In recent years, there has been an unprecedented interest in investigation of biological phenomena by means of computational -rather than experimental- lab methods. Molecular dynamic simulation has shown great promise in investigation of biological processes and design of novel potential pharmaceutical agents. The importance of computational methods is highlighted when we consider the certain limitations of experimental works such as CD spectroscopy, AFM measurements and fluorescence.
However, a common limitation in conventional molecular dynamic simulations is the fact that they are not able to investigate the biological phenomena in longer time scales that enable us to visualize mixing systems reaching equilibrium. Therefore, many techniques are being introduced every day to speed up the computation in order to increase the time scale in which the phenomenon is being investigated. Based on this consideration, coarse graining (CG) methods were introduced as a suitable alternative for the conventional "all atom" simulation.
Despite prodigious efforts and much success in design and development of novel and potent antibiotics, the problem of antibiotic resistance is still a major drawback in chemotherapy of infectious diseases and there has been an increasing interest in the use of alternative agents that by-pass the common problem of antibiotic resistance.
There are a number of reasons that make antimicrobial peptides (AMPs) interesting candidates for drug design and development. AMPs have shown non-specific antimicrobial selectivity which means that they are generally active against both gram positive and gram negative bacteria and even fungi. However, AMPs are shown to be active against pathogens resistant to traditional antibiotics [A], which means that they could be considered as excellent potential new class of antibiotics as they are known to trigger little resistance, compared to the conventional chemical antibiotics. These factors make AMPs suitable candidates for design and development of novel and potent antimicrobial agents.
A number of simulation studies have been carried out on AMPs including melittin [B], magainin [C], and Arenicin-2 [D] while few information is available on crabrolin. Crabrolin has two main characteristics that make it interesting for in-depth investigation of its mechanism of action. First, it has a net charge of +3 (compared to the majority of AMPs that have a net charge of +4 to +6) and second, it is one of the shortest AMPs found in nature with a small size of only 13 amino acid residues (compared to melittin with 26 residues). These unique properties made crabrolin interesting candidate for our simulation study.
Considering the emerging problem of antibiotic resistance, in-depth studies on the mechanism of AMPs and their interaction with lipid bilayers would be of great value. Therefore, the aim of this study is to investigate a less-studied AMP -crabrolin- and its possible interactions with the lipid bilayer, using coarse grained simulation methods.
Lipids and membranes
Lipids are essential components of the biological membranes. They act as a highly permeation-selective barrier, which separates the cell organelles and nucleus from the cytoplasm. Moreover, they are actively involved in a large number of metabolic processes [1,2]. The so-called fluid mosaic model proposed by Singer and Nicolson in 1972 indicates that the proteins are present inside and not on the outside of the lipid bilayer and the membrane can be regarded as a two dimensional fluid in which lipids and proteins diffuse more or less freely [3]. The membrane proteins are floating in a sea of excess lipid molecules organized in a lipid bilayer. The stabilizing force in this system is a variety of intra-molecular and inter-molecular hydrogen bonding, van der Waals interactions, and hydrophobic interactions [4]. Changes in the biological environment, such as change in temperature, pH, or solvent, may disrupt these relatively weak forces, leading to significant alterations in structure, and hence in function. The structural properties of lipid membranes have been the subject of intensive investigations in recent years and the precise physical quantities of bilayer have been discussed and reported before [5].
The building blocks of lipids are fatty acids. Each fatty acid consists of a long hydrophobic hydrocarbon chain called the "tail" and a hydrophilic carboxylic acid called the "head" group. According to the type of fatty acid hydrophobic chain, fatty acids may be considered as either "saturated", "unsaturated", or "poly unsaturated". Saturated fatty acids contain no double bonds while unsaturated and poly unsaturated amino acids contain one or more double bonds, respectively. There are many types of lipids in biological membranes such as phospholipids, sphingolipids (which contain a long chain and an amino alcohol sphingosine as the head), glycolipids (which contain sugar head groups) and steroids (such as cholesterol, which consist of tetracyclic cyclopentaphenantherene skeletons). It is also known that in the fluid mosaic model, lipid bilayers consist of a particular ratio of various lipid types and proteins [6].
Phospholipid bilayers
According to the fluid mosaic model [3], lipids form a two-dimensional sheet consisting of two layers of closely packed lipids in which the hydrophobic tails are directed to each other, while the hydrophilic head groups are oriented towards the aqueous phase. As mentioned earlier, biological membranes consist of many different types of lipids. The most abundant type is the phospholipid bilayer which has two hydrophobic fatty acyl tails and a hydrophilic head group connected through phosphate group to a glycerol backbone. Phospholipid bilayers are considered as the elementary components of bio membranes which separate the protoplasm, from the extra cellular environment. The lipid bilayer is also considered as the fundamental permeability barrier to the passage of polar molecules into or out of the cell. However, as we will discuss later, the stability of the bilayer is very dependent to temperature, and that changes in fluidity and permeability of membranes, denaturation of proteins, and the folding of helices occur within very narrow temperature ranges [7, 8].
DPPC and DOPG
Phosphatidylcholines are considered as one of the major lipid components in many membranes. Among which, dipalmitoylphosphatidylcholine (DPPC) is one of the more studied lipids, and has been used extensively both in experimental work and simulation studies [9,10,11]. DPPC is a major constituent of the pulmonary surfactant (almost 40 wt %) which is able to form a tightly-packed gel phase when compressed at physiological temperatures. It is also the lipid most responsible for lowering surface pressure to near zero levels [12]. It is worth noting that Pulmonary surfactant deficiency is considered as an important contributing factor in the pathogenesis of neonatal respiratory distress syndrome (NRDS), acute respiratory distress syndrome (ARDS), and diseases of small airways such as asthma and bronchiolitis [13].
1, 2-dioleoyl-Sn-glycero-3-[phospho-rac-(1-glycerol)] (DOPG) is a synthetic anionic lipid with an unsaturated hydrophobic acyl chain. In contrast to DPPC, few investigations have been yet carried out on DOPG bilayers [14]. The interaction of DOPG with saposin C [15] and a number of antimicrobial peptides [16] has been investigated before. In addition, The Molecular dynamics simulations of a number of antimicrobial peptides in DOPG Bilayers have been carried out [17].
Physical properties of Phospholipid bilayers
The membrane potential
The "transmembrane potential" (∆Ψ) is referred to the electrochemical gradient which exists as the result of different extents and rates of proton efflux across the lipid membrane. The membrane potential enables cationic peptides to be electrophoretically conducted to the non polar region of the membrane environment, which reduces the energy barrier for pore formation [6]. The normal potential value for bacterial membranes at the logarithmic phase of bacterial growth generally varies between -130 to -150 mV, while in mammalian cells membrane, this amount differs from -90 to -110 mV [6]. This difference in ∆Ψ enables the antimicrobial peptides to act selectively against prokaryotic cells since it has been shown that there is a correlation between the activity of antimicrobial peptides and the reduction in transmembrane potential [6].
Fluidity
Fluidity or the relative rotational or lateral diffusion rates of the membrane constituents is perhaps the most obvious physical feature of a membrane which is considered as an essential requirement for its biological function [18,19]. A number of techniques have been developed to provide information about the membrane fluidity [20].
It is now well understood that there are different phases that lipids can take based on the temperature. These phases can be monitored by techniques such as nuclear magnetic resonance (NMR), electron spin resonance (ESR), differential scanning calorimeter (DSC), fluorescence, etc [21]. At lower temperatures, most phospholipids are in sub gel or Lc phase, in which the hydrocarbon tails are highly ordered [22]. With an increase in temperature, the bilayer, transforms to a lamellar gel phase. Depending on the structural composition of the lipid head group, this gel phase is Lβ phase (such as phosphatidyl ethanol amines) or the Lβ Ì phase (such as phosphatidyl cholines). In Lβ and Lβ Ì phases, the bilayer is more hydrated than in the Lc phase and the hydrocarbon tails are still ordered, but less ordered than in Lc phase. In the Lβ phase, the tails are ordered parallel to the bilayer normal, while in the Lβ Ì phase the tails show a tilt angle with respect to the bilayer normal. At higher temperatures (the physiological temperature), the gel phase undergoes a transition to the fluid (or Lα or the liquid crystalline phase) in which the tails are disordered and do not show any tilt. This Lα phase is physiologically considered as the most important phase [23]. The extent of the fluidity of membrane depends on the nature of acyl chain presented in lipid. The gel-to-liquid phase transition temperature (also known as Tm) is a function of the membrane lipid composition. The transition to the liquid phase occurs when the energy added to the membrane is enough to overcome the van der Waals interactions between the hydrocarbon chains. This transition increases the rotational mobility around carbon-carbon bonds, which gives them more fluid-like conformations. In addition to the change in temperature, the phase transition also occurs by change in pressure and hydration. It also depends on the structural properties of the constituent lipids such as the length of the hydrocarbon tails, the number of double (unsaturated) bonds in the acyl chain, and the composition of the head group [24]. Tm decreases with the decrease in chain length and the presence of cis unsaturated double bonds in the acyl chain or branched methyl or hydroxyl groups. The reason for that is that the double bonds induce kinks in the conformations of the phospholipid tails and such bended chains organize less easily in a crystalline way [25].
The regulation of the lipid phase transition in response to temperature is observed in poikilothermic organisms, such as bacteria and plants. Without regulation, an organism shifted from a high to a low temperature would have membrane lipids with sub optimal fluidity, which results in improper function of the membrane. During the regulation, a proportionally more amount of unsaturated fatty acids (or fatty acids of analogous properties) are introduced into the membrane lipids with the increase in temperature [26].
In addition to the phase transition properties of lipids, lipids can also adopt different liquid structures on hydration; a phenomena which is known as lipid polymorphism. These structures include bilayer, hexagonal and micellar.
The fluidity of the lipid bilayer could be affected by a number of parameters, including the presence of water molecules, cations, sterols, proteins and polypeptides. The presence of cholesterol in phospholipid bilayers tends to increase the extent of hydration of the polar groups which leads to a higher extent of membrane fluidity [21]. The explanation was thought to be due to the fact that cholesterol spaces out the polar head groups of the phospholipids thereby creating more space for the water molecules to orient. In addition, some chemicals such as phenothiazine derivatives may alter the fluidity of the lipid membrane [27]. Alteration in fluidity of bilayers may cause severe damages such as Alzheimers disease and Down syndrome [28]. The phase behavior of lipid bilayers is fully discussed by Kranenburg and Smit [29].
Elasticity
Several elements contribute to the visco-elastic properties of the lipid membrane including the lateral tension, curvature or bending elasticity, shear elasticity, and rubber-like elasticity [30,31]. In 1973, Helfrich proposed that the lipid bilayer could be considered as a thin elastic sheet that undergoes three classical modes of deformation: stretching, shearing and bending. He deduced the expression for the elastic energy of curvature per unit area of the membrane as [32]:
gc = (1/2) k(c1 + c2- c0)2 + ḱÌc1c2 (1)
where c1 and c2 are two principal curvatures of the surface of the membrane, and the constant c0 is called the "spontaneous curvature of the membrane surface". The constant k is the bending rigidity and ḱ is the elastic modulus of the Gaussian curvature (K = c1c2). By comparison with the curvature elasticity of liquid crystals, both k and ḱ are found to be of order of the product of the elastic constants of lipid bilayer and the thickness of the membrane.
The total bending energy of the membrane (F) is often referred to as the total bending energy of the membrane [31]:
(2)
The constant c can be attributed to the mean curvature of the membrane with asymmetric chemical composition of layers in bilayer or the environment and is closely related to the spontaneous splay of the liquid crystals. Equation (2) together with (1) is called the Helfrich free energy of lipid membranes and is generally recognized as the basic quantity in dealing with the mechanical behavior of biomembranes in the liquid crystal phase [33].
Tension
The bilayer membrane maintains a specific lipid packing density with an optimal surface pressure in the order of 30 mN.m-1[34].The change in the bilayer tension occurs when the bilayer is curved. Increasing the lipid spacing by osmotic swelling, for example, is strongly resisted, and leads to rupture when the membrane is strained slightly above its optimal packing. Compression within the plane of the membrane would also be resisted, but the membrane buckles out of plane before significant compression occurs [34].
The surface tension of a compressed or expanded planar bilayer can be described as a function of the relative change of the bilayer area (∆A/A)
ץ= ץ0+ka (∆A/A) (3)
where ka is the compression-expansion modulus which describes the surface tension change in terms of the relative bilayer area change(×¥)[35]
Thermodynamics
A bilayer may be considered as an elementary system with an adiabatic wall that separates two closed systems. Therefore, it is expectable that the thermodynamics of the system changes as the energy or the matter flows across the membrane. A central thermodynamic potential which describes the stability of the lipid bilayer membrane, is the (excess) grand potential given by Ω and is defined by [36]:
(4)
in which U is the total energy of the system, S is the entropic contribution, T the temperature, are the chemical work terms of all molecules and pV is the volume work, with V the volume of the lipid vesicle and p the pressure difference on both sides of the lipid bilayer. The surface area of the bilayer is denoted by A. This bilayer grand potential Ω has is affected by the hydrophobic tail, the interfacial region, and the head group region. The grand potential of the hydrocarbon tails (Ωt ) is determined by van der Waals interaction (attractive effect) and the conformational loss of the aligned and extended chains in the bilayer (repulsive effect). The grand potential of the head group region Ωh depends on several factors, but in general, a repulsive contribution dominates. Indeed the head group repulsion is regarded as the stopping mechanism of the self assembly. The stopping force depends on the charge of the head groups, the hydrophilicity of head groups, type of counter ions, etc [37, 38].
Diffusion
It is now well established that lipids and proteins are asymmetrically distributed in bilayer membrane. Studies on membrane model systems showed that the lateral motion of lipids strongly depends on their chemical structure, physical state, and the lipid-to-cholesterol and lipid-to-protein ratios [39]. Investigating the lateral and transversal motion of lipids and proteins can provide useful information on their distribution within the membrane. The lipid lateral diffusion coefficient can be directly measured in macroscopically aligned lipid bilayers using NMR spectroscopy [40]. The lateral diffusion coefficient for most lipids is in the order of 10-7-10-8 cm2/s; which means that it generally takes about 10-7-10-8 seconds for a lipid molecule to diffuse within a 1cm2 plane of the membrane [41]. The lateral diffusion coefficient of the lipid bilayer D is obtained from the formula
D=
Where x(t) is the center of mass of every single lipid [E].
It is now well known today that the diffusive behavior of lipid bilayers can change upon insertion of a number of elements. For instance it has been suggested that the presence of NaCl results in a significant decrease in DL value of DOPG bilayer [F]. Peptides has shown controversial effects on the diffusive property and fluidity of the lipid bilayers. It has been shown that a cationic peptide known as tridecapeptide a-melanocyte stimulating hormone, has modulation effect on both packing and the hydration of the DMPG lipid which means that the peptide was able to increase the fluidity of the membrane [G]. On the other hand, β-amyloid peptide-25-35 was found to decreases the fluidity of mouse brain membranes in a concentration dependent manner [H]. It is also suggested that binding of the peptide and pore-forming are two distinct steps, and the latter is consistent with the increase in fluidity and the increase in permeability.
Permeability
Permeability is considered as one of the most biologically important functions of lipid bilayers and is generally defined as the property of the cell membranes that regulates the exchange of matter and energy between the cell interior and the external environment [21]. Lipid membranes show different extents of permeation for molecules depending on both the partition coefficient of the permeating molecules between the aqueous phase and the hydrocarbon region of the membrane and the molecular weight of the permeating molecules.
Two main underlying mechanisms have been proposed for permeation process by which ions and small polar molecules cross phospholipid bilayers. In first mechanism called "solubility-diffusion (SD) model" [42], permeation occurs in three steps: partitioning from the aqueous phase into the bilayer, diffusion across the bilayer, and partitioning from the bilayer into the aqueous phase on the other side. Another alternative mechanism of the permeation is permeation through transient pores in the bilayer, which is considered as the dominant pathway for cations under certain circumstances [43]. To date, much data is available on the permeation of different elements such as zinc [44], mercury [45], proton and potassium [46] across the membrane. These data can be obtained from osmotic, radioactive tracer, and NMR measurements [47].
The mathematical expression of permeation (P) is provided by Fick s law where:
(5)
Where dn/dt is the number of molecules per unit time, A is the area of the membrane, and is the difference in the concentration of material across the membrane [21].
The theory of passive permeability through lipid bilayers uses the solubility diffusion model in which the bilayer is assumed as a single layer of hydrocarbon of thickness d. This leads to the following formula:
(6)
where K is the partition coefficient of the solute into the hydrocarbon core of the lipid bilayer and DC is the coefficient of diffusion of the solute in the same environment [48]. For small solutes, DC is often assumed to be weakly dependent upon solute. The strong dependence of P, varying over nearly six orders of magnitude for different solutes for a given lipid bilayer, is interpreted as the dependence of K on the solute [48].
Antimicrobial peptides
Antimicrobial peptides (AMPs) are small peptides which protect the host against a variety of microorganisms. These peptides are produced basically by all groups of organisms including bacteria, insects, plants, vertebrates and mammals. They represent an evolutionarily conserved component of the innate immune system which is generally found among all classes of life [49]. AMPs are considered as a potent class of antibiotics with a wide range of antibiotic activity (Gram negative and gram positive bacteria, mycobacteria, enveloped viruses, fungi and cancer cells). In addition to their antimicrobial efficiency, AMPs have shown significant immunomudulatory activity [50].AMPs are expressed on the primary barriers of the organism such as skin and mucosal epithelia, preventing the colonization of pathogens in host tissues [51]. In addition, these peptides are stored in granules within phagocytes, where they assist in the killing of engulfed microorganisms [52].
Most of AMPs share some common characteristics, such as their low molecular mass (2-5 kDa), the presence of multiple lysine and arginine residues and an amphipathic nature. AMPs have amphipathic properties which allow them to penetrate into the membrane lipid bilayers efficiently. However, it is well documented that many of AMPs are in their unstructured or extended form in free solutions, but they fold into their final configuration upon binding to biological membranes. It has also been shown that the toxicity of AMPs largely depends on the conformation of the peptide so that in their cyclic form, they are less efficient in their initial binding to the phospholipid membrane. Other biological functions of AMPs have been described recently, including: neutralization of endotoxins, chemokine-like activities, immunomodulating properties, and induction of angiogenesis and wound repair [53, 54]. Taken together, the versatile properties of AMPs make these ancestral peptides attractive candidates for novel therapeutic purposes.
Mode of action
The exact mechanism by which AMPs exert their antimicrobial properties is yet unknown, but it is generally accepted that cationic AMPs exhibit their antibiotic effect mainly by causing multiple defects in cell membrane of the target cells. They combine with cell nucleoproteins, phospholipid head groups or other negatively charged surface constituents of bacteria or viruses, and disrupt important cell functions [55]. These defects may result in imbalance in membrane permeability. There are a number of different mechanisms underlying the membrane permeabilization caused by AMPs. The basic concept in all these mechanisms is the electrostatic interactions that occur between the AMPs and the bacterial membranes [6]. These mechanisms mainly include:
In Toroid-pore model, the antimicrobial peptide helices penetrate into the membrane and cause lipid monolayers to bend continuously through the pore so that the water core is lined by both peptide and lipid head groups. This type of transmembrane pore is induced by magainins, protegrins and melittin [56].
In Barrel-Stave pore forming model, the hydrophobic portion of the peptide is inserted into the membrane to an extent corresponding to the hydrophobicity of the membrane outer leaflet [57].
In Wormhole mechanism, peptides in the extracellular environment take on an α-helical structure as they interact with the charged and hydrophobic bacterial membrane [57].
The carpet model, in which a high density of peptides accumulates on the target membrane surface. Examples are cecropin [58] and melittin [59]
Other suggested mechanisms include the formation of ionic channels, and the activation or blockage of intracellular targets after bacterial membrane permeabilization [60,61]. However, studies suggest that apart from membrane permeabilization, AMPs exhibit their antimicrobial effects via impairing the intracellular functions of the cells as well.
Classification of antimicrobial peptides
To date, a large number of antimicrobial peptides have been characterized which fall into one of these four major classes:
Anionic peptides (such as Dermcidin from humans [62]).
Linear cationic α-helical peptides (such as andropin,moricin and ceratotoxin from insects).
Cationic peptides enriched for specific amino acids (such as abaecin from honeybees [63]).
Anionic and cationic peptides that contain cysteine and form disulphide bonds (such as protegrin from pigs) and defensins from humans, cattle, mice, rats, pigs, goats and poultry [64]
Anionic and cationic peptide fragments of larger proteins (such as Lactoferricin from lactoferrin).
Different properties of the major classes of antimicrobial peptides have been recently discussed by Guerra et al. [65].
Physical properties of alpha helical AMPs
It is well known that helical AMPs are in their unstructured conformation in their free, non-bound form. However, after binding to the microbial membrane, these unstructured peptides undergo phase transition to amphiphatic-alpha helical structures [6]. The net charge for helical AMPs is in the range of +2 to +9 (in contrast to normal peptides with a charge of +4 to +6) [6]. This positive charge is important for the introduction of AMP into the bacterial membrane.
In terms of hydrophobicity, most AMPs have high amount of hydrophobic residues (on average %50) which allow them to penetrate into the microbial membrane effectively [6].
Crabrolin
Crabrolin is a member of cationic AMPs and one of the Innate immunity defense peptides which is isolated from venom sacs of the European hornet, Vespa crabro and its analogs [66]. It has a short amino acid sequence of 13 residues (FLPLILRKIVTAL-NH2) and an alpha helical secondary structure. As seen from the sequence, crabrolin has a high amount of hydrophobic residues (9 out of 13 amino acid, %69). It has been chemically synthesized and its structure in solution has been determined by NMR spectroscopy.
In addition to its antimicrobial activity, Crabrolin has shown to have hemolytic activity. It also causes degranulation of mast cells, release of histamine from rat peritoneal mast cells, and lysis of erythrocytes [67]. Crabrolin has also shown to activate phospholipase A2 from different sources, compared to melittin that only activates bee venom phospholipase A2 [68, 69]. The biological properties of Crabrolin are basically the same as melittin and mastoparans [70].
The helical conformation of Crabrolin is known to be necessary for its hemolytic activity yet is not a prerequisite for its antibacterial activity [67]. In addition, increasing the content of lysine results in a decreased minimal inhibitory concentration (MIC) of Crabrolin. Since crabrolin is a small peptide with a short amino acid sequence, it cannot span the entire length of the microbial lipid membrane. Therefore, in order to improve its efficacy, it would be desirable to design novel derivatives of crabrolin which have still alpha helical structure but have increased lengths such that they can span the entire membrane.
In our previous studies, we analyzed a database of 88 helical AMPs with lengths of 18-23 amino acid residues, using C# programming. The results showed that the average charge of the analysed AMPs was +2.97, since the charge of crabroline was only +2. Therefore, to optimize the antimicrobial properties of crabrolin, two different substitutions of crabrolin were prepared in which a substitution of Leu10 to Lysine was used to adjust the charge to +3. Lysine was chosen because based on our experiments, lysine is the most abundant amino acid in the middle section of crabrolin with 15.16% frequency.
Two derivatives of crabrolin namely CR(+1) and CR(+2) were designed by adding 1 and 2 turns to the original crabrolin molecule. The mean hydrophobicities in new derivatives were conserved by adding isoleusines with a hydropathy index of 4.5 to increase the mean hydrophobicity. On the other hand, glutamine, with hydrophaty index of -3.5 was used to decrease the hydrophobicity, without changing the charge. Alanines were added to stabilize the helix and to keep the mean hydrophobicity down without increasing the polar angels.
Coarse-grained molecular dynamics
Despite our good knowledge of membrane structure and physical properties, our understanding of the molecular dynamics of the membrane is very limited. This is partly due to the fact that the common molecular simulations can address only very short time and length scales of the dynamic membrane processes, since what one should deal with are processes taking place over time scales of the order of tens or hundreds of nanoseconds, and length scales of the order of molecular size [71].
However, in recent years, a large amount of work have been dedicated to develop novel force fields that use minimal set of variable to model protein dynamics. Among this, there has been a growing interest in the use of coarse grained (CG) simulations as a reliable alternative to all atom simulations.
A coarse grain model is simply defined as any model in which the basic simulation unit is no longer a single atom, but a pseudo atom. A pseudo atom is basically a cluster of atoms which function as the simulation unit and represents an entire residue [72]. The basic underlying reason for coarse graining is that many of the biological processes occur in a time scale that is too long to be studied by conventional atomistic simulations.
The number of atoms in a pseudo atom depends on our needs which means that more "coarse graining" is needed for larger motions and more complex systems. Coarse grained models may vary in the number of atoms which contribute in a pseudo atom. The basic concept is that by reducing the number of the interactions that have to be evaluated for a given system, one can use much longer time steps (e.g. 40 fs for CG rather than 1 fs for atomistic) in the simulation [73]. This will help us to both speed up the simulation process (up to 2-3 orders of magnitude speed up compared to atomistic simulations [74]) and to simulate the dynamics of more complex systems. In addition, coarse grained models could also be built based on the shape rather than the number of residues which is a considerable approach in long-time simulation of more complex systems such as viral capsids [75].
As mentioned earlier, consequence of using coarse grained instead of all atom simulation is that it increases the efficiency and the speed of our system. The reason for that is that even with large-scale computational resources and well-scaling simulation codes, it is still challenging to reach long time scales for macromoleculs [76]. In fact, most conventional simulations of the large systems can not resolve temporal fluctuations smaller than several milliseconds [77]. Therefore, in addition to faster simulations, one of the primary motivations for developing coarse grained models was to simulate these mesoscopic systems for longer time scales in order to achieve more accurate explanations of the experimental observations. For these reasons, there has been considerable interest in the application of coarse grained models to proteins and related biological systems.
It is worth mentioning that the validity of a number of coarse grained models in predicting the folding and dynamics of the proteins, amino acids and lipids have been proved by the comparison to experimental data [78, 79].
Martini force field
The MARTINI force field is a coarse grained force field introduced Marrink et al. for molecular dynamics simulations of bio molecular systems [80]. It utilizes a coarse-graining method that maps each four heavy atoms to one pseudo-atom (four-to-one mapping). This means that almost each four atoms are represented by a single interaction center. (Hydrogen atoms are not considered at all). The exception is for ring-like molecules such as cholesterol, benzene, etc, that are mapped with higher resolutions (three-to-one or two-to-one) [81]. The coarse-grained mapping model for some basic molecules, together with the DPPC lipid molecule as proposed by Marrink and coworkers, is presented in figure 1. In addition, the extension of martini model to all amino acid residues is shown in figure 2. In coarse graining of the proteins, each amino acid residue is modeled by one pseudo-atom for the backbone and one or two pseudo-atom for the side chain according to their size [I]. For instance, glycine is represented by a single sphere.
In martini force field four main types of interaction sites are defined: polar (P, atoms that can easily dissolve in water), apolar (C, hydrophobic atoms), non-polar (N, group of atoms that are partly polar and partly apolar), and charged (Q, ionized groups) [82]. This classification is simply based on the partitioning free energies between polar and apolar phases of a large number of chemical compounds. Each particle type has a number of subtypes, which allow for an accurate representation of the chemical nature of the underlying atomistic structure.
Nonbonded interactions between the pseudo atoms in martini force field are modeled by Lennard-Jones potential as the equation below [83]:
(7)
where i and j are a pair of particles at distance rij. The value of depends on the particle types (it ranges from =5.6kJ/mol for strongly polar groups to =2.0 for apolar groups). The amount of or the L-J parameter is =0.47 for most normal particle types. Charged groups such as the zwitterionic lipid head groups interact via Coulombic energy function as below [84]:
(8)
Where qi and qj are charges of two particles at distance rij and is the relative dielectric constant and =15.
Furthuremore, the bonded interactions between chemically connected sites [85]:
(9)
with the equilibrium distance RB = σ = 0.47 nm and the force constant of KB = 1250 kJ mol -1 nm -2. In recent years, intensive investigations have been carried out on the coarse grained simulation of various systems using novel extensions of martini force field in order to achieve more efficiency in simulation of bio molecular systems [86]. These achievements made it possible to investigate molecular dynamics of systems within micrometer length scales or millisecond time scales [87]. So far, many investigations have been carried out on dynamics of proteins and lipid bilayers such as the simulation of collagen molecule [88], diffusion of lipids in raft-like membranes [71], and the spontaneous separation of the mixture of saturated phosphatidylcholine, unsaturated phosphatidylcholine, and cholesterol into a liquid-ordered and a liquid-disordered phase [89]. Nevertheless, many studies have focused on martini simulation of the dynamics of cholesterol in lipid bilayer, for instance, the cholesterol's orientational preference in different lipid bilayers, and cholesterol's tilt angle with respect to the bilayer normal [90]. It worth mentioning that the extension of martini model to carbohydrates has been recently introduced by Lopez et al. [91].
