Comparing Membrane Simulations to Scattering Experiments: Introducing the SIMtoEXP Software

Unofficial version J Membrane Biol DOI 10.1007/s00232-010-9254-5 Comparing Membrane Simulations to Scattering Experiments: Introducing the SIMtoEXP Software Norbert Kucˇerka • John Katsaras • John F. Nagle Received: 8 February 2010 / Accepted: 1 April 2010  Her Majesty the Queen in Right of UK 2010 Abstract SIMtoEXP is a software package designed to the component volumes following Petrache et al. (Biophys facilitate the comparison of biomembrane simulations with J 72:2237–2242, 1997). The software then calculates and experimental X-ray and neutron scattering data. It has the displays the contributions of each component group as following features: (1) Accepts number density profiles volume probability profiles, q(z), as well as the contribu- from simulations in a standard but flexible format. (2) tions of each component to e(z) and m(z). Calculates the electron density e(z) and neutron scattering length density m(z) profiles along the z direction (i.e., nor- Keywords MD simulation  X-ray scattering  mal to the membrane) and their respective Fourier trans- Neutron scattering  Computer software forms (i.e., Fe[qz] and Fm[qz]). The resultant four functions are then displayed graphically. (3) Accepts experimental Fe(qz) and Fm(qz) data for graphical comparison with sim- Introduction ulations. (4) Allows for lipids and other large molecules to be parsed into component groups by the user and calculates It is well recognized that atomic-level simulations can provide quantitative detail that surpasses any known experimental data. It is also recognized that simulations N. Kucˇerka  J. Katsaras may produce invalid results due to incorrect force fields or Canadian Neutron Beam Centre, National Research Council, insufficient equilibration times. Based on this, it is there- Chalk River, ON K0J 1J0, Canada fore imperative to compare simulation with experiment. N. Kucˇerka The NMR SCD order parameter has long been used as one Department of Physical Chemistry of Drugs, Faculty such appropriate test, although it focuses only on the lipid’s of Pharmacy, Comenius University, 832 32 Bratislava, Slovakia hydrocarbon chains. Moreover, experimental NMR SCD J. Katsaras data are subject to interpretive ambiguity when perdeu- Guelph-Waterloo Physics Institute and Biophysics terated chains are employed, even for saturated chains; and Interdepartmental Group, University of Guelph, Guelph, the problem is more severe for unsaturated hydrocarbon ON N1G 2W1, Canada chains for which SCD data are usually lacking. More J. Katsaras recently, however, simulations have been tested using Department of Physics, Brock University, 500 Glenridge X-ray scattering data (Sachs et al. 2003; Tristram-Nagle Avenue, St, Catharines, ON L2S 3A1, Canada and Nagle 2004; Klauda et al. 2006; Pandit et al. 2008) and both X-ray and neutron scattering data (Benz et al. 2005; J. F. Nagle (&) Department of Physics, Carnegie Mellon University, Kucˇerka et al. 2008a). Because X-ray and neutron scat- Pittsburgh, PA 15213, USA tering data yield complementary information along the z e-mail: [email protected] direction (i.e., normal to the bilayer plane), the SIMtoEXP software is designed to facilitate comparisons with both J. F. Nagle Department of Biological Sciences, Carnegie Mellon University, kinds of data. It may be noted that there are also scattering Pittsburgh, PA 15213, USA data that provide information in other spatial directions and 123  Unofficial version N. Kucˇerka et al.: Membrane Simulation vs. Scattering which may be used to further test simulations. However, might be to distinguish atoms in the two monolayers, those data are not addressed by the SIMtoEXP software. although that would not affect the computation of e[z] and Two quantities intrinsic to the SIMtoEXP software are m[z]). The only strict SIMtoEXP requirement for the com- the commonly used electron density (ED) profile, e(z), and putation of e(z) and m(z) is that the name of each atom the neutron scattering length density (NSLD) profile, m(z). begins with its (case-insensitive) commonly used abbrevi- Experimental studies often report e(z) and m(z), and simu- ation, i.e., C, N, O, P, H and D for deuterium. For united lators often compare their results to these one-dimensional atoms, the following abbreviations are used: M (CH2), T profiles. However, e(z) and m(z) are not direct experimental (CH3), W (H2O) and V (D2O). If simulations involve other data but are constructed using a number of assumptions. A atoms or groups of atoms, suitable first-letter identifiers better method is to compare simulations to the primary may be developed. experimental scattering data. In the case of X-rays and Beyond the first letter, additional atom identifiers in the neutrons, these are the form factors Fe(qz) and Fm(qz), the *.sim file can be assigned by the user. Figure 1 shows our Fourier transforms (FTs) of e(z) and m(z), respectively. The current preference for the names of all of the atoms in the FT of simulated e(z) and m(z) is very accurate and does not commonly studied DOPC lipid. The first number is the involve any assumptions, in contrast to what is required to ‘‘distance’’ from the lipid backbone to a given atom with produce e(z) and m(z) from experiments. However, physical different hydrogens denoted by the letters a, b and c. The insight is often more easily obtained in real space, so hydrocarbon chains (i.e., c1 and c2) and the headgroup (h) SIMtoEXP allows the user to compare simulated and identifiers then follow. For example, H16bc2 signifies the experimentally derived e(z) and m(z) profiles in real z space, ‘‘second’’ hydrogen atom (b) that is bonded to the sixteenth in addition to the more direct comparison in reciprocal qz carbon in the sn-2 chain (c2). Although one might question space. the utility of being able to distinguish H18bc1 from Other physical quantities that SIMtoEXP calculates H18cc1, NMR (Klauda et al. 2008) indicates that the four from simulations are component volumes, Vi, for the var- D2_c_ atoms are different. As such, our preference is to ious parts of lipids and other molecules. Component vol- include more, rather than less, information in the *.sim file. umes are very useful quantities when one uses models to The first column of the simulation input file contains the obtain e(z) and m(z) from experimental Fe(qz) and Fm(qz) z location of atoms, in discrete bins. The bin size should be data. This utility is an example of the synergy between chosen to be commensurate with the statistics of the sim- simulation and experiment. Although the volumetric fea- ulation; a well-equilibrated simulation with many statisti- ture in SIMtoEXP was developed over a decade ago (Pe- cally independent frames (i.e., snapshots) should contain trache et al. 1997), it has not been widely used by sufficient statistics for a bin size of *0.2 A˚ , resulting in simulators. smooth, one-dimensional profiles. Subsequent columns, Our interaction with simulators over the years has sug- separated by spaces or tabs, give the number density (ND) gested that there is considerable value in having a uniform distribution functions na(z) for each atom of type a. The file format and well-tested software for comparison number of occurrences of type a atoms located within a z between simulation and experiment. We have also tried to bin is counted for each frame and divided by the bin vol- make SIMtoEXP as flexible as possible so as to be able to ume, resulting in na(z) as the average over all frames. Bin accommodate the preferences of different researchers volume is defined as the bin height multiplied by the area working on a variety of systems, including complex lipid of the simulation box for a given frame, which will gen- mixtures and peptides. erally be different for different frames in constant pressure simulations. For nonperiodic boundary conditions, the analysis box should be drawn within any intruding Description of SIMtoEXP boundaries, which means that it should be well inside the simulation box to avoid any edge effects while comprising Simulation Input all atoms of the bilayer. When averaging over many frames in a long simulation SIMtoEXP reads an ASCII data file (sim is the default with periodic boundary conditions in the z direction, the extension) that contains the z distributions of each atom, or center of the bilayer may move in the z direction, artifi- assembly of united atoms, in the solvent, lipids and any cially broadening the real space profiles. It is then very other molecules that are present. The file’s first row assigns important to recenter the bilayer within each frame before the column names, starting with ‘‘z’’ for the z location and averaging over all frames—this can be done with simple continuing with the names of the various atoms. Usually, algorithms. Also, when the simulated system has a large an atom will have the same name when located at the same area and the bilayer bending modulus is small, undulation position on any molecule in the simulation (an exception fluctuations can lead to broadening of the real space 123  Unofficial version N. Kucˇerka et al.: Membrane Simulation vs. Scattering different scattering properties. Nevertheless, this option is not really necessary. While partial charges are important in running an MD simulation, the ED profile is hardly affected by approximating them with atomic number charges because the net local charge is the same with partial charges as for atomic number charges. For example, the charge on the phosphate PO4 is the same even though the partial charges on the phosphorus and the oxygens differ from the atomic number charges. Moreover, such a difference affects A ˚ ngstro¨m-level resolution in the ED profile, which only affects data at q values higher than those observable experimentally. Total e(z) is displayed graphically in the ED window (Fig. 2a), and m(z) is displayed in the NSLD window (Fig. 2b) of the SIMtoEXP graphical user interface (GUI). In addition, it is useful to see which parts of the molecule contribute at different z levels, and this information can also be displayed in the ED and NSLD windows. Because there are usually more atom types in the *.sim file than one wishes to see displayed simultaneously, it is appropriate to define groups of atoms, which we call ‘‘molecular com- ponents.’’ A component file (cmp is the default extension) contains a list of user-defined names for the different components. For each component the user lists the names of the atoms defined in the simulation file that are to be included in the given component. For a proper evaluation of component volumes (see ‘‘Component Volume Deter- mination’’), each atom should be included in one and only one component of the space-filling component model, although for specific display purposes it may be convenient to relax this requirement. It is typical to parse the larger lipid molecules into several localized components (e.g., Fig. 1 Schematic showing one possible naming convention for atoms phosphates, glycerols, terminal methyls). An advantage of in DOPC. Other naming conventions can be used in SIMtoEXP input listing all atom types in the *.sim input file is that any simulation files, subject to the restriction that the first letter is used as the atom type identifier variation in the parsing can easily be performed by small changes in the *.cmp component file rather than recom- piling the entire simulation file. profiles, even within each frame. This correction is con- Loading the *.cmp component file into SIMtoEXP adds siderably less trivial to perform than the recentering cor- the simulated scattering densities ei(z) and mi(z) for the user- rection and is currently under development (Braun et al. defined components to the ED and NSLD windows, in unpublished data). addition to displaying the component number densities ni(z) (normalized by number of atoms per component) in the ND Display of Simulation Data window (see Fig. 2). It is worth emphasizing that SIMtoEXP calculates component scattering densities by first multiply- Upon reading the *.sim file, SIMtoEXP calculates total e(z) ing the number density for each atom by the appropriate and m(z), based on the atom type identifiers defined above. number of electrons or neutron scattering length and then Each ND na(z) is first multiplied by the appropriate number summing over all component atoms. This is in contrast to of electrons or neutron scattering length (Sears 1992), and summing atomic number densities and then multiplying then a summation over all atoms a is carried out. It is worth them by the overall scattering length of each component. noting that the software currently uses atomic number to This way of calculating component distributions is espe- assign the number of electrons and does not account for the cially important when a component includes different atoms partial charges. However, the user can easily change this in with different scattering lengths that are distributed within the scattering length table by defining a new atom type with that component asymmetrically (Kucˇerka et al. 2008a). 123  Unofficial version N. Kucˇerka et al.: Membrane Simulation vs. Scattering Results for e(z) and m(z) obtained from modeling experi- experimental Fe(qz) and Fm(qz) form factors, thereby avoid- mental data can be added to the ED and NSLD windows, ing any model assumptions. The simulated scattering form facilitating comparison to simulated results. However, a factors are readily calculated from the Fourier transforma- more important comparison is the direct comparison to tion of the spatial distribution of all the atoms a as Fig. 2 (Color online) Electron densities (a), neutron scattering length densities (b) and number densities (c) determined from an MD simulation. SIMtoEXP displays graphically the distributions of all of the user- defined components (different color curves) as well as the total scattering density profiles (black curves in a and b) 123  Unofficial version N. Kucˇerka et al.: Membrane Simulation vs. Scattering  P Nq  ZD=2 ! jFs ðqi ÞjjFe ðqi Þj  i¼1 ðDFe ðqi ÞÞ2 k e ¼ PN ð2Þ X jFðqz Þj ¼  fa ðqz Þna ðzÞ  qs  q jFe ðqi Þj2 i¼1 ðDFe ðqi ÞÞ2  a D=2 ð1Þ   where the summation goes through all of the experimental ðcosðzqz Þ þ i sinðzqz ÞÞdz   data (i = 1 … Nq) and DFe(q) is the experimental uncertainty of each datum. The overall agreement/disagreement where na(z) are the atomic number distributions obtained between the simulation and the experimental data can be from simulation and qS is the scattering density of solvent. visually observed from the plots as shown in Fig. 3, or it can In the case of neutron scattering, fa(qz) is the neutron be quantified via a reduced v2, which is calculated by scattering length density, which does not depend on the SIMtoEXP as wave vector qz because nuclei are effectively point sources qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P Nq 2 2 for neutrons with wavelengths corresponding to inter- 2 i¼1 ðjFs ðqi Þj  ke jFe ðqi ÞjÞ =ðDFe ðqi ÞÞ v ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3Þ atomic distances. In the case of X-ray scattering, fa(qz) is Nq  1 the atomic form factor which is given by the FT of the SIMtoEXP allows the user to open several different atomic ED (Benz et al. 2005); it gradually decays by *5% experimental data files. These include X-ray form factors as qz increases to 0.8 A ˚ -1 for the X-ray scattering on for unilamellar vesicles (ULVs) and oriented samples principal atoms (Klauda et al. 2006). For computational (ORIs), and corresponding neutron form factors. Combin- convenience, the X-ray atomic form factors have been ing ULV with ORI data was motivated by our previous expressed by the analytical expression f ðqÞ ¼ work (Kucˇerka et al. 2005). Both these data sets involve 4 2 P aj ebj ðq=4pÞ þ c and the parameters aj, bj and c have data that are essentially continuous in qz. However, the j¼1 program also allows the user to import form factor data been previously determined (Cromer and Mann 1968). from Bragg peaks that provide form factors only at discrete Integration limits in Eq. 1 (i.e., ±D/2) must be located values of qz. Since different sample preparations are mea- in the pure solvent regions, where na(z) = 0 for all the sured on different relative scales, it is necessary to scale atoms except for those in the solvent; regions near the top them separately. This is automatically executed by SIM- or bottom of a simulation cell should be excluded, espe- toEXP (Eq. 2), or it can be overridden manually through a cially when they fluctuate under constant pressure, because user-selected scaling factor. In both cases, the reduced v2 is unrealistic values would then be included. Note that the obtained according to Eq. 3 so that it can be used to imaginary part of Eq. 1 becomes zero for centrosymmetric evaluate the comparison. membranes. However, SIMtoEXP utilizes the complete complex form of the Fourier transformation (Kucˇerka et al. 2007). This is essential for treating asymmetric mem- Component Volume Determination branes, and it allows the user to observe the consequences of less than fully equilibrated simulations for symmetric SIMtoEXP incorporates a procedure for extracting compo- membranes. nent volumes, Vi, from simulations (Petrache et al. 1997). The simulated results for the Fourier-transformed form This method requires that the *.cmp file parses all atoms a, factors appear in the ‘‘X-ray FFs’’ (Fig. 3a) and ‘‘Neutron each into one and only one component i, and that the number FFs’’ (Fig. 3b) windows on the GUI. Experimental data can of components (NC) be smaller than the number of bins (Nz). then be imported into these windows. Component number distributions, ni(z), are obtained as summations over all of the atomic distributions, na(z), Simultaneous Display of Experimental Data making up a particular component divided by the number of atoms in the component i. The method assumes that the Experimental scattering data consist of measured intensi- volume Vi of each component is independent of z and that the ties that can be easily converted to form factors (Kucˇerka bin volume should be completely filled. In terms of proba- et al. 2005). While form factors calculated from simula- bility this means that component probabilities defined as tions are obtained on an absolute scale, experimental data pi(z) = Vini(z) should add to 1 in each bin. In the usual case are usually obtained only on a relative scale. SIMtoEXP when there are many more z bins than components, there are scales the experimental form factors, Fe(qz), to the simu- more equations than unknowns, so the probabilities may not lated form factors, Fs(q). The scaling factor ke by which add precisely to 1, because of either statistical fluctuations or each independent set of Fe(q) is multiplied is obtained from a breakdown in the assumption of a constant Vi(z) (Petrache (Kucˇerka et al. 2008b) et al. 1997). To determine Vi, one minimizes 123  Unofficial version N. Kucˇerka et al.: Membrane Simulation vs. Scattering Fig. 3 (Color online) X-ray (a) and neutron scattering form factors (b) calculated from MD simulation data (solid black line) and compared to experimental data (red and green points are the results of two sample preparations). Experimental points were scaled according to Eq. 2 D=2 X " Nc X #2 (Kucˇerka et al. 2008a). Three different components— 1 Vi ni ðzÞ ð4Þ CholCH3, PCN and CG—define the lipid headgroup; CH2, z¼D=2 i¼1 CH and CH3 define the hydrocarbon chains; and WATER represents water molecules. According to these definitions, by setting its partial derivatives with respect to each Vi SIMtoEXP automatically calculates the number of primi- parameter to zero. This results in the set of Nc linear tive groups in each component, as well as the corre- equations sponding number of electrons and neutron scattering Nc Nz Nz X X X lengths. The last column at the bottom of the GUI (see Vj nj ðzk Þni ðzk Þ ¼ ni ðzk Þ; i ¼ 1. . .Nc ð5Þ Fig. 4) displays the volumes calculated based on these j¼1 k¼1 k¼1 user-defined components. Besides the SDP model used in A simple linear equation solution by Gauss-Jordan this example, two other models are included in the current elimination (Press et al. 2007) then provides component SIMtoEXP package, the HB model (Wiener et al. 1989) volumes and the root mean square deviation of total and the H2 model (Klauda et al. 2006). Of course, other probability from unity, which is defined as models can easily be developed by the user. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P Nz  P Nc k¼1 i¼1 pi ðzk Þ  1 rms ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð6Þ Graphical User Interface Nz  Nc Figure 4 displays an example of such probability We believe that an attractive feature of SIMtoEXP is its distributions, where the rms is approximately 0.2%. user-friendly GUI, shown in Fig. 4. The most prominent The example shown in Fig. 4 uses a recently developed portion of the software’s GUI is the graphical display, in space-filling model to define the various lipid components which the various graphs can be displayed using the 123  Unofficial version N. Kucˇerka et al.: Membrane Simulation vs. Scattering Fig. 4 (Color online) Snapshot of the SIMtoEXP GUI in which the volume probability distributions pi(z) = Vini(z) of the components (colors) and their sum (black) are displayed graphically. The lower part of the GUI has a column giving the names of the user-defined components, followed by characterization columns that include the calculated volume per group, given in angstroms cubed. The tabs at the top of the GUI allow the user to view graphs for electron density, neutron scattering length density, X-ray form factors, neutron form factors, number density and volume probability (the one shown here) overlaying tabs. Successive tabs display the ‘‘Electron the File menu allow the user to load simulation data Densities’’ graph (see Fig. 2a), the ‘‘Neutron SL Densities’’ (OpenSIM), experimental data (OpenEXPx and OpenEXPn) graph (Fig. 2b), the ‘‘X-ray FFs’’ graph (Fig. 3a), the consisting respectively of X-ray and neutron scattering form ‘‘Neutron FFs’’ graph (Fig. 3b), the ‘‘Number Densities’’ factors and ED or NSLD profiles (i.e., OpenEDP and graph (Fig. 2c) and the ‘‘Volume Probabilities’’ graph OpenNSLD) obtained previously using SIMtoEXP or simi- (Fig. 4). SIMtoEXP provides the user with basic manipu- lar software. The latter two commands were designed to lations (e.g., bring forward, hide, delete) to organize each allow the user to perform a visual comparison between the graph and an option to export into postscript graphics. A various models in real space. Any of the inputted data can be zoom and an x–y coordinate readout allow for convenient exported after performing the desired operation and saved quantitative comparisons. for future reference as an ASCII file. Below the graphical display, the lower part of the GUI panel includes four buttons for performing the data manipulation described above (i.e., Fourier transform, Conclusions and Availability scaling the X-ray and neutron data, and volume calcula- tion). When each calculation is finished, the appropriate Our aim has been to develop software that allows conve- graphs are updated and quantitative results are displayed in nient comparison of simulation and experimental scattering the bottom part of the main panel. The bottom left location data. Strong features of SIMtoEXP are its user-friendly includes all of the user-entered information necessary for graphical interface and the inclusion of all necessary pro- plotting the form factor results and scaling factors for the cedures in one package. The program also features an different experimental data files (Eqs. 2 and 3). integrated ‘‘Help’’ menu. The current functionalities of The bottom right part of the main panel shows the average SIMtoEXP make it a suitable tool for the final stages of rms of the volume calculation (Eq. 6) and a summary of the molecular dynamics simulations. The emphasis on inverse user-defined space-filling model for the molecular compo- space allows for a direct comparison of simulation to nents. Most of the information here is automatically entered experimental data, which can then be further scrutinized by using *.cmp files, which can be chosen using the comparing to the results of modeling experimental data in ‘‘File ? OpenCMP’’ menu. Other ‘‘Open’’ commands in real space. 123  Unofficial version N. Kucˇerka et al.: Membrane Simulation vs. Scattering The current version of SIMtoEXP is written in C?? with modeling of membrane bilayers. In: Feller SE (ed) Current topics GUI implemented in script language Tcl/Tk with BLT in membranes, vol 60. Elsevier, San Diego, pp 1–48 Kucˇerka N, Liu Y, Chu N, Petrache HI, Tristram-Nagle S, Nagle JF extension. The executable program has been compiled in (2005) Structure of fully hydrated fluid phase DMPC and DLPC the MS Windows operating system and is available in a lipid bilayers using X-ray scattering from oriented multilamellar bundle with all of the necessary libraries. Linux and Mac arrays and from unilamellar vesicles. Biophys J 88:2626–2637 OS X executables are also available, although proper Kucˇerka N, Pencer J, Sachs JN, Nagle JF, Katsaras J (2007) Curvature effect on the structure of phospholipid bilayers. Langmuir linking to the essential libraries (Tcl/Tk/BLT) is required 23:1292–1299 of the user. The program bundle, a user guide that supplies Kucˇerka N, Nagle JF, Sachs JN, Feller SE, Pencer J, Jackson A, additional details and tutorial commands, and sample input Katsaras J (2008a) Lipid bilayer structure determined by the files are available upon request from any of the coauthors. simultaneous analysis of neutron and X-ray scattering data. Biophys J 95:2356–2367 Subsequent versions may be developed to accommodate Kucˇerka N, Perlmutter JD, Pan J, Tristram-Nagle S, Katsaras J, Sachs user-suggested features that we have not anticipated. JN (2008b) The effect of cholesterol on short- and long-chain monounsaturated lipid bilayers as determined by molecular Acknowledgements We thank Scott Feller, Jonathan Sachs, Jason dynamics simulations and X-ray scattering. Biophys J 95: Perlmutter and Jeffery Klauda for providing us with simulation data, 2792–2805 and Olle Edholm and Frank Heinrich for valuable feedback. N. K. Pandit SA, Chiu SW, Jakobsson E, Grama A, Scott HL (2008) acknowledges partial funding from the Advanced Foods and Mate- Cholesterol packing around lipids with saturated and unsaturated rials Network (AFMNet), a Network of Centres of Excellence of chains: a simulation study. Langmuir 24:6858–6865 Canada. J. F. N. was supported by the U.S. National Institutes of Petrache HI, Feller SE, Nagle JF (1997) Determination of component Health, Institute of General Medicine (grant GM44976). volumes of lipid bilayers from simulations. Biophys J 72: 2237–2242 Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes: the art of scientific computing. 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