Modeling of Microscale Transport in Biological Processes

Modeling of Microscale Transport in Biological Processes provides a compendium of recent advances in theoretical and computational modeling of biotransport phenomena at the microscale. The simulation strategies presented range from molecular to continuum models and consider both numerical and exact solution method approaches to coupled systems of equations.

The biological processes covered in this book include digestion, molecular transport, microbial swimming, cilia mediated flow, microscale heat transfer, micro-vascular flow, vesicle dynamics, transport through bio-films and bio-membranes, and microscale growth dynamics.

The book is written for an advanced academic research audience in the fields of engineering (encompassing biomedical, chemical, biological, mechanical, and electrical), biology and mathematics. Although written for, and by, expert researchers, each chapter provides a strong introductory section to ensure accessibility to readers at all levels.

• Features recent developments in theoretical and computational modeling for clinical researchers and engineers
• Furthers researcher understanding of fluid flow in biological media and focuses on biofluidics at the microscale
• Includes chapters expertly authored by internationally recognized authorities in the fundamental and applied fields that are associated with microscale transport in living media

• Language: English
• Publisher: Academic Press
• Release date: Dec 27, 2016
• ISBN: 9780128046197

Book preview

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Preface

Sid M. Becker

This book presents a collection of 14 chapters each of which considers the modeling of transport phenomena in biological processes. The unique characteristic of this collection is that it is primarily concerned with the transport behavior occurring at the microscale. The chapters presented in this book consider a wide range of biological processes including microscale bio-heat transfer, molecular transport involved in the lipid bilayer environment, swimming of microorganisms, digestion of food, microbial degradation of oils, transport of mucus in the lung, transport of pollen in flowering plants, and transport of organelles in neural networks.

Each of this book's chapters is authored by internationally recognized researchers and research groups. The chapters provide detailed introductions so that the reader new to the field is not alienated by the technical diction. In fact, it is anticipated that both the advanced academic and the emerging researcher will find the material presented here as laid out in a clear and interesting manner.

Chapter 1 presents an extensive review of molecular dynamics modeling strategies with a focus on their application to simulate transport through biological membranes. The chapter provides a contextual narrative describing the recent developments in this field and describes how this has enhanced the understanding of the biophysical phenomena associated with these complex membranes.

Chapter 2 presents a detailed and informative review of the biodegradation of oily substrates by microbial communities. This chapter provides the reader with a comprehensive description of the underlying physics and the different regimes of microbe-induced degradation. The reader is provided with a detailed compendium of the predominant theories describing this process.

Chapter 3 addresses the theoretical handling of practical challenges associated with the measurement of bio-molecular and cellular transport. The work presents a review of the applications of microscale transport and microfluidic devices. With this practical background established, current modeling strategies are presented which are able to link macroscale flow phenomena with microscale molecular kinetics. The chapter presents different theoretical approaches and links the mathematics directly to the underlying physical phenomena in a direct and clear manner.

Chapter 4 considers the mathematical modeling of the coupled mechanical-transport problem found in arterial physiopathology. The chapter provides an extensive description of the physiology and the microstructure of the arterial wall and explains how these are coupled to the molecular transport problem. The details of the most recent developments of the mechanistic descriptions of the multi-scale multi-physics are presented.

Chapter 5 presents the most recent review of the modeling of cystic fibrosis and mucociliary clearance. An in depth introduction to the physiology of the airway and the pathology of cystic fibrosis is followed by a comprehensive description of the associated theoretical mathematical modeling. Numerical approaches to capturing the effects of mucus transport at the ciliated epithelium are presented. The models of the rheology of mucus are presented and evaluated in comparison to experiment.

Chapter 6 considers microscale transport in flowering plants. The theoretical and numerical models are developed that describes the micro-hydrodynamics and the advection–diffusion dynamics of fountain streaming in pollen tubes. The models are used to investigate the coupled effect between this streaming and the dynamic fast tip growth of pollen tubes. Experimental comparison is presented to confirm the results.

Chapter 7 presents a comprehensive introduction to the transport mechanisms employed by micro-organisms. The swimming dynamics of these microbial life forms is presented in the context of the micro-organisms' responses to stimuli. The chapter provides extraordinary scope and detail of the historical development of the field's description of swimming phenomena including gyrotaxis, phototaxis, and chemotaxis.

Chapter 8 continues the theme of microscale propulsion with an interesting perspective of the transport of proteins in the lipid membrane in which the proteins exhibit cyclical motion resulting in a type of swimming. The authors use molecular dynamics models to simulate the lipid environment and capture the associated molecular transport.

Chapter 9 considers the dynamic phenomena associated with inhomogeneous lipid membranes. A review of current theoretical descriptions of the energy of the lipid bilayer and the hydrodynamics describing the shape of lipid vesicles is presented. These descriptions are extended to include inhomogeneous bilayer membranes. The chapter then demonstrates the applicability of the phase field method to capture the behavior of multicomponent membranes and endocytosis.

Chapter 10 considers the transfer of thermal energy by a pulsed laser to perfuse biological tissue. The problem is considered numerically in a finite element model, and the system is cleverly reproduced experimentally in a novel synthetic tissue phantom.

Chapter 11 considers analytical approaches to the problem of the rapid heating of living perfused biological tissue. The chapter provides a detailed description of the development of the dual phase lag bio-heat equations governing this system and their associated boundary conditions. The reader is presented with a detailed description of the determination of the dual phase lag Green's functions and their related equations. Exact solutions are provided and their numerical representations are illustrated in case studies.

Chapter 12 addresses the modeling of the multi-scale problem involving the transport of fluid and nutrients in biological tissue in which the local tissue structure experiences growth in response to nutrient concentration. The work begins by providing a theoretical description of the microscale transport and associated tissue growth. The macroscale representations of transport are then developed by multiscale homogenization. The chapter applies this model in a well-considered analysis of the influence of microscale growth on macroscale transport.

Chapter 13 is concerned with the modeling of the transport of micro-organelles in neural networks. The chapter provides a comprehensive review of existing modeling strategies and details the mathematical equations that are used to simulate dense core vesicle transport in axon terminals.

Chapter 14 presents an extensive review of the historical approaches to the modeling of food digestion. The work opens with an in depth discussion of the physical processes that underlie digestion. The existing mathematical representations of digestion and absorption are provided and microscale phenomena are highlighted.

This book presents the physics, physiology, and mathematics involved in the modeling of microscale transport phenomena occurring in biological processes. It is anticipated that the reader will find this book of great help in bridging the gap between transport modeling and biology.

Chapter 1

Molecular Simulations of Complex Membrane Models

D. Jefferies; S. Khalid¹    School of Chemistry, University of Southampton, Southampton, United Kingdom

¹Chapter coordinator.

Abstract

Biological membranes have been an active area of research within the biomolecular simulation community for two decades or so now. Thus there is a rich body of literature describing computational studies of membrane proteins, lipids, drugs that interact with membranes, and the interactions between these different types of molecule. The models used in these studies were simplified for a number of reasons, including computational feasibility.

More recently, simulations have started to incorporate the biochemical complexity of real biological membranes. The chemical heterogeneity of the membrane lipids is considered, as well as the crowded protein environment of in vivo membranes. In this chapter, several simulation studies of complex membranes are discussed.

Keywords

Molecular dynamics; Simulation; Membrane; Complex; Atomistic; Coarse-grain

1.1 Introduction

Over the last decade, molecular simulation has emerged as a powerful tool for studying the structural and functional properties of complex biological membranes. The application of simulation methodologies such as molecular dynamics simulations, at both atomistic and coarse-grain resolutions, is increasingly providing information about lipid membranes that is hardly accessible by any single experimental method alone. Simulations provide crucial information about the interaction of lipid membranes with natural and synthetic molecules, while also resolving the complexities of macroscopic biophysical phenomena, which have so far otherwise proved to be elusive (Lindahl and Sansom, 2008; Ingólfsson et al., 2016; Hedger and Sansom, 2016). The rapidly growing field of molecular simulation is now established as an indispensable tool for providing insights into unresolved issues in the molecular level behavior of biological membranes and related systems. In the following, we briefly review how molecular dynamics has evolved recently in terms of scope, and how the development of this simulation technique has enhanced the understanding of complex membranes.

This chapter provides a review and puts into context some specific case studies from the large and still rapidly expanding body of literature on membrane and membrane protein simulations. The intention of this chapter is not to provide an exhaustive list, but rather to give a flavor of how the field is growing, and to put into context the development of the existing modeling strategies.

1.1.1 Methods: Molecular Dynamics Simulations

Molecular dynamics is a simulation methodology often used for studying the conformational rearrangements of molecules and their interactions with other molecular species in a range of environments. The method provides a dynamic description of the temporal behavior of atoms and molecules by using finite difference methods to numerically solve Newton's equations of motion (Fig. 1.1) (Alder and Wainwright, 1959; Rahman, 1964). The forces between the atoms or atom-like particles are described with interatomic potentials, or molecular mechanics ‘force fields’. The force fields most commonly decompose the N-body interactions into two parts: (i) bonded interactions are treated as a series of harmonic bonds, with associated angle and dihedral potentials (the latter being represented by a periodic function usually a cosine function); (ii) non-bonded interactions are modeled as pair-potentials that are split into long-range electrostatics, and a van der Waals component which incorporates repulsion and dispersion interactions.

Figure 1.1 A flow chart summarizing the sequence of processes involved in a molecular dynamics simulation.

Molecular dynamics simulations of biological membranes are most commonly performed at two different levels of detail or resolution: the atomistic or near atomistic level in which the CHARMM (Mackerall et al., 1998, 2004), GROMOS (van Gunsteren et al., 1998), AMBER (Cornell et al., 1995) and OPLS (Jorgensen and Tirado-Rives, 1988) families of force-fields are very popular and a more coarse-grain level in which the Martini force field (Marrink et al., 2007) is perhaps the most widely used within the biomolecular simulation community. The atomistic approach includes the explicit consideration of every atom that makes up the system while the near atomistic approach considers every atom other than non-polar hydrogen atoms. An example of the atomistic approach is the CHARMM force field, which is used to model fluid membranes by explicitly defining every atom type for all lipids. The near atomistic approach of the GROMOS force field employs a united-atom approach, in which non-polar CH, CH2, and CH3 groups are represented as a single interaction center. Aside from the differing representation of alkyl groups, there are small differences in the functional form of the bonded and non-bonded pair-potentials. For example, the CHARMM force field includes a Urey–Bradley term for covalent angles, as well as a more sophisticated description for the dihedral potentials. The CHARMM and GROMOS force fields have been used in many simulations of lipid membranes in the last two decades, and have been found to satisfactorily mimic the most salient features of fluid bilayers such as acyl tail order parameters, area per lipid values, and partial mass density distributions (Klauda et al., 2010; Piggot et al., 2012). The two force field families have been successful at clarifying many intricate details about lipid membranes, but computationally expensive pair-potentials limit their application to spatio-temporal scales that preclude the study of larger systems, e.g. those that incorporate many copies of native membrane proteins.

To expand the scope of molecular dynamics and bridge it with experimental techniques, coarse-grain force fields were developed for the simulation of biomolecular systems (Marrink et al., 2007; Orsi and Essex, 2011; Shinoda et al., 2011; Izvekov and Voth, 2005). Due to space limitations, this chapter will focus on just one of these force fields, the Martini developed by Siewert-Jan Marrink. Instead of explicitly representing individual atoms, the Martini force field bundles multiple heavy atoms into single interaction centers. By averaging out expensive atomistic detail in this way, the coarse-grain force field significantly simplifies the description of biological systems, which enables access to simulation scales that are beyond the scope of CHARMM and GROMOS. It is important to highlight here that coarse-grain and atomistic force fields are often used to study different aspects of a molecular system in a serial approach by using dual resolution methods, thus combining the advantages of both, and overcoming their individual limitations. The Martini force field is parameterized in a systematic way: non-bonded interactions are based on experimental partitioning free energies, while bonded interactions are derived from all-atom simulations. The relative simplicity and versatility of the Martini force field lends itself to a wide range of biological systems, and many different biophysical phenomena (Marrink and Tieleman, 2013).

1.2 Unsaturated Carbon Chains

Given the use of expensive pair-potentials in molecular dynamics, simulations initially ignored the full complexity of the cellular membrane environment, and represented bilayers with minimal lipid models. Early simulations attempted to capture the most important physical features of hydrated membranes by focusing on basic lipids like dipalmitoyl-glycero-phosphatidylcholine (DPPC) which contains a single phosphoglycerol head group attached to two saturated lipid tails (Berger et al., 1997). These minimal lipid models provided a good representation of many experimental in vitro conditions, but their applicability to in vivo scenarios was limited.

As molecular dynamics methodology evolved and as access to greater computational power became more readily available, larger spatio-temporal scales became feasible; efforts were made to simulate membranes that displayed increasing levels of complexity, in the form of acid chain heterogeneity. One of the first and most pivotal studies concerned the simulation of a palmitoyl-oleoyl-glycero-phosphatidylcholine (POPC, 16:0/18:1) membrane, which provides one of the simplest saturated/unsaturated mixed chain environments (Chiu et al., 1999). Simulations revealed that unsaturated carbon–carbon double bonds have a tendency to alter lipid chain conformations, making it difficult for POPC molecules to achieve tight packing in a bilayer. As a result, POPC membranes have increased area per lipid values when compared to bilayers of simpler saturated lipids.

Later simulation studies focused on more complex stearoyl-docosahexaenoyl-glycero phosphocholine (SDPC) lipid bilayers, providing insights into saturated/polyunsaturated acid chain mixtures (Saiz and Klein, 2001a, 2001b, 2002). These simulations helped to resolve the origin of the different packing parameters for lipids of different saturation levels. The disparate area per lipid values was found to be due to differing conformational energetics. The incorporation of carbon–carbon double bonds led to a more complex conformational landscape for unsaturated carbon tails, permitting a broader distribution of projected area per chain values, and larger local fluctuations. This high degree of inhomogeneity makes it difficult for the component lipids to achieve tight packing in the bilayer. Interestingly, the broad distribution of area per chain values and high degree of inhomogeneity also explains the capacity of polyunsaturated environments to accommodate the large structural shifts of membrane embedded proteins.

1.3 Membrane Proteins

Membrane proteins are present in all cells and are pivotal to a variety of cellular processes such as nutrient uptake, disposal of metabolic by-products, and product manufacture (Almén et al., 2009). Additionally the proteins are involved in controlling the various mechanical, chemical, and electrical gradients that are paramount to cell viability. Given that membrane proteins play such key roles in basic cell functioning, they are found in high concentrations on the surfaces of all cells. This is true for integral membrane proteins, which are permanently embedded within the lipid core, and peripheral membrane proteins, which form more fleeting interactions with the surrounding lipids (Johnson and Cornell, 1999). The awareness that membrane proteins have an intricate interdependency on their membrane environment has led the drive to increasingly integrate the simulated proteins into their complex bilayer models, as larger spatio-temporal scales became accessible.

1.3.1 Ion Channel Functioning

Some of the first membrane protein simulations focused on the functioning of channel proteins which regulate the flux of ions and small molecules across the cell membrane (Hille, 1978). Different ion channels were incorporated into lipid bilayers to study the effects of membranes on the structure, function, and dynamics of the proteins. Consider the two cases of particular interest: the prototypical gramicidin A ion channel (Andersen et al., 1998; Woolf and Roux, 1994; Roux and Karplus, 1994), and the light-sensitive rhodopsin receptor protein (Litman and Mitchell, 1996; Bloom, 1998; Brown, 1994). Atomistic simulations revealed that the membrane environment directly influenced the conformational energetics of the rhodopsin receptor protein: lipids tending to form lamellar phases did not support the full native-like photochemical functioning of the protein, while cholesterol molecules reduced the photochemical activity of the protein. Specific lipid–peptide interactions similarly distorted the ideal β-helical symmetry of gramicidin A channels, which affected the ability of the channel protein to regulate the flux of ions.

1.3.2 Transmembrane Protein Clustering

While fine-grain simulation techniques have proved useful for discerning the specific interactions of individual channel proteins with their encompassing phospholipids, coarse-grain potentials like the Martini force field have made it possible to investigate how multiple integral membrane proteins interacted with each other in a lipid environment. Rhodopsin receptors were found to self-associate, and self-assemble in a range of different lipid bilayers, owing to non-specific lipid mediated forces, and specific side chain-side chain interactions at the protein surface (Periole et al., 2007). The simulations helped to refute the classical view of rhodopsin as a mobile monomer, and explained atomic-force microscopy images that showed rhodopsin proteins arranged in rows that were 25–50 nm long (Fotiadis et al., 2003). The clustering of integral proteins within membrane cores has since been proven to be a more general phenomenon, with a wide range of α-helices, β-barrels, and obligate heterodimers self-assembling in different lipid systems (Chng and Tan, 2011; Kalli et al., 2011; Marius et al., 2012; Sengupta and Marrink, 2010; Psachoulia et al., 2009; Monticelli et al., 2010; Bond and Sansom, 2004). Interestingly, the simulations show that β-barrel proteins tend to form one-dimensional string like assemblies, whereas α-helices preferentially form two-dimensional clusters.

1.3.3 Membrane Adaptation Around Protein Clusters

One of the most important results of these protein simulations was a better understanding of the interface between integral membrane proteins and the surrounding expanse of the membrane. Through the use of molecular simulation, it was demonstrated that single α-helices and β-barrels have little effect on the surrounding lipid dynamics, but that clusters of proteins can significantly perturb the local membrane properties. For example, OmpF helices had little effect on the local lipid environment when they roamed the bilayer as isolated monomers, but induced significant changes in acyl tail order parameters when they bundled into tetramers and hexamers (Bond and Sansom, 2004). Later simulations demonstrated that the clustering of transmembrane channel proteins could even mediate the complete lateral reorganization of a multi-component membrane model. For example, when WALP peptides were incorporated into compositionally heterogeneous multi-component membranes of saturated and unsaturated phospholipids, the transmembrane α-helices clustered into discrete bundles, which partitioned the membrane surface into distinct liquid-ordered and liquid-disordered domains (Domański et al., 2012). Additional membrane adaptations in the vicinity of transmembrane protein clusters include changes to the hydrophobic thickness, the lipid lateral diffusion rates, the area per lipid values, as well as the formation of toroidal pores, increases in membrane buckling, and the triggering of phase changes and fusion events (Risselada et al., 2011; Xu et al., 2011; Louhivuori et al., 2010; Ollila et al., 2011; Monticelli et al., 2008).

1.4 Sterols

Sterols play an essential role in modulating bilayer structure and dynamics. In eukaryotes, cholesterol molecules are closely connected to the regulation of membrane fluidity and the formation of lipid rafts (Simons and Ikonen, 1997), while fungal sterols have putative roles in protecting membranes from the pernicious effects of metabolic by-products (Sahm and Bringer-Meyer, 1987). Given the incredible importance of sterols in the maintenance of membrane structure and function, the molecules were incorporated into atomistic membranes alongside proteins and phospholipids, leading to important discoveries about their interactions with lipids.

Most notably, the cholesterol molecules were found to partition multicomponent membrane models into distinct liquid-ordered and liquid-disordered domains (Sodt et al., 2014). The phase segregation was induced as the cholesterol molecules interacted with their neighboring molecules to adopt a specific multilobed distribution (Martinez-Seara et al., 2010). This emergent three-dimensional structure sensitively depends on specific properties of cholesterol molecules, including their planarity and the flexibility of their off-plane methyl groups, providing some rationale for the disparate phase separating characteristics of seemingly similar sterols and hopanoids. Additionally the simulations revealed that the cholesterol molecules increase the order parameters of lipids in their immediate vicinity, and tend to reduce their area per lipid values (Khelashvili et al., 2010). The fine-grain simulations paved the way for the production of accurate coarse-grain cholesterol models (Melo et al., 2015; Daily et al., 2014), which could be mixed with lipids and proteins to construct realistic eukaryotic membranes.

1.5 Eukaryotic Membranes

With an accurate parameterization of cholesterol and an ever-increasing suite of topologies for related organic molecules, increasingly sophisticated representations of eukaryotic membranes are being simulated at the coarse-grain level. One of the most recent high-resolution models of the eukaryotic mammalian membrane consists of 63 different lipid species, combining 14 types of headgroup and 11 types of tail asymmetrically distributed across two leaflets (Fig. 1.2) (Ingólfsson et al., 2014). This membrane model is an order of magnitude more complex in its composition than any other membrane simulated to date. The simulation of this incredibly complex lipid bilayer provided an unprecedented view of the eukaryotic cell membrane that was otherwise unattainable. The study revealed that non-ideal lateral mixing was a common occurrence for the component lipid species. The lipids tended to form transient nano-domains within the inner and outer leaflets, but the coupling of liquid-ordered domains across the two leaflets was not uncommon. In the inner leaflet, distinct phosphoinositides domains were most commonly observed, while gangliosides were found to aggregate in the outer leaflet. The formation of these transient glycolipid domains was later correlated to local curving effects in another study (Koldsø et al., 2014), suggesting that mammalian membranes are most commonly laced with nanoscale arcs and grooves in vivo.

Figure 1.2 Panel A shows a model eukaryotic plasma membrane. The constituents of the membrane are summarized in the pie charts in panel B ( Ingólfsson et al., 2016).

In addition to the simulation of cellular membranes, atomistic and coarse-grain molecular dynamics have also been used to explore the characteristics of the membranes that envelop single, small, prokaryote organelles. Most interesting are the simulations that explained specific organelle function as an emergent property of membrane dynamics. For example, when curvature-inducing proteins were adsorbed onto the surface of a membrane model for endoplasmic reticulum, they experienced attractive interactions due to local bilayer buckling, which mediated the formation of protein clusters (Reynwar et al., 2007). The initial aggregating action of the organelle was the emergent product of simple protein–lipid interactions. Additional molecular dynamic simulations of complete ribosome subunits allowed theoreticians to calculate the free energy barriers associated with subsequent stages of peptide translocation and protein assembly (Bock et al., 2013).

Coarse-grain simulations were likewise performed to determine how thylakoid membranes are organized, and thereby elucidate important details about the photosynthetic function of chloroplasts. Importantly, Martini coarse-grain modeling revealed that thylakoid membranes have an uncommon propensity for forming the inverted hexagonal phase (Fig. 1.3) (van Eerden et al., 2015), which was proposed to facilitate the flip-flop of antheraxanthin, and regulate the activity of the violaxanthin cycle (Goss et al., 2007; Jahns et al., 2009; Schaller et al., 2010). Meanwhile, coarse-grain and all-atom simulations explained how transmembrane protein cofactor complexes initiate the photosynthetic process and how they diffuse through crowded chromatophore membranes. The all-atom simulations identified the position and functioning of protein channels that control different water oxidation mechanisms (Linke and Ho, 2014; Vassiliev et al., 2010), while the coarse-grain simulations described the motilities of quinone molecules that are crucial for completing energy conversion steps in the photosynthesis process (de Jong et al., 2015). Taken together, the simulations provide a more complete picture of how specific protein and lipid architecture and organization manages to optimize the photosynthetic functioning of thylakoid membranes.

Figure 1.3 Coarse-grain (Martini) model of a thylakoid membrane from cyanobacteria. Phosphatidylglycerol lipids are colored green, digalactosyldiacylglycerol lipids are colored white, monogalactosyldiacylglycerol lipids are colored blue, and the two types of sulfoquinovosyldiacylglycerol lipids are colored yellow and red.

1.6 Prokaryotic Membranes

Some of the most structurally diverse membranes are found within the family of single-celled prokaryotic microorganisms. Extreme diversity in lipid composition and cell wall structure has helped these primordial life-forms to thrive in the most inhospitable of environments from freezing arctic tundra, to heated hydrothermal vents, and even symbiotically, within the bodies of other organisms (Lauro and Bartlett, 2008; Madigan and Orent, 1999; Nap and Bisseling, 1990). Molecular simulation studies have thus far provided important insights into the characteristics of prokaryotic membranes, and on-going simulations are being used to address fundamental questions relating to the growth, and resilience of these microbes.

Gram-negative bacteria have one of the most complex cell envelope structures among all of the prokaryotes. The bacteria have a cell envelope that contains an inner cytoplasmic bilayer, and an outer membrane, which contains proteins, phospholipids, and lipopolysaccharides (Fig. 1.4). The two membranes are separated by the periplasm or periplasmic space, which contains peptidoglycan, a sugar-peptide polymer, this provides the cell with rigidity and mechanical strength (Beveridge, 1999). The periplasm is also host to a range of proteins. Atomistic simulations have shown that the outer membrane has many peculiar properties when compared with eukaryotic lipid systems. For one, the structural integrity of the membrane depends acutely on the availability of divalent metal ions. In the absence of metal ion coordination, the membrane completely disaggregates on a picosecond timescale. Simulations also indicated that the outer membrane is less fluid than conventional phospholipid systems. The lipopolysaccharide molecules achieved unusually tight packing due to multiple stabilizing electrostatic interactions with metal ions, which immobilized the lipids and dramatically decreased surface accessibility to solvent (Wu et al., 2013; Soares et al., 2008; Soares and Straatsma, 2008).

Figure 1.4 Panel A shows a coarse-grain (Martini) model of the E. coli outer membrane. The outer leaflet is composed of LPS and the inner leaflet contains a mixture of phospholipids. Carbon tails are colored cyan, phosphate groups are colored brown, glucosamine and glycerol groups are colored pink, choline head groups are colored blue, and the remaining core saccharide sections of LPS are colored yellow. Panel B shows a CG LPS molecule and panel C shows a POPE phospholipid, color schemes as panel A.

In the case of Gram-positive membranes, molecular simulations have recently addressed fundamental questions relating to the growth and organization of the thick (20–35 nm) peptidoglycan network, which encases their single phospholipid membranes. By elucidating the mechanisms behind a distinct curling effect observed in three-dimensional electron cryo-tomography images, atomistic simulations were used to show that peptidoglycan polymers run circumferentially around Gram-positive cell bodies, providing support for a disorganized, layered model of the cell wall structure (Beeby et al., 2013). Coarse-grain simulations subsequently provided an explanation for how peptidoglycan layers are remodeled during the growth of cells. Local coordination of peptidoglycan remodeling enzymes sufficed to maintain the shape and structural integrity of the bacterial exoskeleton in molecular simulations, providing insight into the basic morphogenesis of Gram-positive and Gram-negative bacteria (Nguyen et al., 2015).

Extremophiles are some of the most durable life-forms owing to the intercalation of atypical tetraether lipids in their outer membranes. The lipids consist of two polar head groups, joined by two long hydrocarbon chains. The hydrocarbon chains can have a relatively simple saturated alkyl structure in-line with conventional phospholipid tails, but other mimetics with branching modifications are quite common (Longworthy et al., 1982). Molecular dynamics simulations revealed that the low permeability and unique durability of archaeal membranes could be ascribed to the tight packing of the tetraether lipid tails, which suppress fast-fluctuating void space formation (Chugunov et al., 2014; Shinoda et al., 2005). More recently, simulations showed that modifying the links between the tetraether lipid tails could drastically alter archaeal membrane properties, making tetraether lipid systems suitable for the design of artificial membranes and vesicles with increased durability and carrying capacity (Bulacu et al., 2011).

1.7 Viral Membranes

In general, viruses are much smaller than prokaryote and eukaryote life forms. The infectious agents are so small (20–1500 nm scale) that molecular dynamics studies regularly consider all of the atoms that comprise entire viral particles, providing a view of hierarchal processes and large-scale emergent phenomena that are inaccessible in simulations of smaller viral subunits and fragments. For example, recent simulations of a complete Influenza A virion revealed that the overarching interactions of component Forssman glycolipids are responsible for the even spacing of spike proteins on the viral surface (Fig. 1.5) (Reddy et al., 2015). When the glycolipids are included into a model for the virus, the spike proteins were suitably spaced to facilitate their crosslinking by immunoglobulin G (IgG) antibodies. Aside from affecting antibody-mediated immunity, the overarching interactions of Forssman glycolipids were speculated to confer physical robustness to the viral particles by reducing the mobility of proteins and lipids.

Figure 1.5 Snapshot of influenza A in water after ∼5 μs of simulation. The spike glycoproteins are colored blue, lipids are colored orange, and the glycans of the Forssman glycolipids are colored green. The diameter is ∼84 nm.

Moving forward, it will be interesting to simulate the interaction of Influenza A viruses with complex mammalian membrane models. Simulations exploring the pathogenicity of component viral fragments have already indicated that surface level hemagglutinin proteins can promote positive membrane curvature (Fuhrmans and Marrink, 2012). Simulations involving entire viral particles interacting with host membranes will resolve the full effects of the multiple affinities formed between surface level viral proteins and mammalian membranes at the host–pathogen interface.

Coarse-grain simulations were additionally used to model the complete dengue virion, including its complex lipid bilayer and peripheral E and M envelope proteins. The simulations revealed that protein–lipid interactions confer raft-like robustness to the cholesterol-free bilayer, providing resilience from environmental pressures and perturbations (Ayton and Voth, 2010). Other than this, a combination of coarse-grain and fine-grain modeling techniques were used to explore the structure of the immature HIV-1 virion. The multiscale simulations revealed the existence of an incomplete hexameric lattice formed from hexameric bundles of Gag polypeptide domains.

1.8 Membrane Fusion

Membrane fusion was one of the first applications of coarse-grain molecular modeling given its pertinence to fundamental processes in cell biology, such as viral infection, endocytosis and exocytosis, and fertilization. From the outset, the coarse-grain simulation method successfully unraveled the molecular details of the process of membrane fusion, including the initial merging of apposed membranes, and the form of fusion intermediates (Marrink and Mark, 2003, 2004; Kasson and Pande, 2007). But as time progressed and fusion pathways became well established, efforts were directed at calculating the molecular free energy barriers involved in stalk formation, and investigating the role of fusion promoting peptides and polymers (Smirnova et al., 2010; Raudino et al., 2012).

The simulations showed that the prevailing notions of protein mediated membrane fusion were incomplete. Fusion promoting molecules like the SNARE complex did more than merely trigger fusion events by forcing opposing membranes into close proximity, the complexes overcame subsequent fusion barriers, and played an important role in actively guiding the membrane fusion reaction. It is now realized that the fusion process occurs as the SNARE complex releases mechanical stress to drive the expansion of a small stalk intermediate, which bridges the apposed membranes. The elucidation of the SNARE complex's full functional diversity helped to explain why so many molecular components are recruited in its functioning (Risselada and Grubmüller, 2012).

1.9 Graphitic Nanomaterials

Molecular dynamics proved useful for elucidating important information about lipid bilayers as membrane models became increasingly complex, but the simulation technique had still more to offer. The simplicity and versatility of molecular dynamics encouraged studies that explored the interaction of complex membranes with a range of different organic and inorganic compounds.

Some of the most noteworthy simulations sought to decipher how novel nanomaterials interact with cellular membranes, given that many of these compounds are becoming more common, despite their cytotoxic effects being unknown. Graphitic nanomaterials, including zero-dimensional fullerenes, one-dimensional nanotubes, and two-dimensional nanosheets were placed in close apposition with eukaryotic and prokaryotic membrane models to elucidate their impact on human health or bacterial communities.

Starting with the molecular dynamics simulations of graphene and its different derivatives, it was discovered that the carbon nanosheets had the capacity to degrade the inner and outer membranes of Gram-negative bacteria. This degradation was mediated by the destructive extraction of phospholipids, once the nanosheets had intercalated among the inner and outer lipid membranes (Tu et al., 2013). The disruptive extraction of phospholipid molecules led not only to a sparser membrane, but also to a deformation of the basic bilayer structure. Additional simulation studies revealed that the specific orientation adopted by nanosheets in phospholipid membranes depends on their on their specific size and oxidation state, suggesting that the degree of membrane deformation may be sensitive to these physical and chemical properties (Wang et al.,