Abstract
The partitioning of the lipidated signaling proteins N-Ras and K-Ras4B into various membrane systems, ranging from single-component fluid bilayers, binary fluid mixtures, heterogeneous raft model membranes up to complex native-like lipid mixtures (GPMVs) in the absence and presence of integral membrane proteins have been explored in the last decade in a combined chemical-biological and biophysical approach. These studies have revealed pronounced isoform-specific differences regarding the lateral distribution in membranes and formation of protein-rich membrane domains. In this context, we will also discuss the effects of lipid head group structure and charge density on the partitioning behavior of the lipoproteins. Moreover, the dynamic properties of N-Ras and K-Ras4B have been studied in different model membrane systems and native-like crowded milieus. Addition of crowding agents such as Ficoll and its monomeric unit, sucrose, gradually favors clustering of Ras proteins in forming small oligomers in the bulk; only at very high crowder concentrations association is disfavored.
Introduction: Ras proteins
The transduction of extracellular signals across the plasma membrane via activation of receptor proteins and a well-defined set of membrane-bound and cytosolic downstream proteins is one of the most important mechanisms for the regulation of biological processes. Peripheral membrane proteins, such as proteins of the Ras family, pick up these signals from activated cell-surface receptors and transmit them to intracellular signaling cascades by recruiting effector proteins to the plasma membrane (Casey, 1995). Ras proteins are small GTPases (approx. 21 kDa), which act as molecular switches cycling between the inactive GDP-bound and the active GTP-bound state, whereas the latter one interacts with a considerable number of effector proteins regulating essential cellular functions including cell survival, proliferation and differentiation (Wittinghofer and Pal, 1991; Wittinghofer and Waldmann, 2000). The activation of Ras proteins is highly regulated by guanine nucleotide exchange factors (GEFs) catalyzing the replacement of bound GDP by the more abundant GTP, which induces conformational changes in the Ras switch domains (switch 1 and switch 2) revealing effector binding sites (Vetter and Wittinghofer, 2001; Bos et al., 2007). The most characterized Ras GEF is Sos, which is recruited to the adaptor protein Grb2 that in turn is bound to activated receptor tyrosine kinases (RTKs) on the plasma membrane enabling Sos to interact and activate membrane associated Ras proteins (Aronheim et al., 1994). However, distinct families of Ras exchange factors have been identified activating Ras proteins very differently, e.g. Ras-guanine-nucleotide releasing factors (Ras-GRFs) are controlled by Ca2+ influx (Farnsworth et al., 1995), whereas Ras guanine nucleotide-releasing proteins (Ras-GRPs) require Ca2+ and diacylglycerol (DAG) for activation and membrane binding (Ebinu et al., 1998). Once in its GTP-bound state, Ras initiates multiple downstream effectors including the firstly identified and mostly investigated Ras effectors Raf and phosphatidylinositol 3-kinase (PIK3), which promote cell proliferation and differentiation via the MAP kinase (MAPK) pathway and generate anti-apoptotic signaling, respectively. Up till now, at least 20 distinct Ras effectors have been discovered, such as other GEFs for Ral proteins and phospholipase C-ε (PLC-ε) (Marshall, 1996; Cullen, 2001). The slow intrinsic GTPase activity of the Ras proteins returning the protein to its inactive GDP-bound state is accelerated by GTPase-activating proteins (GAPs) by several orders of magnitude to ensure rapid down-regulation of Ras signaling (Wittinghofer et al., 1997).
Although the most abundant mammalian isoforms – H-Ras, N-Ras and K-Ras – are highly conserved in their catalytic G-domain comprising the effector binding surface, they generate distinct signal outputs in vivo (Hancock, 2003; Hancock and Parton, 2005; Rocks et al., 2006). These isoform-specific signaling responses can be ascribed to distinct posttranslational modifications these proteins undergo in their divergent C-terminal hypervariable region (HVR), which consists of an unstructured linker and an isoform-specific membrane anchor region (Figure 1). All isoforms contain a farnesyl (Far) moiety at the C-terminal and carboxymethylated cysteine residue. While H-Ras and N-Ras are additionally palmitoylated on two or one cysteine residues, respectively, adjacent to the farnesyl anchor, the splicing variant K-Ras4B features a polybasic domain comprising six lysine residues as second membrane-targeting motif (Hancock et al., 1990; Wittinghofer and Waldmann, 2000; Hancock and Parton, 2005). These lipid anchors and the polybasic domain of K-Ras4B are thought to provide the required Gibbs energy for stable membrane association, which is pivotal for their correct biological functioning. The differences in the lipidation pattern among the Ras isoforms influence the subcellular distribution of the proteins, enabling accessibility to a different set of regulator and effector proteins that are responsible for the isoform-specific signaling responses (Omerovic et al., 2007; Prior and Hancock, 2012). The residence time of the Ras proteins in such different signaling environments is regulated by dynamic processes, such as the acylation/deacylation cycle, which also affect cellular signal outputs (Rocks et al., 2005, 2006). Apart from the subcellular distribution, the Ras isoforms additionally partition into different subdomains of the plasma membrane, comprising domains of distinct lipid order. For example, H-Ras is thought to be targeted to highly ordered lipid domains (Prior et al., 2001, 2003), also denoted as lipid rafts, which are dispersed in a fluid lipid environment. These raft domains are supposed to provide a platform for specific membrane-bound proteins facilitating interaction between them and thus playing an important role in signaling pathways (Simons and Toomre, 2000). Moreover, it has been reported that the partitioning of the Ras isoforms in to the subdomains of the plasma membrane depends on the nucleotide binding state (Parton and Hancock, 2004). Recent studies have shown that the nucleotide binding state has also an effect on the reorientation of the catalytic G-domain of Ras isoforms at the membrane surface, thereby occluding binding sites for effector and regulatory proteins. A distinct membrane orientation of the Ras isoforms revealing dimerization sites might contribute to their functional diversity as well (Kapoor et al., 2012a,b; Mazhab-Jafari et al., 2015; Prakash and Gorfe, 2016). An alternative model suggests that the signal transduction is regulated by transient and spatially segregated nanoclusters formed by Ras proteins on the plasma membrane, serving as signaling platforms (Zhou and Hancock, 2015).

Membrane anchors of N- and K-Ras4B proteins.
The Ras isoform specific, posttranslationally modified C-terminal sequence constitutes together with the linker domain the hypervariable region (HVR) of Ras. The membrane anchor is composed of a common C-terminal farnesylated (Far) and carboxymethylated cysteine residue for all Ras isoforms. Exemplarily, the structure of K-Ras4B is schematically drawn with the G-domain adopted from the pdb (3GFT).Whereas K-Ras4B contains a polybasic stretch of six contiguous lysine residues in a total of eight as a second membrane targeting signal, N-Ras bears a palmitoyl chain (replaced by a nonhydrolyzable hexadecyl (HD) group as palmitoyl analog in our study). Reproduced from Weise et al. (2013) with permission of The Royal Society of Chemistry.
Since mutations in Ras genes that increase the protein activity are present in ca. 20–30% of all human cancers, most frequently in K-Ras and N-Ras (Bos, 1989; Downward, 2003), the corresponding proteins are considered as important targets in cancer treatment (Wittinghofer and Waldmann, 2000). A promising approach for anti-cancer therapy is the inhibition of Ras membrane binding. Hence, the determinants of membrane association of such lipoproteins and all the distinct membrane- and protein-related effects influencing these interactions need to be fully understood.
In this review, we discuss the influence of isoform-specific lipid modifications of N-Ras and K-Ras4B on the lateral organization in and partitioning into membrane systems of distinct composition and complexity including isolated plasma membranes. In this context, we will elaborate on the various physical-chemical contributions to the membrane partitioning process of lipidated proteins, allowing us to propose a molecular mechanism for lateral segregation and nanoclustering of both lipidated proteins, N-Ras and K-Ras4B, in membranes. In the second part, we will focus on a detailed analysis of the dynamic properties of Ras proteins in various model membranes and under cell-like crowding conditions to link their dynamic mobility to their function.
Chemical biology
In the last decades, chemical biological approaches have been developed by the Waldmann group, giving access to preparative amounts of posttranslationally modified and fully functional lipidated proteins, thus enabling biochemical and biophysical studies of these lipoproteins under defined in vitro conditions (Brunsveld et al., 2006). Here, we briefly refer to the semisynthetic approach for generating N-Ras and K-Ras4B, whose interactions with distinct membrane model systems and whose dynamic properties are the focus of this review. After expression of the protein isoforms lacking the C-terminal sequence, these truncated proteins were coupled to synthetic peptide sequences bearing the desired lipid modification and a C-terminal methyl ester. For N-Ras, the lipidated peptide was incorporated by a maleimidocaproyl (MIC) ligation that requires an accessible and free C-terminal cysteine in the truncated protein, providing a reactive thiol group to couple the N-terminally MIC-modified peptide. As long as only one cysteine is exposed, this reaction proceeds selectively (Bader et al., 2000). The advantage of using semisynthetic Ras lipoproteins is the possibility of inserting selective modifications of the natural membrane anchor. For example, in order to prevent the hydrolysis of the palmitoyl thioester, this lipid anchor was replaced by a non-hydrolysable hexadecyl (HD) thioether featuring identical saturation, conformation and length of fatty acid chain. On this account, a similar membrane binding stability can be envisaged (Bader et al., 2000).
The synthesis of fully functional and posttranslationally modified K-Ras4B was achieved by a combination of expressed protein ligation (EPL) and lipopeptide synthesis. In EPL, a thioester is generated in the C-terminus of the recombinant protein by thiolysis of an intein fusion protein allowing the coupling to synthetic lipidated peptide with an N-terminal cysteine residue to yield a native amid bond (Chen et al., 2010).
Partitioning of lipoproteins into membranes
Influence of membrane heterogeneity on N-Ras insertion
The multicomponent character of cellular membranes containing hundreds of different lipids and proteins results in a membrane heterogeneity forming transient and discrete subdomains with higher lipid chain order, denoted as lipid rafts (Simons and Toomre, 2000; Jacobson et al., 2007; Lingwood et al., 2009). The lateral organization of the membrane is generally regulated by hydrophobic mismatch between lipid species, charge repulsion, and line tension effects at domain boundaries, among others (García-Sáez et al., 2007). Still little is known how these effects influence lipoprotein partitioning and nanoclustering in heterogeneous membranes. To address this question, different model membrane system of various complexity showing phase coexistence of two fluid lipid phases, liquid-disordered (ld) and liquid-ordered (lo), have been used in partitioning studies of semi-synthetic fully functional lipoproteins. To this end, various microscopic approaches were used, such as confocal fluorescence microscopy and atomic force microscopy (AFM), the latter one enabling high-resolution imaging of membrane heterogeneity and protein localization on a nanometer length scale. In contrast to AFM measurements using planar lipid bilayers on a solid-support, fluorescence microscopy experiments were carried out on free-standing giant unilamellar vesicles (GUVs) with diameters of about 30 μm. Detection of the lipoproteins in fluorescence microscopy experiments was allowed by labeling the protein with the fluorescent probe BODIPY FL. In all experiments, the natural palmitoyl thioester of N-Ras was replaced by a non-hydrolysable hexadecyl thioether to ensure stable membrane binding of the protein in the course of the experiments.
To evaluate the effect of membrane heterogeneity on the lateral organization of the GDP-bound dually lipidated N-Ras bearing a farnesyl and hexadecyl moiety (GDP loaded N-Ras HD/Far), binding studies were first performed in a homogenous fluid membrane consisting of pure DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) for comparison with different more-component membrane systems. AFM experiments have shown that GDP loaded N-Ras HD/Far is uniformly distributed in homogenous DOPC membranes forming, however, small protein nanoclusters in the membrane plane with time (Erwin et al., 2016). Small N-Ras clusters, such as dimers, have been observed in other fluid membranes made of POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) by FRET (Förster resonance energy transfer) experiments as well (Güldenhaupt et al., 2012).
Heterogeneous membranes with coexisting ld and lo domains were prepared from canonical raft-like lipid mixtures containing DOPC/DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine)/cholesterol in a molar ratio of 1:2:1. The thickness of the lipid bilayer is ~5 nm for the lo phase and ~4 nm for the ld phase, hence the coexisting phases can be distinguished by their height difference of ~1 nm, and the localization of protein can be clearly attributed to one of the domains. In such phase-separated membranes, partitioning of inactive N-Ras HD/Far occurs preferentially into ld domains, since the bulky and branched farnesyl anchor appears to hinder insertion of N-Ras HD/Far into ordered raft-like lipid phases. This membrane insertion is followed by diffusion of N-Ras HD/Far into the ld/lo phase boundary region, which is visualized in the AFM images by bordering of the non-Ras-containing lipid domains with the N-Ras HD/Far protein (Figure 2) (Weise et al., 2009, 2010; Erwin et al., 2016). Interfacial localization of N-Ras proteins leads to a decrease of the unfavorable line tension between domains. By these means, the self-association and formation of elongated clusters at the domain boundaries is fostered, which is reflected in a decrease in the initial height difference between the lo and surrounding ld phase with incorporated protein until the lo/ld phase coexistence is nearly completely abolished at high lipoprotein concentrations (Weise et al., 2009). These results are in accordance with comparable two-photon excitation fluorescence microscopy partitioning studies of N-Ras HD/Far in another canonical raft-like lipid mixture consisting of POPC/BSM (bovine sphingomyelin)/cholesterol (Nicolini et al., 2006; Weise et al., 2010).

Schematic model for N-Ras localization in heterogeneous model biomembranes with liquid-disordered (ld) and liquid-ordered (lo) domains (right).
Note that the schematic view is not to scale. N-Ras partitions into the fluid-like phase of the membrane and subsequently diffuses to the ld/lo phase boundaries of the subcompartments (depicted by the AFM image). Reproduced (adapted) with permission from Weise et al. (2011). © 2011 American Chemical Society.
To explore the impact of multi-component native-like membranes comprising hundreds of different lipid species and membrane proteins on the partitioning mechanism of Ras proteins, viral membrane systems and giant plasma membrane vesicles (GPMV) directly isolated from RBL-2H3 cells were used (Vogel et al., 2009; Erwin et al., 2016). As the GPMVs additionally contain natural membrane proteins (40 wt%) from plasma membrane (Seeliger et al., 2015), the GPMV lipids were extracted to generate protein-free GUVs in order to evaluate whether the membrane proteins affect N-Ras partitioning (Erwin et al., 2016). All these biological membrane systems mimic the lipid composition of plasma membranes with hundreds of different lipid species and show lo/ld phase separation at ambient and physiologically relevant conditions (Scheiffele et al., 1999; Seeliger et al., 2015).
In fluorescence microscopy, the coexisting fluid domains can be distinguished by using appropriate fluorescent lipid analogs preferring localization in one of both domains, such as N-Rh-DHPE (N-(lissamine rhodamine B sulfonyl)-1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine triethylammonium salt), which preferentially partitions into the ld domain. The bright red areas with embedded, homogeneously distributed N-Rh-DHPE correspond to ld domains, whereas the dark domains consist mainly of lo phase. Similar to the scenario observed for the ternary canonical raft-like mixture consisting of DOPC/DPPC/cholesterol, GDP-bound N-Ras HD/Far is mainly localized in the ld domains of all used native-like membranes, clearly indicated by the superposition of both fluorescence channels (Vogel et al., 2009; Erwin et al., 2016). However, the diffusion to and significant clustering in lo/ld domain boundaries with time could be observed for the viral membrane system, only (Vogel et al., 2009). An accumulation of N-Ras HD/Far in the interfacial region of the domains in the protein-containing GPMVs and the protein-free GUVs formed from GPMV lipid extracts could not be detected (Erwin et al., 2016). It has been shown that the incorporation of proteins into the phase boundary results in a decrease of the energetically unfavorable line tension between the domains (Vogel et al., 2009; Weise et al., 2009, 2010). In complex multi-component membranes such as those of the GPMVs, the line tension can be expected to be much smaller (Simons and Vaz, 2004; Baumgart et al., 2007) – owing to the possibility of efficient lipid sorting to avoid hydrophobic mismatch – which is probably why the localization of the N-Ras proteins is not fostered into the boundaries of the membrane domains of the GPMVs. It is also possible that these domains are much smaller so that they cannot be optically resolved anymore. Complementary high-resolution AFM images were not technically feasible due to the large heterogeneity of this native-like membrane and the low yields of the isolated GPMVs (Erwin et al., 2016).
Hence, overall these data obtained for the various membrane systems reveal that, besides the fact that N-Ras HD/Far generally partitions into fluid-like domains, the lateral organization of N-Ras depends on the lipid composition of the membrane. Remarkedly, it was reported that membrane-integrated proteins of GPMVs did not have any marked effect on N-Ras HD/Far partitioning in multi-component membranes as revealed by examing the lateral organization of N-Ras HD/Far in protein-free GUVs prepared from the extracted GPMV lipids (Erwin et al., 2016). Although the cell-derived GPMVs represent a suitable model membrane system for the plasma membrane of living cells regarding the complex and native-like lipid and membrane protein composition, they are likely in a state of thermodynamic equilibrium in contrast to the dynamic and non-equilibrated plasma membrane. This might be caused by the absence of important cellular structures in GPMVs such as the cytoskeleton, by lipid synthesis and turnover, and by specific time-dependent protein-protein and protein-lipid interactions (Sezgin et al., 2012). Also, potential lipid rafts in the plasma membrane are transient and nanometre-sized only, which could have an impact on the partitioning behavior of the lipidated Ras proteins. For these reasons, there remains some ambiguity in postulating native-like partitioning behavior and lateral segregation of the proteins in vivo from studies using model membrane system with micrometer-scale coexisting lipid domains. However, biophysical partitioning studies using model membrane systems of various compositions and complexities are able to uncover major driving forces of the partitioning process, and therefore help better understand how lipidated proteins partition into the plasma membrane of living cells.
Influence of GTP/GDP loading of N-Ras on the partitioning into heterogeneous membranes
As evidence has been provided that H-Ras exhibits a GTP-dependent lateral segregation on the plasma membrane (Prior et al., 2001, 2003), the influence of GTP/GDP loading on the lateral organization of N-Ras proteins in heterogeneous membrane model system has also been explored. Instead of GTP, the lipoprotein was loaded with GppNHp, a non-hydrolysable analog, to ensure that the protein remains in its active state during the experiments. In contrast to H-Ras that binds to raft domains in its inactive GDP-bound form, but is redistributed to bulk plasma membrane upon GTP loading, N-Ras HD/Far displays no significant GDP/GTP-dependent partitioning behavior in model membranes (Weise et al., 2009; Erwin et al., 2016). Both the active and inactive form of the lipoprotein is preferentially localized in the bulk ld phase and diffuses to the domain boundaries and forms clusters with time. GTP-bound N-Ras HD/Far differs from the GDP state only, in showing some extent of clustering also in the bulk fluid phase detected in AFM images (Weise et al., 2009). This difference may be caused by other factors, such as a GTP/GDP-dependent reorientation of the catalytic G-domains of N-Ras at the lipid interface (Kapoor et al., 2012b), which has in fact been shown to have an influence on the localization of H-Ras within the heterogeneous plasma membrane as well (Rotblat et al., 2004).
Influence of various lipid anchor systems on N-Ras partitioning into heterogeneous membranes
Cellular studies have demonstrated that the subcellular distribution of N-Ras is regulated by a dynamic de/re-acylation cycle. The dually lipidated N-Ras Pal/Far is stably associated with the plasma membrane, whereas the loss of palmitate detaches N-Ras from plasma membrane and redirects the solely farnesylated protein to any endomembrane by cytosolic diffusion. The repalmitoylation then occurs on the surface of the Golgi from where N-Ras is transported back to the plasma membrane via the secretory pathway (Rocks et al., 2005, 2006). Consequently, the reversibility of the palmitoylation is critical for the correct localization of N-Ras in a particular cellular membrane. However, the influence of various lipidation motifs on N-Ras partitioning into heterogeneous membranes remains still largely unresolved.
The effect of various lipidation patterns of N-Ras on the lateral organization and clustering behavior in heterogeneous membranes has been studied to understand the underlying partitioning mechanism. Apart from the already discussed N-Ras HD/Far protein, dually hexadecylated (HD/HD), dually farnesylated (Far/Far), as well as monofarnesylated N-Ras protein derivatives have been studied. Time-lapse tapping mode AFM measurements were carried out to obtain structural data on a nanometer length-scale (Weise et al., 2009). Independent of the lipid anchor system, partitioning of GDP-bound N-Ras (HD/HD, HD/Far, Far/Far, Far) preferentially occurs into the ld lipid domains. N-Ras proteins bearing at least one farnesyl anchor display a comparable membrane partitioning behavior and show subsequent lateral diffusion of the protein into the lo/ld phase boundaries with time, whereas N-Ras HD/HD remains in the bulky ld lipid phase, indicating that the rigid and bulky farnesyl moiety is responsible for the interfacial N-Ras protein accumulation. No pronounced clustering in the interfacial region of the domains was observed for monofarnesylated N-Ras as one lipid anchor is not sufficient for stable membrane association (Weise et al., 2009). In general, the insertion at phase boundaries is energetically favorable, resulting in a decrease of line energy (tension) between the lipid domains, which depends quadratically on the phase height mismatch (Kuzmin et al., 2005), and can be expected for proteins that have no particular preference for any lipid domain, e.g. due to hydrophobic mismatch and/or entropic reasons, which is why they are expelled to phase boundaries (Nielsen et al., 2000; Zuckermann et al., 2004; Khandelia et al., 2008). For that reason, line tension is likely to be one of the key parameters controlling not only the lateral organization of the membrane but also the size and dynamic properties of the lipoprotein clusters. As the effective concentration of the proteins clustered in phase boundaries is markedly increased, interfaces in natural membranes may serve as an important vehicle for protein-protein-interactions in signaling pathways and nanoclustering. In fact, the biophysical and biochemical properties of different types of nanoclusters are believed to regulate the variety and time course of effector interactions allowing different signaling outputs. Nanocluster formation is probably also required for recording and transmitting signaling inputs to ensure a sufficient signal-to-noise ratio.
On the contrary, N-Ras HD/HD partitions into the bulk ld phase without lateral diffusion into the domain boundary region, although it is generally believed that long saturated and unbranched lipid anchors such as in N-Ras HD/HD enable insertion into ordered, raft-like domains (Weise et al., 2009). Residing of this dually hexadecylated protein largely in the fluid-like lipid phase is fostered, however, probably due to the preservation of the high conformational entropy of the two lipid chains separated by a dynamic peptide linker. In fact, NMR experiments have reported that the lipid modifications experience a high degree of motional freedom, which is also transmitted to the adjacent polypeptide chain (Reuther et al., 2006; Vogel et al., 2007).
Influence of membrane heterogeneity on the lateral organization of K-Ras4B
In addition to the S-farnesylated cysteine carboxymethylester, the splice variant K-Ras4B comprises a polybasic domain of six contiguous lysines in a total of eight as a second membrane targeting motif enabling electrostatic interactions with the negatively charged cytosolic leaflet of the plasma membrane that contains acidic phospholipids, such as phosphatidylserine (PS) and phosphatidylinositol (PI) (Silvius, 2002; Okeley and Gelb, 2004). It has been suggested that K-Ras4B forms distinct nanoclusters in plasma membranes, resulting in formation of a local environment highly enriched in acidic phospholipids via an effective lipid sorting mechanism. These nanoclusters are critical regulators of Ras-effector interactions and subsequent signal transduction, since they serve as platforms for the assembly of signaling complexes (Prior et al., 2003; Plowman et al., 2005, 2008). However, the mechanism underlying K-Ras4B nanoclustering is currently also still largely unknown. Recent simulation studies revealed two major dimerization interfaces in K-Ras4B proteins, involving either a highly populated β-sheet or a helical dimer interface. The presence of these two distinct dimerization interfaces might support formation of higher oligomerization states such as protein nanoclusters (Muratcioglu et al., 2015).
To yield a pictorial view of the localization process of K-Ras4B in heterogeneous membranes up to the single-molecule level, high-resolution imaging using confocal laser scanning and tapping-mode atomic force microscopy have been applied to semisynthetic fully functional lipidated K-Ras4B proteins in heterogeneous anionic model membrane systems as well as complex membrane systems that mimic the lipid composition of biological membranes.
In the first set of experiments, a canonical anionic raft-like model membrane containing 10 mol% phosphatidylglycerol (PG) was used, since previous reports revealed no specific binding of the polybasic K-Ras4B domain to any of the common mono- and polyanionic phospholipids of the inner plasma membrane (Leventis and Silvius, 1998). The lipid mixture is composed of DOPC/DOPG (1,2-dioleoyl-sn-glycero-3-phospho-(10-rac-glycerol) sodium salt)/DPPC/DPPG (1,2-dipalmitoyl-sn-glycero-3-phospho-(10-rac-glycerol) sodium salt)/cholesterol in a molar ratio of 20:5:45:5:25, and shows lo/ld phase coexistence at ambient conditions (Kapoor et al., 2011). Fluorescence microscopy and AFM images have clearly revealed a preferred ld phase partitioning of inactive K-Ras4B in this anionic raft-like lipid bilayer, which is followed by a spontaneous self-assembly of the protein to form new protein-rich domains wīthin the bulk fluid phase (Figure 3) (Weise et al., 2011). Similar as for N-Ras, the bulky and branched farnesyl anchor prevents partitioning of K-Ras4B into highly ordered raft-like domains and accommodates more easily into disordered lipid regions, however, in contrast to farnesylated N-Ras, no significant accumulation in the interfacial region of the domains could be detected (Weise et al., 2009, 2010). Consistently, recent atomic-scale MD simulations of the HVR of K-Ras4B in different types of lipid bilayers revealed that the farnesyl moiety is preferentially inserted into the loosely packed lipid bilayers made of DOPC or DOPC/DOPS, but not into gel-like lipid bilayers consisting of DPPC (Jang et al., 2015). Nevertheless, Jang et al. observed by using surface plasmon resonance (SPR) that the HVR of K-Ras4B is attached to DPPC lipid bilayers in a cooperative manner, suggesting a binding mechanism with a solvent-exposed oligomerization of the farnesyl anchors via hydrophobic interactions at the bilayer surface.

Schematic model for K-Ras4B localization in heterogeneous model biomembranes with liquid-disordered (ld) and liquid-ordered (lo) domains (left).
Note that the schematic view is not to scale. K-Ras4B forms new protein-enriched fluid domains within the bulk fluid phase upon membrane binding and is thought to recruit multivalent anionic lipids by an effective, electrostatic lipid sorting mechanism as visualized by AFM (bottom). Reproduced (adapted) with permission from Weise et al. (2011). © 2011 American Chemical Society.
To evaluate whether the lipid sorting of K-Ras4B can be solely ascribed to electrostatic interactions with the anionic lipids in the membrane, the partitioning of K-Ras4B was also investigated in neutral heterogeneous membranes (DOPC/DPPC/cholesterol 25:50:25) that were as well applied in partitioning studies of N-Ras proteins. Rather unexpectedly, a similar membrane partitioning behavior was detected in both neutral and negatively charged membranes for K-Ras4B (Weise et al., 2011). Thus, the formation of new protein enriched domains in the fluid phase of the membrane is not solely controlled by electrostatic interactions between the polybasic domain of K-Ras-4B and anionic lipids, but probably also with the negatively charged phosphate of the zwitterionic lipid head groups as the solely farnesylated and noncharged N-Ras displays clustering at the lipid domain boundaries under similar conditions (Weise et al., 2009).
To further address the question whether native-like membranes have an impact on the K-Ras4B membrane partitioning process, corresponding studies have been performed with the envelope membrane of influenza viruses and with GPMVs in the presence and absence of membrane-embedded proteins. The isolated GPMVs even contained low amounts of PI and PIP2 (Baumgart et al., 2007; Seeliger et al., 2015). By using protein-containing GPMVs and lipid extracts thereof, the influence of membrane proteins on Ras membrane insertion could also be evaluated (Erwin et al., 2016). In all of these complex native-like membrane systems, partitioning of inactive K-Ras4B has been found to occur preferentially into the ld lipid phase, as clearly displayed by the co-localization of the ld domain marked by N-Rh-DHPE and BODIPY FL-labeled K-Ras4B protein in the fluorescence microscopy images (Weise et al., 2011; Erwin et al., 2016). The protein distribution within the ld lipid phase appears to be heterogeneous in GPMVs and the protein-free GUVs, indicating formation of protein enriched domains of K-Ras4B in the fluid membrane regions (Erwin et al., 2016), similar to the scenario observed in simpler five-component raft-like lipid bilayers (Weise et al., 2011). As the partitioning behavior of K-Ras4B seems to be the same in both GPMV membrane systems (protein-containing and protein-free GUVs) used in these studies, the membrane-integrated proteins do not seem to have a major impact on the lateral organization of K-Ras4B in GPMVs (Erwin et al., 2016). Thus, the formation of new protein-enriched fluid domains of the lipoprotein K-Ras4B seems to be a general phenomenon, being largely independent of the details of the membrane composition.
Influence of GTP/GDP loading of K-Ras4B on the partitioning into heterogeneous membranes
Moreover, the influence of GTP/GDP loading on the lateral organization of K-Ras4B has been explored in heterogeneous membrane model systems. In order to ensure that the protein remains in its active state during the partitioning studies, GTP was replaced by the non-hydrolysable analog GppNHp. Similar to N-Ras HD/Far, K-Ras4B does not display a GDP/GTP-dependent partitioning behavior in heterogeneous membrane systems (Weise et al., 2011; Erwin et al., 2016). Both the active and the inactive state of K-Ras4B are preferentially localized in the ld lipid phase and form new protein-containing clusters within the ld phase, whereas the clustering effect is more pronounced for the active K-Ras4B as the thicker domains argue for a stronger enrichment of protein (Weise et al., 2011). Different orientations of both protein states at the membrane interface could explain the difference in protein cluster size, as a tighter packing of the Ras molecules could be promoted for GTP-bound K-Ras4B. Complementary infrared reflection absorption spectroscopy (IRRAS) experiments revealed that the active K-Ras4B undergoes reorientations at the lipid interface during membrane insertion, whereas inactive K-Ras4B seems to adopt a relatively fixed orientation at the membrane interface (Kapoor et al., 2012b). Recent NMR studies provided evidence for a nucleotide-dependent reorientation of K-Ras4B upon membrane binding as well (Mazhab-Jafari et al., 2015).
Influence of PS and PIP2 on the lateral organization and clustering of K-Ras4B
The cytosolic leaflet of the plasma membrane from a typical mammalian cell contains both monovalent and polyvalent acid lipids (Leventis and Silvius, 1998). Proteins endowed with a hydrophobic side chain in the immediate vicinity of a stretch of positively charged residues, such as K-Ras4B, are thought to interact with negatively charged phospholipids in a non-selective manner. However, previous studies also suggested specific interactions of polybasic domains with the monovalent acidic lipid PS and polyvalent phosphatidylinositol-4,5-bisphosphate (PIP2) (Golebiewska et al., 2006; Zhou et al., 2014). Recent in vivo experiments have shown that plasma membrane depolarization induces nanoscale reorganization of PS and PIP2, enhancing K-Ras4B nanoclustering (Zhou et al., 2015).
To evaluate potential specific interactions and changes in lateral membrane organization of K-Ras4B, physiologically relevant amounts (10–20 mol%) of PS and PIP2 (<1 mol%) were added to homogeneous and heterogeneous model membranes. In the first set of experiments, PS was added in different amounts to homogeneous fluid DOPC-containing lipid bilayers. Independent whether PS was present or absent in the membrane, K-Ras4B formed protein-enriched clusters upon membrane insertion, which were in the μm range and of toroidal shape. Moreover, the formation of K-Ras4B clusters leads to a slight disturbance (thinner bilayer thickness) of the surrounding lipid bilayer of K-Ras4B clusters in the AFM images (Erwin et al., 2016). Such an acidic-lipid independent clustering behavior detected for inactive K-Ras4B was also observed in heterogeneous neutral and anionic model membrane systems (Weise et al., 2011). McLaughlin and co-workers have suggested that membrane-bound basic peptides induce sequestration of polyvalent (PIP2 and PIP3) but not monovalent acidic lipids via nonspecific interactions, indicated by a twofold lower diffusion coefficient of the peptide in membranes containing PIP2 in comparison to membranes comprising PS (Golebiewska et al., 2006). Recent AFM experiments revealed a similar clustering behavior of K-Ras4B in homogeneous (DOPC) and heterogeneous [DOPC/DPPC/cholesterol (1:2:1)] lipid bilayers in the presence of physiological concentrations of PIP2 (0.8 mol%) (Figure 4). The protein clusters are predominantly formed in the liquid-disordered phase with an annular ring around them, which, again, might be a consequence of disturbance in lipid packing due to lipoprotein insertion (Figure 4A,B), as was observed in previous studies with other anionic lipids (Weise et al., 2011; Erwin et al., 2016). However, minor differences in lateral dimensions and shape of K-Ras4B clusters are observed in homogeneous DOPC bilayers doped with small amounts of PIP2 (Figure 4C), implying a change in line tension, which controls the size and shape of clusters acting on the protein.

K-Ras4B clustering in the heterogeneous membrane system DPPC/DOPC/cholesterol (1:2:1)+0.8 mol% PIP2 (A), (B) at different time points after protein insertion.
(C) and (D) represent a magnified image of (A) and (B), respectively. K-Ras4B clustering in a homogenous membrane system containing DOPC+0.8 mol% PIP2. Color scale 0–10 nm (E), (F).
These results clearly reveal that lateral organization and clustering of K-Ras4B occur largely independently of the membrane composition. Moreover, specific monovalent or polyvalent acidic lipids, such as PS or PIP2, are not required for the characteristic membrane partitioning scenario observed for K-Ras4B. Thus, besides attractive hydrophobic interactions between the K-Ras4B lipid anchor and the phospholipid hydrocarbon chains of the bilayer that drive farnesyl insertion into the membrane, hydrogen bond formation of the amino group of lysine side chains with phosphatidylcholine phosphate head groups seems to be sufficient to induce stable clustering of K-Ras4B (Janosi and Gorfe, 2010). In vivo studies have proposed the existence of K-Ras4B nanoclusters with higher contents of acidic phospholipids, which might enhance the formation of fluid domains with higher anionic charge density and incorporated K-Ras4B protein (Prior et al., 2003; Plowman et al., 2005, 2008). The spontaneous Ras isoform-specific sorting and the collective lateral organization of induced membrane domains could potentially operate as an effective, high fidelity signaling platform with distinct signal outputs for the Ras isoforms. In fact, nanoclustering has been proposed in in vivo experiments to be critical for signal transmission, as it allows the cell to respond to low signal inputs with a fixed output (Tian et al., 2007).
Dynamic properties of Ras isoforms
Dynamic properties of the Ras proteins upon targeting to model membrane systems
Despite various intriguing observations of Ras partitioning in different membrane subdomains and formation of Ras nanoclusters in vivo (Hancock, 2003; Tian et al., 2007; Plowman et al., 2008; Janosi and Gorfe, 2010), very little is known so far regarding the dynamic properties of the membrane associated lipidated Ras proteins. Therefore, a detailed analysis of the dynamic properties of Ras proteins in various model biomembranes is crucial in order to link their dynamic properties to their lateral membrane organization and function. Recent fluorescence anisotropy and fluorescence correlation spectroscopy (FCS) studies have tried to fill this gap by exploring the rotational and translational dynamics of BODIPY FL labeled full-length lipidated N-Ras and K-Ras4B in different model membrane systems including pure fluid, ordered and phase separated lo/ld heterogeneous charged and uncharged model membrane systems (Werkmüller et al., 2013).
It was clearly demonstrated that the addition of a lipid anchor to the truncated forms of the proteins leads to a significant difference in the rotational mobility (defined by the rotational correlation time, θprotein, obtained from the fluorescence anisotropy measurements) in the case of N-Ras but not for K-Ras4B in bulk solution (Figure 5). The θprotein value apparently doubles for N-Ras HD/Far (GDP and GTP loaded) compared to the truncated form (Figure 5A,B), indicating dimerization upon lipidation. Conversely lipidated K-Ras4B is essentially monomeric in bulk solution as there is no significant change in the θprotein value (Figure 5C). These differences in the rotational mobility upon lipidation arise from the nature of their individual lipid anchor. N-Ras HD/Far contains an additional hexadecyl (HD) chain, which probably favors a micellar-type of interaction between the lipoproteins, leading to the dimerization, and possibly also population of slightly higher oligomeric states to a minor extent. Dimers along with higher oligomers formed due to such micellar-like interaction, unlike dimers or smaller oligomers interacting by strong direct protein-protein interactions, can lead to a large change in the hydrodynamic radius of the molecule and hence a drastic change in the rotational mobility as observed here. The HVR of K-Ras4B contains a polybasic lysine stretch adjacent to the farnesyl moiety, which leads to a repulsive interaction, preventing association of the protein in bulk solution. Of note, formation of K-Ras4B dimers has been observed in a gel filtration chromatography study (Dementiev, 2012) where the concentrations were 20–40 times higher than the concentration used in the study of Werkmüller et al.

Overall rotational correlation time (θprotein) of BODIPY FL labeled (A) GDP loaded N-Ras, (B) GTP loaded N-Ras and (C) K-Ras4B (GDP and GTP bound) in bulk solution and in the presence of different lipid bilayers at T=25°C.
Reproduced (adapted) with permission from Werkmüller et al. (2013). © 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Remarkably, incorporation of the proteins into the lipid membranes does not alter the rotational mobility significantly. The rotational correlation time of the both inactive and active N-Ras HD/Far is found to be ~20 ns in all the model biomembrane systems (Figure 5A,B). This clearly indicates that the rotational mobility is essentially determined by the free rotation of the G-domain, which is exposed to the bulk solution. K-Ras4B exhibits a large rotational mobility in membranes as well. However, the electrostatic interaction between the negatively charged membrane and positively charged HVR of K-Ras4B significantly affects the rotational mobility. Addition of 20 mol% negatively charged PG into the uncharged raft like membrane (DOPC/DPPC/cholesterol) increases θprotein of K-Ras4B from 17 ns to 25 ns (Figure 5C). This value is still very high, confirming that the rotational mobility of the protein in the membrane bound state is indeed dominated by the free rotation of the G-domain.
The translational diffusion coefficient, D (obtained from the FCS measurement), of the Ras proteins further supports the observation obtained from the fluorescence anisotropy measurements (Figure 6). An almost two-fold decrease in the D-value is observed for lipidated N-Ras compared to the truncated form in the bulk solution (Figure 6A). This clearly indicates an increase in the size of the N-Ras upon lipidation. The HVR of N-Ras contains an additional HD unit which favors hydrophobic interactions, leading to formation of dimers and also higher oligomers to some extent. On the other hand, a negligible change is observed for the D-value of K-Ras4B upon introduction of the lipid anchor (Figure 6B), confirming that K-Ras4B remains monomeric in the bulk solution.

Lateral diffusion coefficient, D, of the BODIPY FL labeled (A) N-Ras and (B) K-Ras4B in bulk solution and in various model membranes. (C) Impact of native charge density on the D-value of K-Ras4B.
Reproduced (adapted) with permission from Werkmüller et al. (2013). © 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Upon binding to membranes, the D-value of the proteins is retarded but remains still quite high. The D-value of N-Ras HD/Far GDP in pure fluid DOPC is 8.7 μm2/s and in the ld phase of the uncharged lipid raft mixture (the localization is confirmed by the AFM and fluorescence microscopy data; Weise et al., 2009, 2011) is 9.3 μm2/s. GTP loaded forms of the proteins behave similarly, indicating that the nucleotide exchange does not play a significant role on the mobility of the proteins. Upon binding to liquid-ordered membranes (DPPC/cholesterol, 2:1), the D-value of N-Ras HD/Far decreases at least one order of magnitude (<1 μm2/s) compared to the fluid-like lipid bilayers. This value is similar to the D-value obtained for a fluorescence lipid analog in DOPC (DDiD=10 μm2/s) and lo lipid bilayers, respectively (Kahya et al., 2008; Heinemann et al., 2012) but significantly faster than those of integral membrane proteins in lipid bilayers (D≈0.01–0.5 μm2/s) (Goodwin et al., 2005). These results indicate that the membrane viscosity largely determines the mobility of the lipoproteins, and nanocluster formation does not seem to largely reduce the mobility of the membrane-bound lipoproteins.
K-Ras4B exhibits a similar fast diffusivity upon incorporation into membranes (Figure 6B). However, electrostatic interactions retard the lateral mobility of K-Ras4B, though not dramatically. The D-value decreases from ~8 μm2/s in pure DOPC to ~5 μm2/s in DOPG (Figure 6C), i.e. by ~40%. In vivo measurements also suggest a minor retarding influence of the negative charges on the lateral diffusion of K-Ras4B (Niv et al., 2002).
Altogether, Ras proteins exhibit a quite high diffusional mobility in all model biomembrane systems. This result would be consistent from a biological point of view: fast rotational and translational mobility allow for rapid recognition and binding and therefore facilitates interaction between the G-domain of Ras and scaffolding and effector proteins, ensuring efficient signaling outputs.
Translational mobility of the Ras proteins in the presence of crowding agents and compatible osmolytes
A considerable path of the Ras cycle involves the cytoplasm. The cell cytoplasm is crowded with large biomolecules, which occupy almost 30% of the overall volume (Zimmerman and Minton, 1993; Fulton, 2016). The thermodynamic and kinetic properties of the biomolecules will be different in such highly crowded environments, largely due to the excluded volume effect (Ralston, 1990). Hence, a detailed study of the diffusion of the Ras proteins in crowded environments and in the presence of compatible osmolytes, which are also abundant in cells, is very important to be able to relate their dynamics to their biological function. The particular interest here is the solution state of the Ras proteins, i.e. whether they are monomeric or form clusters, which influences their membrane targeting and partitioning behavior and their interplay with cytosolic interaction partners.
To address this point, the translational diffusion of full-length and BODIPY FL-labeled N-Ras HD/Far and K-Ras4B was studied in the presence of the macromolecular crowder Ficoll PM 70 and the nanocrowder and compatible osmolyte sucrose by using FCS (Patra et al., 2016). Ficoll forms a network structure at higher concentrations and serves as a good mimetic of the intracellular macromolecular environment. Sucrose is chosen because it is the monomeric unit of Ficoll and also a protein stabilizing agent. Autocorrelation curves obtained from the FCS measurements were fitted to a 2-component diffusion model, which has been found to offer the best scheme (Figure 7). The fast component (denoted as D2) obtained from this fit resembles the diffusion coefficient (D) of the free BODIPY FL dye alone, indicating that D2 arises from free BODIPY FL dye in the solution. The slow component of the diffusion model (denoted D1, here) originates from the fluorescent labeled Ras proteins, in good agreement with literature data (Werkmüller et al., 2013). From the D1 values, the association state of these proteins was calculated in the presence of macomolecular crowder Ficoll and the nanocrowder sucrose, respectively.

Fit of the autocorrelation curve obtained from the FCS measurement of N-Ras in buffer using (A) a simple 1-component diffusion model (i=1 in the equation
Here, the red solid line represents the fit to the black FCS trace. Residuals, which determine the quality of the fits, are provided at the lower panel of each curve. The residuals clearly indicate that the 2-component diffusion model is superior. A similar kind of behavior is observed for the protein in Ficoll and sucrose solution. The fits for K-Ras4B data are similar to those for N-Ras. Reproduced (adapted) with permission from Patra et al. (2016). © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
The results obtained at various concentrations of Ficoll is summarized in Figure 8. Addition of Ficoll leads to a retardation in the D1-value. From these D1-values, the hydrodynamic radius, R, of the proteins at different concentrations of Ficoll can be approximately determined by using the Stokes-Einstein equation for spherical particles and the microviscosity data obtained by probe molecules (functionalized CdTe quantum dots of similar size) (Erlkamp et al., 2014; Rashid et al., 2015; Patra et al., 2016), which shed light on the association states of the proteins. The R-value of the monomeric form of the proteins is 2.7 nm and 2.4 nm for N-Ras and K-Ras4B, respectively as determined from the diffusion coefficient of their truncated forms (80 μm2/s for N-Ras and 89.6 μm2/s) for K-Ras4B) (Werkmüller et al., 2013). The addition of Ficoll up to 20 wt% leads to a 3-fold enhancement in the R-value in the case of N-Ras compared to its truncated form (Figure 8C). For K-Ras4B, this enhancement is ~2-fold upon addition of Ficoll (Figure 8D). The 3-fold and 2-fold enhancement in the R-values obtained for N-Ras HD/Far and K-Ras4B, respectively, in Ficoll suggests formation oligomeric clusters of N-Ras and K-Ras4B upon addition of Ficoll. The clusters are probably formed due to a micellar type of interaction induced by the lipidation motifs (the hexadecyl and farnesyl unit) of the proteins. Even the smallest clusters, i.e. a dimer, for such kind of micellar interaction leads to significant change in the D1 and hence R-value, in contrast to a conventional dimer structure where the proteins are in direct contact with each other. Approximating the protein corpus of Ras to be a spherical bead, the micellar type of dimer formed can be best described by a dumbbell shape (Bloomfield et al., 1967; García de la Torre and Bloomfield, 1977; García de la Torre et al., 2003, 2005), where two identical spherical beads are connected by a lipid linker. The computationally determined radius of gyration for such system is found to be about 1.7 times larger than a single spherical subunit (García de la Torre et al., 2005). Hence, the experimentally observed 2-fold enhancement in the R-value for K-Ras4B in Ficoll may be attributed to mostly dimer formation along with some contribution of larger oligomers. The 3- fold enhancement in R obtained for N-Ras in Ficoll would then be due to the formation of larger N-Ras clusters, including trimers. Further, the large scattering of data associated with D1 (the error associated with the D-value of pure BODIPY FL in buffer is very low) (Patra et al., 2016) indicates a distribution of different clusters of the Ras proteins present in the solution. The addition of Ficoll promotes the association of the proteins due to the excluded volume effect and thus shifts the equilibrium to the higher oligomeric species, along with trimers for N-Ras HD/Far and dimers for K-Ras4B. Very high concentrations of Ficoll (35 wt%) again favour the formation of smaller N-Ras clusters (mostly dimers). At very high concentrations, Ficoll forms a network type of polymer structure, resulting in smaller cavity volumes, which can probably not accommodate larger oligomers anymore. Furthermore, the higher viscosity of the highly concentrated macromolecular solution is expected to retard the association reaction, resulting in smaller clusters. Larger protein clusters are favored in the case of N-Ras owing to its additional lipid anchor, which favors hydrophobic association of the proteins. On the other hand, for K-Ras4B molecules, the excluded volume effect leads to formation of smaller oligomers, most probably dimers, which is expected to be due to the electrostatic repulsion of their highly charged HVR.

Variation of the lateral diffusion coefficient, D1, of (A) N-Ras and (B) K-Ras4B at various concentrations of Ficoll.
Hydrodynamic radius (R) of (C) N-Ras and (D) K-Ras4B as a function of Ficoll concentration. Reproduced (adapted) with permission from Patra et al. (2016). © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
The results obtained in the presence of sucrose are summarized in Figure 9. The R-value initially increases up to 10 wt% sucrose and then decreases again (Figure 9C,D). Up to 10 wt%, sucrose favors the formation of mostly trimers for N-Ras and dimers for K-Ras4B along with some amount of larger oligomers. At higher sucrose concentrations (50 wt%), essentially monomers are detected. In general, sucrose is preferentially excluded from the protein surface (excluded volume effect) which stabilizes the protein conformation with lower solvent-accessible surface area (SASA), i.e. the native monomeric state of the protein (Timasheff, 1993; Kendrick et al., 1997; Luong et al., 2015). Moreover, proteins can also minimize the SASA by association, leading to the formation of oligomers. At very high sucrose concentrations, however, almost all the H2O molecules are required to solvate the sucrose and no bulk water is left, thereby reducing the preferential hydration effect and tendency to associate.

Variation of the lateral diffusion coefficient, D1, of (A) N-Ras and (B) K-Ras4B at various concentrations of sucrose.
Hydrodynamic radius, R, of (C) N-Ras and (D) K-Ras4B as a function of sucrose concentration. Reproduced (adapted) with permission from Patra et al. (2016). © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Hence, not only macromolecular crowding, but also nanocrowders and osmolytes at high concentrations mimicking cell-like environments are able to modulate the association state of the Ras proteins, which affects their activity (effective concentration) and interactions with cytosolic partners, but also their membrane targeting and partitioning behavior.
Acknowledgments
This research was supported by the Deutsche Forschungsgemeinschaft (SFB 642). We are grateful to Simone Möbitz for technical assistance with GPMV isolation and lipid extraction, and Christine Nowak for technical assistance with Ras protein expression and ligation. We thank Prof. H. Waldmann and his group for a long standing fruitful cooperation in the field of Ras-membrane interactions.
References
Aronheim, A., Engelberg, D., Li, N., Al-Alawi, N., Schlessinger, J., and Karin, M. (1994). Membrane targeting of the nucleotide exchange factor Sos is sufficient for activating the Ras signaling pathway. Cell 78, 949–961.10.1016/0092-8674(94)90271-2Search in Google Scholar
Bader, B., Kuhn, K., Owen, D.J., Waldmann, H., Wittinghofer, A., and Kuhlmann, J. (2000). Bioorganic synthesis of lipid-modified proteins for the study of signal transduction. Nature 403, 223–226.10.1038/35003249Search in Google Scholar
Baumgart, T., Hammond, A.T., Sengupta, P., Hess, S.T., Holowka, D.A., Baird, B.A., and Webb, W.W. (2007). Large-scale fluid/fluid phase separation of proteins and lipids in giant plasma membrane vesicles. Proc. Natl. Acad. Sci. USA 104, 3165–3170.10.1073/pnas.0611357104Search in Google Scholar
Bloomfield, V., Dalton, W. O., and Van Holde, K. E. (1967). Frictional coefficients of multisubunit structures: I. Theory Biopolymers 5, 135–148.10.1002/bip.1967.360050202Search in Google Scholar
Bos, J.L. (1989). Ras oncogenes in human cancer: a review. Cancer Res. 49, 4682–4689.Search in Google Scholar
Bos, J.L., Rehmann, H., and Wittinghofer, A. (2007). GEFs and GAPs: critical elements in the control of small G proteins. Cell 129, 865–877.10.1016/j.cell.2007.05.018Search in Google Scholar
Brunsveld, L., Kuhlmann, J., Alexandrov, K., Wittinghofer, A., Goody, R.S., and Waldmann, H. (2006). Lipidated Ras and Rab peptides and proteins – synthesis, structure, and function. Angew. Chemie Int. Ed. 45, 6622–6646.10.1002/anie.200600855Search in Google Scholar
Casey, P.J. (1995). Protein lipidation in cell signaling. Science 268, 221–225.10.1126/science.7716512Search in Google Scholar
Chen, Y.-X., Koch, S., Uhlenbrock, K., Weise, K., Das, D., Gremer, L., Brunsveld, L., Wittinghofer, A., Winter, R., Triola, G., et al. (2010). Synthesis of the Rheb and K-Ras4B GTPases. Angew. Chemie Int. Ed. 49, 6090–6095.10.1002/anie.201001884Search in Google Scholar
Cullen, P.J. (2001). Ras effectors: buying shares in Ras plc. Curr. Biol. 11, R342–R344.10.1016/S0960-9822(01)00189-0Search in Google Scholar
Dementiev, A. (2012). K-Ras4B lipoprotein synthesis: biochemical characterization, functional properties, and dimer formation. Protein Expr. Purif. 84, 86–93.10.1016/j.pep.2012.04.021Search in Google Scholar PubMed
Downward, J. (2003). Targeting RAS signalling pathways in cancer therapy. Nat. Rev. Cancer 3, 11–22.10.1038/nrc969Search in Google Scholar
Ebinu, J.O., Bottorff, D.A., Chan, E.Y.W., Stang, S.L., Dunn, R.J., and Stone, J.C. (1998). RasGRP, a Ras guanyl nucleotide-releasing protein with calcium- and diacylglycerol-binding motifs. Science 280, 1082 LP–1086.10.1126/science.280.5366.1082Search in Google Scholar
Erlkamp, M., Grobelny, S., and Winter, R. (2014). Crowding effects on the temperature and pressure dependent structure, stability and folding kinetics of staphylococcal nuclease. Phys. Chem. Chem. Phys. 16, 5965–5976.10.1039/c3cp55040kSearch in Google Scholar
Erwin, N., Sperlich, B., Garivet, G., Waldmann, H., Weise, K., and Winter, R. (2016). Lipoprotein insertion into membranes of various complexity: lipid sorting, interfacial adsorption and protein clustering. Phys. Chem. Chem. Phys. 18, 8954–8962.10.1039/C6CP00563BSearch in Google Scholar
Farnsworth, C.L., Freshney, N.W., Rosen, L.B., Ghosh, A., Greenberg, M.E., and Feig, L.A. (1995). Calcium activation of Ras mediated by neuronal exchange factor Ras-GRF. Nature 376, 524–527.10.1038/376524a0Search in Google Scholar
Fulton, A.B. (2016). How crowded is the cytoplasm? Cell 30, 345–347.10.1016/0092-8674(82)90231-8Search in Google Scholar
García de la Torre, J. and Bloomfield, V. A. (1977). Hydrodynamic properties of macromolecular complexes. I. Translation: Biopolymers 16, 1747–1763.Search in Google Scholar
García de la Torre, J., Pérez Sánchez, H.E., Ortega, A., Hernández, J.G., Fernandes, M.X., Diaz, F.G., and López Martínez, M.C. (2003). Calculation of the solution properties of flexible macromolecules: methods and applications. Eur. Biophys. J. 32, 477–486.10.1007/s00249-003-0292-0Search in Google Scholar PubMed
García de la Torre, J., Ortega, A., Pérez Sánchez, H. E., and Hernandez Cifre, J. G. (2005). MULTIHYDRO and MONTEHYDRO: conformational search and monte carlo calculation of solution properties of rigid or flexible bead models. Biophys. Chem. 116, 121–128.10.1016/j.bpc.2005.03.005Search in Google Scholar PubMed
García-Sáez, A.J., Chiantia, S., and Schwille, P. (2007). Effect of line tension on the lateral organization of lipid membranes. J. Biol. Chem. 282, 33537–33544.10.1074/jbc.M706162200Search in Google Scholar PubMed
Golebiewska, U., Gambhir, A., Hangyás-Mihályné, G., Zaitseva, I., Rädler, J., and McLaughlin, S. (2006). Membrane-bound basic peptides sequester multivalent (PIP2), but not monovalent (PS), acidic lipids. Biophys. J. 91, 588–599.10.1529/biophysj.106.081562Search in Google Scholar PubMed PubMed Central
Goodwin, J.S., Drake, K.R., Remmert, C.L., and Kenworthy, A.K. (2005). Ras diffusion is sensitive to plasma membrane viscosity. Biophys. J. 89, 1398–1410.10.1529/biophysj.104.055640Search in Google Scholar
Güldenhaupt, J., Rudack, T., Bachler, P., Mann, D., Triola, G., Waldmann, H., Kötting, C., and Gerwert, K. (2012). N-Ras forms dimers at POPC membranes. Biophys. J. 103, 1585–1593.10.1016/j.bpj.2012.08.043Search in Google Scholar
Hancock, J.F. (2003). Ras proteins: different signals from different locations. Nat Rev Mol Cell Biol 4, 373–385.10.1038/nrm1105Search in Google Scholar
Hancock, J.F. and Parton, R.G. (2005). Ras plasma membrane signalling platforms. Biochem. J. 389, 1–11.10.1042/BJ20050231Search in Google Scholar
Hancock, J.F., Paterson, H., and Marshall, C.J. (1990). A polybasic domain or palmitoylation is required in addition to the CAAX motif to localize p21ras to the plasma membrane. Cell 63, 133–139.10.1016/0092-8674(90)90294-OSearch in Google Scholar
Heinemann, F., Betaneli, V., Thomas, F.A., and Schwille, P. (2012). Quantifying lipid diffusion by fluorescence correlation spectroscopy: a critical treatise. Langmuir 28, 13395–13404.10.1021/la302596hSearch in Google Scholar PubMed
Jacobson, K., Mouritsen, O.G., and Anderson, R.G.W. (2007). Lipid rafts: at a crossroad between cell biology and physics. Nat Cell Biol 9, 7–14.10.1038/ncb0107-7Search in Google Scholar PubMed
Jang, H., Abraham, S.J., Chavan, T.S., Hitchinson, B., Khavrutskii, L., Tarasova, N.I., Nussinov, R., and Gaponenko, V. (2015). Mechanisms of membrane binding of small GTPase K-Ras4B farnesylated hypervariable region. J. Biol. Chem. 290, 9465–9477.10.1074/jbc.M114.620724Search in Google Scholar PubMed PubMed Central
Janosi, L. and Gorfe, A.A. (2010). Segregation of negatively charged phospholipids by the polycationic and farnesylated membrane anchor of kras. Biophys. J. 99, 3666–3674.10.1016/j.bpj.2010.10.031Search in Google Scholar PubMed PubMed Central
Kahya, N., Merkle, D., and Schwille, P. (2008). Pushing the complexity of model bilayers: novel prospects for membrane biophysics. In: Fluorescence of Supermolecules, Polymers, and Nanosystems SE – 10, M.N. Berberan-Santos, ed. (Berlin-Heidelberg: Springer), pp. 339–359.Search in Google Scholar
Kapoor, S., Werkmüller, A., Denter, C., Zhai, Y., Markgraf, J., Weise, K., Opitz, N., and Winter, R. (2011). Temperature-pressure phase diagram of a heterogeneous anionic model biomembrane system: Results from a combined calorimetry, spectroscopy and microscopy study. Biochim. Biophys. Acta Biomembr. 1808, 1187–1195.10.1016/j.bbamem.2011.01.011Search in Google Scholar PubMed
Kapoor, S., Triola, G., Vetter, I.R., Erlkamp, M., Waldmann, H., and Winter, R. (2012a). Revealing conformational substates of lipidated N-Ras protein by pressure modulation. Proc. Natl. Acad. Sci. 109, 460–465.10.1073/pnas.1110553109Search in Google Scholar
Kapoor, S., Weise, K., Erlkamp, M., Triola, G., Waldmann, H., and Winter, R. (2012b). The role of G-domain orientation and nucleotide state on the Ras isoform-specific membrane interaction. Eur. Biophys. J. 41, 801–813.10.1007/s00249-012-0841-5Search in Google Scholar
Kendrick, B.S., Chang, B.S., Arakawa, T., Peterson, B., Randolph, T.W., Manning, M.C., and Carpenter, J.F. (1997). Preferential exclusion of sucrose from recombinant interleukin-1 receptor antagonist: Role in restricted conformational mobility and compaction of native-state. Proc. Natl. Acad. Sci. USA 94, 11917–11922.10.1073/pnas.94.22.11917Search in Google Scholar
Khandelia, H., Ipsen, J.H., and Mouritsen, O.G. (2008). The impact of peptides on lipid membranes. Biochim. Biophys. Acta – Biomembr. 1778, 1528–1536.10.1016/j.bbamem.2008.02.009Search in Google Scholar
Kuzmin, P.I., Akimov, S.A., Chizmadzhev, Y.A., Zimmerberg, J., and Cohen, F.S. (2005). Line tension and interaction energies of membrane rafts calculated from lipid splay and Tilt. Biophys. J. 88, 1120–1133.10.1529/biophysj.104.048223Search in Google Scholar
Leventis, R. and Silvius, J.R. (1998). Lipid-binding characteristics of the polybasic carboxy-terminal sequence of K-ras4B. Biochemistry 37, 7640–7648.10.1021/bi973077hSearch in Google Scholar
Lingwood, D., Kaiser, H.-J., Levental, I., and Simons, K. (2009). Lipid rafts as functional heterogeneity in cell membranes. Biochem. Soc. Trans. 37, 955 LP–960.10.1042/BST0370955Search in Google Scholar
Luong, T.Q., Kapoor, S., and Winter, R. (2015). Pressure – a gateway to fundamental insights into protein solvation, dynamics, and function. ChemPhysChem 16, 3555–3571.10.1002/cphc.201500669Search in Google Scholar
Marshall, C.J. (1996). Ras effectors. Curr. Opin. Cell Biol. 8, 197–204.10.1016/S0955-0674(96)80066-4Search in Google Scholar
Mazhab-Jafari, M.T., Marshall, C.B., Smith, M.J., Gasmi-Seabrook, G.M.C., Stathopulos, P.B., Inagaki, F., Kay, L.E., Neel, B.G., and Ikura, M. (2015). Oncogenic and RASopathy-associated K-RAS mutations relieve membrane-dependent occlusion of the effector-binding site. Proc. Natl. Acad. Sci. USA 112, 6625–6630.10.1073/pnas.1419895112Search in Google Scholar PubMed PubMed Central
Muratcioglu, S., Chavan, T.S., Freed, B.C., Jang, H., Khavrutskii, L., Freed, R.N., Dyba, M.A., Stefanisko, K., Tarasov, S.G., Gursoy, A., et al. (2015). GTP-dependent K-Ras dimerization. Structure 23, 1325–1335.10.1016/j.str.2015.04.019Search in Google Scholar PubMed PubMed Central
Nicolini, C., Baranski, J., Schlummer, S., Palomo, J., Lumbierres-Burgues, M., Kahms, M., Kuhlmann, J., Sanchez, S., Gratton, E., Waldmann, H, et al. (2006). Visualizing association of N-ras in lipid microdomains: influence of domain structure and interfacial adsorption. J. Am. Chem. Soc. 128, 192–201.10.1021/ja055779xSearch in Google Scholar PubMed
Nielsen, L.K., Bjornholm, T., and Mouritsen, O.G. (2000). Critical phenomena: fluctuations caught in the act. Nature 404, 352.10.1038/35006162Search in Google Scholar PubMed
Niv, H., Gutman, O., Kloog, Y., and Henis, Y.I. (2002). Activated K-Ras and H-Ras display different interactions with saturable nonraft sites at the surface of live cells. J. Cell Biol. 157, 865 LP–872.10.1083/jcb.200202009Search in Google Scholar PubMed PubMed Central
Okeley, N.M. and Gelb, M.H. (2004). A designed probe for acidic phospholipids reveals the unique enriched anionic character of the cytosolic face of the mammalian plasma membrane. J. Biol. Chem. 279, 21833–21840.10.1074/jbc.M313469200Search in Google Scholar PubMed
Omerovic, J., Laude, A.J., and Prior, I.A. (2007). Ras proteins: paradigms for compartmentalised and isoform specific signalling. Cell. Mol. Life Sci. 64, 2575–2589.10.1007/s00018-007-7133-8Search in Google Scholar PubMed PubMed Central
Parton, R.G. and Hancock, J.F. (2004). Lipid rafts and plasma membrane microorganization: insights from Ras. Trends Cell Biol. 14, 141–147.10.1016/j.tcb.2004.02.001Search in Google Scholar PubMed
Patra, S., Erwin, N., and Winter, R. (2016). Translational dynamics of lipidated ras proteins in the presence of crowding agents and compatible osmolytes. ChemPhysChem 17, 2164–2169.10.1002/cphc.201600179Search in Google Scholar PubMed
Plowman, S.J., Muncke, C., Parton, R.G., and Hancock, J.F. (2005). H-ras, K-ras, and inner plasma membrane raft proteins operate in nanoclusters with differential dependence on the actin cytoskeleton. Proc. Natl. Acad. Sci. USA 102, 15500–15505.10.1073/pnas.0504114102Search in Google Scholar PubMed PubMed Central
Plowman, S.J., Ariotti, N., Goodall, A., Parton, R.G., and Hancock, J.F. (2008). Electrostatic interactions positively regulate K-Ras nanocluster formation and function. Mol. Cell. Biol. 28, 4377–4385.10.1128/MCB.00050-08Search in Google Scholar PubMed PubMed Central
Prakash, P. and Gorfe, A.A. (2016). Membrane orientation dynamics of lipid-modified small GTPases. Small GTPases, in press.10.1080/21541248.2016.1211067Search in Google Scholar PubMed PubMed Central
Prior, I.A. and Hancock, J.F. (2012). Ras trafficking, localization and compartmentalized signalling. Semin. Cell Dev. Biol. 23, 145–153.10.1016/j.semcdb.2011.09.002Search in Google Scholar PubMed PubMed Central
Prior, I.A., Harding, A., Yan, J., Sluimer, J., Parton, R.G., and Hancock, J.F. (2001). GTP-dependent segregation of H-ras from lipid rafts is required for biological activity. Nat Cell Biol 3, 368–375.10.1038/35070050Search in Google Scholar PubMed
Prior, I.A., Muncke, C., Parton, R.G., and Hancock, J.F. (2003). Direct visualization of Ras proteins in spatially distinct cell surface microdomains. J. Cell Biol. 160, 165–170.10.1083/jcb.200209091Search in Google Scholar PubMed PubMed Central
Ralston, G.B. (1990). Effects of ‘crowding’ in protein solutions. J. Chem. Educ. 67, 857.10.1021/ed067p857Search in Google Scholar
Rashid, R., Chee, S.M., Raghunath, M., and Wohland, T. (2015). Macromolecular crowding gives rise to microviscosity, anomalous diffusion and accelerated actin polymerization. Phys. Biol. 12, 34001.10.1088/1478-3975/12/3/034001Search in Google Scholar PubMed
Reuther, G., Tan, K.-T., Vogel, A., Nowak, C., Arnold, K., Kuhlmann, J., Waldmann, H., and Huster, D. (2006). The lipidated membrane anchor of full length N-Ras protein shows an extensive dynamics as revealed by solid-state NMR spectroscopy. J. Am. Chem. Soc. 128, 13840–13846.10.1021/ja063635sSearch in Google Scholar PubMed
Rocks, O., Peyker, A., Kahms, M., Verveer, P.J., Koerner, C., Lumbierres, M., Kuhlmann, J., Waldmann, H., Wittinghofer, A., and Bastiaens, P.I. (2005). An acylation cycle regulates localization and activity of palmitoylated Ras isoforms. Science 307, 1746–1752.10.1126/science.1105654Search in Google Scholar PubMed
Rocks, O., Peyker, A., and Bastiaens, P.I.H. (2006). Spatio-temporal segregation of Ras signals: one ship, three anchors, many harbors. Curr. Opin. Cell Biol. 18, 351–357.10.1016/j.ceb.2006.06.007Search in Google Scholar PubMed
Rotblat, B., Prior, I.A., Muncke, C., Parton, R.G., Kloog, Y., Henis, Y.I., and Hancock, J.F. (2004). Three separable domains regulate GTP-dependent association of H-ras with the plasma membrane. Mol. Cell. Biol. 24, 6799–6810.10.1128/MCB.24.15.6799-6810.2004Search in Google Scholar PubMed PubMed Central
Scheiffele, P., Rietveld, A., Wilk, T., and Simons, K. (1999). Influenza viruses select ordered lipid domains during budding from the plasma membrane. J. Biol. Chem. 274, 2038–2044.10.1074/jbc.274.4.2038Search in Google Scholar PubMed
Seeliger, J., Erwin, N., Rosin, C., Kahse, M., Weise, K., and Winter, R. (2015). Exploring the structure and phase behavior of plasma membrane vesicles under extreme environmental conditions. Phys. Chem. Chem. Phys. 17, 7507–7513.10.1039/C4CP05845CSearch in Google Scholar PubMed
Sezgin, E., Kaiser, H.-J., Baumgart, T., Schwille, P., Simons, K., and Levental, I. (2012). Elucidating membrane structure and protein behavior using giant plasma membrane vesicles. Nat. Protoc. 7, 1042–1051.10.1038/nprot.2012.059Search in Google Scholar PubMed
Silvius, J.R. (2002). Mechanisms of Ras protein targeting in mammalian cells. J. Membr. Biol. 190, 83–92.10.1007/s00232-002-1026-4Search in Google Scholar PubMed
Simons, K. and Toomre, D. (2000). Lipid rafts and signal transduction. Nat Rev Mol Cell Biol 1, 31–39.10.1038/35036052Search in Google Scholar PubMed
Simons, K. and Vaz, W.L.C. (2004). Model systems, lipid rafts, and cell membranes. Annu. Rev. Biophys. Biomol. Struct. 33, 269–295.10.1146/annurev.biophys.32.110601.141803Search in Google Scholar PubMed
Tian, T., Harding, A., Inder, K., Plowman, S., Parton, R.G., and Hancock, J.F. (2007). Plasma membrane nanoswitches generate high-fidelity Ras signal transduction. Nat. Cell Biol. 9, 905–914.10.1038/ncb1615Search in Google Scholar PubMed
Timasheff, S.N. (1993). The Control of protein stability and association by weak interactions with water: how do solvents affect these processes? Annu. Rev. Biophys. Biomol. Struct. 22, 67–97.10.1146/annurev.bb.22.060193.000435Search in Google Scholar PubMed
Vetter, I.R. and Wittinghofer, A. (2001). The Guanine nucleotide-binding switch in three dimensions. Science 294, 1299 LP–1304.10.1126/science.1062023Search in Google Scholar PubMed
Vogel, A., Tan, K.-T., Waldmann, H., Feller, S.E., Brown, M.F., and Huster, D. (2007). Flexibility of ras lipid modifications studied by 2H solid-state NMR and molecular dynamics simulations. Biophys. J. 93, 2697–2712.10.1529/biophysj.107.104562Search in Google Scholar PubMed PubMed Central
Vogel, A., Reuther, G., Weise, K., Triola, G., Nikolaus, J., Tan, K.-T., Nowak, C., Herrmann, A., Waldmann, H., Winter, R., et al. (2009). The lipid modifications of Ras that sense membrane environments and induce local enrichment. Angew. Chemie Int. Ed. 48, 8784–8787.10.1002/anie.200903396Search in Google Scholar
Weise, K., Triola, G., Brunsveld, L., Waldmann, H., and Winter, R. (2009). Influence of the lipidation motif on the partitioning and association of N-Ras in model membrane subdomains. J. Am. Chem. Soc. 131, 1557–1564.10.1021/ja808691rSearch in Google Scholar
Weise, K., Triola, G., Janosch, S., Waldmann, H., and Winter, R. (2010). Visualizing association of lipidated signaling proteins in heterogeneous membranes–Partitioning into subdomains, lipid sorting, interfacial adsorption, and protein association. Biochim. Biophys. Acta Biomembr. 1798, 1409–1417.10.1016/j.bbamem.2009.12.006Search in Google Scholar
Weise, K., Kapoor, S., Denter, C., Nikolaus, J., Opitz, N., Koch, S., Triola, G., Herrmann, A., Waldmann, H., and Winter, R. (2011). Membrane-mediated induction and sorting of K-Ras microdomain signaling platforms. J. Am. Chem. Soc. 133, 880–887.10.1021/ja107532qSearch in Google Scholar
Weise, K., Huster, D., Kapoor, S., Triola, G., Waldmann, H., and Winter, R. (2013). Gibbs energy determinants of lipoprotein insertion into lipid membranes: the case study of Ras proteins. Faraday Discuss. 161, 549–561.10.1039/C2FD20100CSearch in Google Scholar
Werkmüller, A., Triola, G., Waldmann, H., and Winter, R. (2013). Rotational and translational dynamics of Ras proteins upon binding to model membrane systems. ChemPhysChem 14, 3698–3705.10.1002/cphc.201300617Search in Google Scholar
Wittinghofer, A. and Pal, E.F. (1991). The structure of Ras protein: a model for a universal molecular switch. Trends Biochem. Sci. 16, 382–387.10.1016/0968-0004(91)90156-PSearch in Google Scholar
Wittinghofer, A. and Waldmann, H. (2000). Ras – A molecular switch involved in tumor formation. Angew. Chemie Int. Ed. 39, 4192–4214.10.1002/1521-3773(20001201)39:23<4192::AID-ANIE4192>3.0.CO;2-YSearch in Google Scholar
Wittinghofer, A., Scheffzek, K., and Ahmadian, M.R. (1997). The interaction of Ras with GTPase-activating proteins. FEBS Lett. 410, 63–67.10.1016/S0014-5793(97)00321-9Search in Google Scholar
Zhou, Y. and Hancock, J.F. (2015). Ras nanoclusters: versatile lipid-based signaling platforms. Biochim. Biophys. Acta Mol. Cell Res. 1853, 841–849.10.1016/j.bbamcr.2014.09.008Search in Google Scholar
Zhou, Y., Liang, H., Rodkey, T., Ariotti, N., Parton, R.G., and Hancock, J.F. (2014). Signal integration by lipid-mediated spatial cross talk between Ras nanoclusters. Mol. Cell. Biol. 34, 862–876.10.1128/MCB.01227-13Search in Google Scholar
Zhou, Y., Wong, C.-O., Cho, K., Hoeven, D. van der, Liang, H., Thakur, D.P., Luo, J., Babic, M., Zinsmaier, K.E., Zhu, M.X., et al. (2015). Membrane potential modulates plasma membrane phospholipid dynamics and K-Ras signaling. Science 349, 873 LP–876.10.1126/science.aaa5619Search in Google Scholar
Zimmerman, S.B. and Minton, A.P. (1993). Macromolecular crowding: biochemical, biophysical, and physiological consequences. Annu. Rev. Biophys. Biomol. Struct. 22, 27–65.10.1146/annurev.bb.22.060193.000331Search in Google Scholar
Zuckermann, M.J., Ipsen, J.H., Miao, L., Mouritsen, O.G., Nielsen, M., Polson, J., Thewalt, J., Vattulainen, I., and Zhu, H. (2004). Modeling lipid-sterol bilayers: applications to structural evolution, lateral diffusion, and rafts. In: Numerical Computer Methods, Part D, Methods in Enzymology, Vol. 383, L. Brand and M.L. Johnson, eds. (San Diego, USA: Academic Press), pp 198–229.10.1016/S0076-6879(04)83009-XSearch in Google Scholar
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