ВЫСОКОМОЛЕКУЛЯРНЫЕ СОЕДИНЕНИЯ, Серия C, 2013, том 55, № 7, с. 971-989
УДК 541.64:539.199
COMPUTER SIMULATION OF LIPID MEMBRANES: METHODOLOGY AND ACHIEVEMENTS
© 2013 г. A. L. Rabinovich and A. P. Lyubartsev*
a Institute of Biology, Karelian Research Centre, Russian Academy of Sciences,
11 Pushkinskaya st., 185910 Petrozavodsk, Russia
b Division of Physical Chemistry, Department of Material and Environmental Chemistry, Stockholm University, Svante
Arrhenius väg 16C, S106 91, Stockholm, Sweden
E-mail: rabinov@krc.karelia.ru
Abstract — Rapid development of computer power during the last decade has made molecular simulations of lipid bilayers feasible for many research groups, which, together with the growing general interest in investigations of these very important biological systems has lead to tremendous increase of the number of research on the computational modeling of lipid bilayers. In this review, we give account of the recent progress in computer simulations of lipid bilayers covering mainly the period of the last 7 years, and covering only several selected subjects: methodological (development of the force fields for lipid bilayer simulations, use of coarsegrained models) and scientific (studies of the role of lipid unsaturation, and the effect of cholesterol and other inclusions on properties of the bilayer).
DOI: 10.7868/S050754751307012X
INTRODUCTION
Biomembranes are very complex heterogeneous systems consisting of many different types of lipids, sterols, proteins, carbohydrates and various membrane associated molecules which are involved in a variety of cellular processes; consequently, membranes play an active part in the life of the cell, they exist as dynamic structures. Lipid molecules differ with respect to the type of hydrophilic head-group and occur with a wide variety of hydrophobic hydrocarbon chains of fatty acids (FAs). Usually the most abundant phospholipid in animal and plants is phosphatidylcholine (PC): it is the key building block of membrane bilayers. Cholesterol (CHOL) molecules are essential component of mammalian cell membranes playing an important role in formation of heterogeneites (known also as rafts) which are supposed to be responsible for cell signaling. Knowledge of physical-chemical properties of lipid bilayers is a key element of our general understanding of biomembrane functioning, which is one of the greatest challenging problems in biophysical and biomedical sciences.
A characteristic feature of lipid bilayers is that, in a physiological form, they exist in a liquid crystalline (fluid) state which implies a relatively high degree of disorder. Experimental measurements of structural and dynamical properties are obtained as averages over a large number of lipids and over a certain time interval, which not always can give an unambiguous picture of individual lipids and their interactions.
During the last decades computer simulations have become a well established tool of modern investigations of molecular structure. Monte Carlo (MC) or molecular dynamics (MD) can provide three-dimensional real-time imaging of the system with atomistic-level resolution, and hence can give essential structural and dynamical information which otherwise is hardly accessible by any experimental method. The first attempts of computer simulations of model bilayers composed of amphiphilic molecules with atomistic resolution were made by 30 years ago [1—3]. The amount of works on simulations of lipid membrane systems has increased tremendously, and a number of reviews appeared accounting for this in the past decade [4—15] and more recently [16—30]. The rapid development of the accessible computer power has made simulations of more and more complicated systems feasible, and allowed also increase the size of the simulated systems. Now simulation of an order of hundred fully hydrated lipids during a few hundred nanoseconds can be considered as a routine.
In this review, we give account of the recent development in computer simulations of lipid bilayers covering mainly the period of the last 7 years. About three hundred papers have been chosen but this is a moderate part of the simulation studies performed recently in this active area of research. It is beyond the scope of this review to touch upon other topics and types of membrane systems. Unfortunately, as a result a number of important areas are not represented here sufficiently (or even mentioned). Some reviews can be
enumerated here in this respect, e.g. reviews devoted to computer simulation studies of protein — nucleic acid complexes [31], membrane proteins [32], biomo-lecular folding [33], protein folding [34] and unfolding [35], large conformational changes in proteins [36], infrared spectra in peptides and proteins [37], blood coagulation proteins [38], thermodynamic properties of biomolecular recognition [39], biomembrane dynamics and the importance of hydrodynamic effects [40], block copolymers having biocompatible and functionalizable properties required for mimicking cell membranes [41], etc. The absence of some references in our review is related with an existence of many excellent above-mentioned and similar reviews.
Throughout this review, notation of N:k(n—j)cis for describing the structure of each hydrocarbon chain of lipids will be used, where N refers to the total number of carbon atoms in the chain, k is the number of the methylene-interrupted double bonds (i.e., one methylene group is localized between each pair of double bonds), whereas cis refers to the conformation around the double bonds; letter "n" means that so called "n minus" nomenclature is used, i.e., the position "j" of the first double bond is counted from the methyl, CH3, terminus of the chain (with the methyl carbon as number 1). The first double bond extends from the /h carbon to the (j + 1)th carbon from the end. For brevity, the fragment (n — j)cis in the notation is frequently omitted.
Some of the commonly occurring types of FA chains and PC molecules discussed in the text are listed below, with the given systematic name, trivial name in paranthesis (if it exists), and shorthand designation:
Saturated FAs: dodecanoic (lauric, 12 : 0); tet-radecanoic (myristic, 14 : 0); hexadecanoic (palmitic, 16 : 0); octadecanoic (stearic, 18 : 0); eicosanoic (arachidic, 20 : 0).
Monounsaturated FAs: cis-9-hexadecenoic (palmitoleic, 16 : 1(n-7)cis); cis-9-octadecenoic (oleic, 18 : 1(n-9)cis).
Polyunsaturated FAs with methylene — interrupted double bonds : cis-9,12-octadecadienoic (linoleic, 18 : 2(n-6)cis); cis-9,12,15-octadecatrieno-ic (a-linolenic, 18 : 3(n-3)cis); cis-5,8,11,14-eico-satetraenoic (arachidonic, 20 : 4(n-6)cis); cis-5,8,11,14,17-eicosapentaenoic (20 : 5(n-3)cis); cis-4,7,10,13,16,19-docosahexaenoic (22 : 6(n-3)cis).
PC molecules : 1,2-dilauroyl-sn-glycero-3-PC (DLPC), 12 : 0/12 : 0 PC; 1,2-dimyristoyl-sn-glyce-ro-3-PC (DMPC), 14 : 0/14 : 0 PC; 1,2-dipalmitoyl-sn-glycero-3-PC (DPPC), 16 : 0/16 : 0 PC; 1,2-dis-tearoyl-sn-glycero-3-PC (DSPC), 18 : 0/18 : 0 PC; 1,2-dioleoyl-sn-glycero-3-PC (DOPC), 18 : 1(n-9)cis/18 : 1(n-9)cis PC; 1-palmitoyl-2-oleoyl-sn-glycero-3-PC (POPC), 16 : 0/18 : 1(n-9)cis PC; 1-stearoyl-2-oleoyl-sn-glycero-3-PC (SOPC), 18 : : 0/18 : 1(n-9)cis PC; 1-palmitoyl-2-linoleoyl-sn-glycero-3-PC, 16 : 0/18 : 2(n-6)cis PC; 1-stearoyl-2-
linoleoyl-sn-glycero-3-PC, 18 : 0/18 : 2(n-6)cis PC;
1-palmitoyl-2-linolenoyl-sn-glycero-3-PC, 16 : 0/18 : : 3(n-3)cis PC; 1-stearoyl-2-linolenoyl-sn-glycero-3-PC, 18 : 0/18 : 3(n-3)cis PC; 1-palmitoyl-2-arahi-donoyl-sn-glycero-3-PC (PAPC), 16 : 0/20 : 4(n-6)cis PC; 1-stearoyl-2-arahidonoyl-sn-glycero-3-PC (SAPC), 18 : 0/20 : 4(n-6)cis PC; 1-palmitoyl-
2-eicosapentaenoyl-sn-glycero-3-PC (PEPC), 16 : : 0/20 : 5(n-3)cis PC; 1-stearoyl-2-eicosapentaenoyl-sn-glycero-3-PC (SEPC), 18 : 0/20 : 5(n-3)cis PC; 1-palmitoyl-2-docosahexaenoyl-sn-glycero-3-PC (PDPC), 16 : 0/22 : 6(n-3)cis PC; 1-stearoyl-2-docosahexaenoyl-sn-glycero-3-PC (SDPC), 18 : : 0/22 : 6(n-3)cis PC.
Some other types of lipids abundant in living cells and discussed in this review are phosphatidylethanola-mine (PE), sphingomyelin (SM), phosphatidylserine (PS), and phosphatidylglycerol (PG).
FORCE FIELD DEVELOPMENT
Proper parametrization of the force field (FF) defining molecular interactions is ongoing problem in molecular simulations. A good FF should provide agreement with all available experimental data within the simulation and experimental uncertainty. As simulations becoming longer, uncertainties caused by the equilibration stage and statistical error are decreasing. Experimental techniques are also improving. At some point, the FF which earlier provided satisfactory agreement with experimental data, may begin to show discrepancies. This in turn may initiate further improvements of the FF leading to better description of the molecular interactions and better agreement between computer simulations and experimental results.
In simulation of lipid bilayers, two families of FFs were typically used in recent years: GROMOS [42— 44] and CHARMM [45, 46]. GROMOS employs united atoms approach representing each of non-polar CH, CH2 and CH3 groups of hydrocarbons as a single particle which allows to reach about 3-fold speedup comparing to all-atomic simulations. There exists several versions of the GROMOS FF which essentially fall into two groups, one with original GROMOS non-bonded parameters (for example, 45A3 and similar parameter sets [44]), and Berger modification [47] which is the most frequently used. In the latter one, besides modification of the non-bonded interaction parameters, the Ryckaert-Bellemans potential is implemented to describe torsion rotations of the hydrocarbon chains of lipids. GROMOS FF is fully supported in GROMACS simulation package [48]. An overview over the different types of analysis implemented in the GROMOS++ software has been given in ref. [49].
The CHARMM FF [46] describes all hydrogens explicitly. A
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