tm lipid have been valuable in studying lipid phase behavior. However, developing phase diagrams over the entire composition space and with precise tie-lines requires significant experimental effort. In this study, a machine learning approach was used to predict the Tm of lipids and generate phase diagrams from lipid mixtures. First, artificial neural network (ANN) was used for the prediction of Tm. The network was trained using available Tm data and was able to generate Tm values that closely matched literature results for its testing dataset. This model was then used to predict the Tm for lipids that have not yet been experimentally tested. Then, random forests (RF) and support vector machines (SVM) were trained and tested for their ability to predict a test three-component phase diagram. The model from the RF algorithm was able to generate a diagram that closely matched published results. This model was then used to generate phase diagrams for lipid mixtures at various temperatures and various degrees of unsaturation. This machine learning approach to the generation of lipid phase diagrams has the potential to save significant time and resources in studies of lipid phase behavior.