Conformational dynamics of helix S6 from Shaker potassium channel: simulation studies

Prolines in transmembrane (TM) alpha-helices are believed to play an important structural and/or functional role in membrane proteins. At a structural level a proline residue distorts alpha-helical structure due to the loss of at least one stabilizing backbone hydrogen bond, and introduces flexibility in the helix that may result in substantial kink and swivel motions about the effective "hinge." At a functional level, for example in Kv channels, it is believed that proline-induced molecular hinges may have a direct role in gating, i.e., the conformational change linked to opening/closing the channel to movement of ions. In this article we study the conformational dynamics of the S6 TM helix from of the Kv channel Shaker, which possesses the motif PVP--a motif that is conserved in Kv channels. We perform multiple molecular dynamics simulations of single S6 helices in a membrane-mimetic environment in order to effectively map the kink-swivel conformational space of the protein, exploiting the ability of multiple simulations to achieve greater sampling. We show that the presence of proline locally perturbs the helix, disrupting local dihedral angles and producing local twist and unwinding in the region of the hinge--an effect that is relaxed with distance from the PVP motif. We furthermore show that motions about the hinge are highly anisotropic, reflecting a preferred region of kink-swivel conformation space that may have implications for the gating process.     

Molecular dynamics simulations of inwardly rectifying (Kir) potassium channels: a comparative study

Inward rectifier potassium (Kir) channels regulate cell excitability and transport K+ ions across membranes. Homotetrameric models of three mammalian Kir channels (Kir1.1, Kir3.1, and Kir6.2) have been generated, using the KirBac3.1 transmembrane and rat Kir3.1 intracellular domain structures as templates. All three models have been explored by 10 ns molecular dynamics simulations in phospholipid bilayers. Analysis of the initial structures revealed conservation of potential lipid interaction residues (Trp/Tyr and Arg/Lys side chains near the lipid headgroup-water interfaces). Examination of the intracellular domains revealed key structural differences between Kir1.1 and Kir6.2 which may explain the difference in channel inhibition by ATP. The behavior of all three models in the MD simulations revealed that they have conformational stability similar to that seen for comparable simulations of, for example, structures derived from cryoelectron microscopy data. Local distortions of the selectivity filter were seen during the simulations, as observed in previous simulations of KirBac and in simulations and structures of KcsA. These may be related to filter gating of the channel. The intracellular hydrophobic gate does not undergo any substantial changes during the simulations and thus remains functionally closed. Analysis of lipid-protein interactions of the Kir models emphasizes the key role of the M0 (or "slide") helix which lies approximately parallel to the bilayer-water interface and forms a link between the transmembrane and intracellular domains of the channel.     

Filter flexibility and distortion in a bacterial inward rectifier K+ channel: simulation studies of KirBac1.1

The bacterial channel KirBac1.1 provides a structural homolog of mammalian inward rectifier potassium (Kir) channels. The conformational dynamics of the selectivity filter of Kir channels are of some interest in the context of possible permeation and gating mechanisms for this channel. Molecular dynamics simulations of KirBac have been performed on a 10-ns timescale, i.e., comparable to that of ion permeation. The results of five simulations (total simulation time 50 ns) based on three different initial ion configurations and two different model membranes are reported. These simulation data provide evidence for limited (<0.1 nm) filter flexibility during the concerted motion of ions and water molecules within the filter, such local changes in conformation occurring on an approximately 1-ns timescale. In the absence of K(+) ions, the KirBac selectivity filter undergoes more substantial distortions. These resemble those seen in comparable simulations of other channels (e.g., KcsA and KcsA-based homology models) and are likely to lead to functional closure of the channel. This suggests filter distortions may provide a mechanism of K-channel gating in addition to changes in the hydrophobic gate formed at the intracellular crossing point of the M2 helices. The simulation data also provide evidence for interactions of the "slide" (pre-M1) helix of KirBac with phospholipid headgroups.     

Conformational dynamics of the ligand-binding domain of inward rectifier K channels as revealed by molecular dynamics simulations: toward an understanding of Kir channel gating

Inward rectifier (Kir) potassium channels are characterized by two transmembrane helices per subunit, plus an intracellular C-terminal domain that controls channel gating in response to changes in concentration of various ligands. Based on the crystal structure of the tetrameric C-terminal domain of Kir3.1, it is possible to build a homology model of the ATP-binding C-terminal domain of Kir6.2. Molecular dynamics simulations have been used to probe the dynamics of Kir C-terminal domains and to explore the relationship between their dynamics and possible mechanisms of channel gating. Multiple simulations, each of 10 ns duration, have been performed for Kir3.1 (crystal structure) and Kir6.2 (homology model), in both their monomeric and tetrameric forms. The Kir6.2 simulations were performed with and without bound ATP. The results of the simulations reveal comparable conformational stability for the crystal structure and the homology model. There is some decrease in conformational flexibility when comparing the monomers with the tetramers, corresponding mainly to the subunit interfaces in the tetramer. The beta-phosphate of ATP interacts with the side chain of K185 in the Kir6.2 model and simulations. The flexibility of the Kir6.2 tetramer is not changed greatly by the presence of bound ATP, other than in two loop regions. Principal components analysis of the simulated dynamics suggests loss of symmetry in both the Kir3.1 and Kir6.2 tetramers, consistent with "dimer-of-dimers" motion of subunits in C-terminal domains of the corresponding Kir channels. This is suggestive of a gating model in which a transition between exact tetrameric symmetry and dimer-of-dimers symmetry is associated with a change in transmembrane helix packing coupled to gating of the channel. Dimer-of-dimers motion of the C-terminal domain tetramer is also supported by coarse-grained (anisotropic network model) calculations. It is of interest that loss of exact rotational symmetry has also been suggested to play a role in gating in the bacterial Kir homolog, KirBac1.1, and in the nicotinic acetylcholine receptor channel.     

High count rates with total internal reflection fluorescence correlation spectroscopy

We have modeled the structure of KirBac1.1 in an open state using as a starting point the structure of KirBac1.1 in its closed conformation (Protein Data Bank 1P7B). To test the validity of the open-state model, molecular dynamics simulations in octane, a lipid bilayer mimetic, were carried out. Simulations of the closed conformer were used for comparison purposes. The total simulation time was approximately 138 ns. The initial open model was refined by using projection maps obtained from electron microscopy experiments on two-dimensional crystals of the inwardly rectifying K+ channel KirBac3.1 from Magentospirillum magnetotacticum captured in its open state (C. Vénien-Bryan, unpublished data). Significant movements of the outer helices take place in going from the closed to the open model in agreement with structural and biochemical data in potassium channels, which suggests that gating is accomplished by a conformational change that takes place in the transmembrane domain upon an external stimulus. The motion of the inner helices is mainly achieved by bending at conserved glycine residues that have been previously reported to act as molecular hinges. Overall, these simulations suggest that the open conformer is stable, providing a plausible all-atom model that will enable the study of potential gating mechanisms in more detail.     

Functional Complementation and Genetic Deletion Studies of KirBac Channels: ACTIVATORY MUTATIONS HIGHLIGHT GATING-SENSITIVE DOMAINS*

The superfamily of prokaryotic inwardly rectifying (KirBac) potassium channels is homologous to mammalian Kir channels. However, relatively little is known about their regulation or about their physiological role in vivo. In this study, we have used random mutagenesis and genetic complementation in K⁺-auxotrophic Escherichia coli and Saccharomyces cerevisiae to identify activatory mutations in a range of different KirBac channels. We also show that the KirBac6.1 gene (slr5078) is necessary for normal growth of the cyanobacterium Synechocystis PCC6803. Functional analysis and molecular dynamics simulations of selected activatory mutations identified regions within the slide helix, transmembrane helices, and C terminus that function as important regulators of KirBac channel activity, as well as a region close to the selectivity filter of KirBac3.1 that may have an effect on gating. In particular, the mutations identified in TM2 favor a model of KirBac channel gating in which opening of the pore at the helix-bundle crossing plays a far more important role than has recently been proposed.     

Structure and dynamics of K channel pore-lining helices: a comparative simulation study

Isolated pore-lining helices derived from three types of K-channel have been analyzed in terms of their structural and dynamic features in nanosecond molecular dynamics (MD) simulations while spanning a lipid bilayer. The helices were 1) M1 and M2 from the bacterial channel KcsA (Streptomyces lividans), 2) S5 and S6 from the voltage-gated (Kv) channel Shaker (Drosophila melanogaster), and 3) M1 and M2 from the inward rectifier channel Kir6.2 (human). In the case of the Kv and Kir channels, for which x-ray structures are not known, both short and long models of each helix were considered. Each helix was incorporated into a lipid bilayer containing 127 palmitoyloleoylphosphatidylcholine molecules, which was solvated with approximately 4000 water molecules, yielding approximately 20, 000 atoms in each system. Nanosecond MD simulations were used to aid the definition of optimal lengths for the helix models from Kv and Kir. Thus the study corresponds to a total simulation time of 10 ns. The inner pore-lining helices (M2 in KcsA and Kir, S6 in Shaker) appear to be slightly more flexible than the outer pore-lining helices. In particular, the Pro-Val-Pro motif of S6 results in flexibility about a molecular hinge, as was suggested by previous in vacuo simulations (, Biopolymers. 39:503-515). Such flexibility may be related to gating in the corresponding intact channel protein molecules. Analysis of H-bonds revealed interactions with both water and lipid molecules in the water/bilayer interfacial region. Such H-bonding interactions may lock the helices in place in the bilayer during the folding of the channel protein (as is implicit in the two-stage model of membrane protein folding). Aromatic residues at the extremities of the helices underwent complex motions on both short (<10 ps) and long (>100 ps) time scales.     

Proline-induced hinges in transmembrane helices: possible roles in ion channel gating

A number of ion channels contain transmembrane (TM) alpha-helices that contain proline-induced molecular hinges. These TM helices include the channel-forming peptide alamethicin (Alm), the S6 helix from voltage-gated potassium (Kv) channels, and the D5 helix from voltage-gated chloride (CLC) channels. For both Alm and KvS6, experimental data implicate hinge-bending motions of the helix in an aspect of channel gating. We have compared the hinge-bending motions of these TM helices in bilayer-like environments by multi-nanosecond MD simulations in an attempt to describe motions of these helices that may underlie possible modes of channel gating. Alm is an alpha-helical channel-forming peptide, which contains a central kink associated with a Gly-x-x-Pro motif in its sequence. Simulations of Alm in a TM orientation for 10 ns in an octane slab indicate that the Gly-x-x-Pro motif acts as a molecular hinge. The S6 helix from Shaker Kv channels contains a Pro-Val-Pro motif. Modeling studies and recent experimental data suggest that the KvS6 helix may be kinked in the vicinity of this motif. Simulations (10 ns) of an isolated KvS6 helix in an octane slab and in a POPC bilayer reveal hinge-bending motions. A pattern-matching approach was used to search for possible hinge-bending motifs in the TM helices of other ion channel proteins. This uncovered a conserved Gly-x-Pro motif in TM helix D5 of CLC channels. MD simulations of a model of hCLC1-D5 spanning an octane slab suggest that this channel also contains a TM helix that undergoes hinge-bending motion. In conclusion, our simulations suggest a model in which hinge-bending motions of TM helices may play a functional role in the gating mechanisms of several different families of ion channels.     

Activation gating of hERG potassium channels: S6 glycines are not required as gating hinges

The opening of ion channels is proposed to arise from bending of the pore inner helices that enables them to pivot away from the central axis creating a cytosolic opening for ion diffusion. The flexibility of the inner helices is suggested to occur either at a conserved glycine located adjacent to the selectivity filter (glycine gating hinge) and/or at a second site occupied by glycine or proline containing motifs. Sequence alignment with other K+ channels shows that hERG possesses glycine residues (Gly648 and Gly657) at each of these putative hinge sites. In apparent contrast to the hinge hypotheses, substitution of both glycine residues for alanine causes little effect on either the voltage-dependence or kinetics of channel activation, and open state block by intracellular blockers. Substitution of the glycines with larger hydrophobic residues causes a greater propensity for the channel to open. We propose that in contrast to Shaker the pore of hERG is intrinsically more stable in the open than the closed conformation and that substitution at Gly648 or Gly657 further shifts the gating equilibrium to favor the open state. Molecular dynamics simulations indicate the S6 helices of hERG are inherently flexible, even in the absence of the glycine residues. Thus hERG activation gating exhibits important differences to other Kv channels. Our findings indicate that the hERG inner helix glycine residues are required for the tight packing of the channel helices and that the flexibility afforded by glycine or proline residues is not universally required for activation gating.     

Interaction of anesthetics with open and closed conformations of a potassium channel studied via molecular dynamics and normal mode analysis

A variety of experiments suggest that membrane proteins are important targets of anesthetic molecules, and that ion channels interact differently with anesthetics in their open and closed conformations. The availability of an open and a closed structural model for the KirBac1.1 potassium channel has made it possible to perform a comparative analysis of the interactions of anesthetics with the same channel in its open and closed states. To this end, all-atom molecular dynamics simulations supplemented by normal mode analysis have been employed to probe the interactions of the inhalational anesthetic halothane with both an open and closed conformer of KirBac1.1 embedded in a lipid bilayer. Normal mode analysis on the closed and open channel, in the presence and absence of halothane, reveals that the anesthetic modulates the global as well as the local dynamics of both conformations differently. In the case of the open channel, the observed reduction of flexibility of residues in the inner helices suggests a functional modification action of anesthetics on ion channels. In this context, preferential quenching of the aromatic residue motion and modulation of global dynamics by halothane may be seen as steps toward potentiating or favoring open state conformations. These molecular dynamics simulations provide the first insights into possible specific interactions between anesthetic molecules and ion channels in different conformations.     

Control of KirBac3.1 Potassium Channel Gating at the Interface between Cytoplasmic Domains

KirBac channels are prokaryotic homologs of mammalian inwardly rectifying potassium (Kir) channels, and recent structures of KirBac3.1 have provided important insights into the structural basis of gating in Kir channels. In this study, we demonstrate that KirBac3.1 channel activity is strongly pH-dependent, and we used x-ray crystallography to determine the structural changes that arise from an activatory mutation (S205L) located in the cytoplasmic domain (CTD). This mutation stabilizes a novel energetically favorable open conformation in which changes at the intersubunit interface in the CTD also alter the electrostatic potential of the inner cytoplasmic cavity. These results provide a structural explanation for the activatory effect of this mutation and provide a greater insight into the role of the CTD in Kir channel gating.     

Conserved gating hinge in ligand- and voltage-dependent K+ channels

Ion channels open and close their pore in a process called gating. On the basis of crystal structures of two voltage-independent K(+) channels, KcsA and MthK, a conformational change for gating has been proposed whereby the inner helix bends at a glycine hinge point (gating hinge) to open the pore and straightens to close it. Here we ask if a similar gating hinge conformational change underlies the mechanics of pore opening of two eukaryotic voltage-dependent K(+) channels, Shaker and BK channels. In the Shaker channel, substitution of the gating hinge glycine with alanine and several other amino acids prevents pore opening, but the ability to open is recovered if a secondary glycine is introduced at an adjacent position. A proline at the gating hinge favors the open state of the Shaker channel as if by preventing inner helix straightening. In BK channels, which have two adjacent glycine residues, opening is significantly hindered in a graded manner with single and double mutations to alanine. These results suggest that K(+) channels, whether ligand- or voltage-dependent, open when the inner helix bends at a conserved glycine gating hinge.     

The intrinsic flexibility of the Kv voltage sensor and its implications for channel gating

Analysis of the crystal structures of the intact voltage-sensitive potassium channel KvAP (from Aeropyrum pernix) and Kv1.2 (from rat brain), along with the isolated voltage sensor (VS) domain from KvAP, raises the question of the exact nature of the voltage-sensing conformational change that triggers activation of Kv and related voltage-gated channels. Molecular dynamics simulations of the isolated VS of KvAP in a detergent micelle environment at two different temperatures (300 K and 368 K) have been used to probe the intrinsic flexibility of this domain on a tens-of-nanoseconds timescale. The VS contains a positively charged (S4) helix which is packed against a more hydrophobic S3 helix. The simulations at elevated temperature reveal an intrinsic flexibility/conformational instability of the S3a region (i.e., the C-terminus of the S3 helix). It is also evident that the S4 helix undergoes hinge bending and swiveling about its central I130 residue. The conformational instability of the S3a region facilitates the motion of the N-terminal segment of S4 (i.e., S4a). These simulations thus support a gating model in which, in response to depolarization, an S3b-S4a "paddle" may move relative to the rest of the VS domain. The flexible S3a region may in turn act to help restore the paddle to its initial conformation upon repolarization.     

Structure and dynamics of the pore-lining helix of the nicotinic receptor: MD simulations in water, lipid bilayers, and transbilayer bundles

Multiple nanosecond duration molecular dynamics simulations on the pore-lining M2 helix of the nicotinic acetylcholine receptor reveal how its structure and dynamics change as a function of environment. In water, the M2 helix partially unfolds to form a molecular hinge in the vicinity of a central Leu residue that has been implicated in the mechanism of ion channel gating. In a phospholipid bilayer, either as a single transmembrane helix, or as part of a pentameric helix bundle, the M2 helix shows less flexibility, but still exhibits a kink in the vicinity of the central Leu. The single M2 helix tilts relative to the bilayer normal by 12 degrees, in agreement with recent solid state NMR data (Opella et al., Nat Struct Biol 6:374-379, 1999). The pentameric helix bundle, a model for the pore domain of the nicotinic receptor and for channels formed by M2 peptides in a bilayer, is remarkably stable over a 2-ns MD simulation in a bilayer, provided one adjusts the pK(A)s of ionizable residues to their calculated values (when taking their environment into account) before starting the simulation. The resultant transbilayer pore shows fluctuations at either mouth which transiently close the channel. Proteins 2000;39:47-55.     

A Kv channel with an altered activation gate sequence displays both "fast" and "slow" activation kinetics

The Kv1-4 families of K+ channels contain a tandem proline motif (PXP) in the S6 helix that is crucial for channel gating. In human Kv1.5, replacing the first proline by an alanine resulted in a nonfunctional channel. This mutant was rescued by introducing another proline at a nearby position, changing the sequence into AVPP. This resulted in a channel that activated quickly (ms range) upon the first depolarization. However, thereafter, the channel became trapped in another gating mode that was characterized by slow activation kinetics (s range) with a shallow voltage dependence. The switch in gating mode was observed even with very short depolarization steps, but recovery to the initial "fast" mode was extremely slow. Computational modeling suggested that switching occurred during channel deactivation. To test the effect of the altered PXP sequence on the mobility of the S6 helix, we used molecular dynamics simulations of the isolated S6 domain of wild type (WT) and mutants starting from either a closed or open conformation. The WT S6 helix displayed movements around the PXP region with simulations starting from either state. However, the S6 with a AVPP sequence displayed flexibility only when started from the closed conformation and was rigid when started from the open state. These results indicate that the region around the PXP motif may serve as a "hinge" and that changing the sequence to AVPP results in channels that deactivate to a state with an alternate configuration that renders them "reluctant" to open subsequently.     

Investigating the putative glycine hinge in Shaker potassium channel

The crystal structure of an open potassium channel reveals a kink in the inner helix that lines the pore (Jiang, Y.X., A. Lee, J.Y. Chen, M. Cadene, B.T. Chait, and R. MacKinnon. 2002. Nature 417:523-526). The putative hinge point is a highly conserved glycine residue. We examined the role of the homologous residue (Gly466) in the S6 transmembrane segment of Shaker potassium channels. The nonfunctional alanine mutant G466A will assemble, albeit poorly, with wild-type (WT) subunits, suppressing functional expression. To test if this glycine residue is critical for activation gating, we did a glycine scan along the S6 segment in the background of G466A. Although all of these double mutants lack the higher-level glycosylation that is characteristic of mature Shaker channels, one (G466A/V467G) is able to generate voltage-dependent potassium current. Surface biotinylation shows that functional and nonfunctional constructs containing G466A express at comparable levels in the plasma membrane. Compared with WT channels, the shifted-glycine mutant has impairments in voltage-dependent channel opening, including a right-shifted activation curve and a decreased rate of activation. The double mutant has relatively normal open-channel properties, except for a decreased affinity for intracellular blockers, a consequence of the loss of the side chain of Val467. Control experiments with the double mutants M440A/G466A and G466A/V467A suggest that the flexibility provided by Gly466 is more important for channel function than its small size. Our results support roles for Gly466 both in biogenesis of the channel and as a hinge in activation gating.     

Two different conformational states of the KirBac3.1 potassium channel revealed by electron crystallography

Potassium channels allow the selective flow of K(+) ions across membranes. In response to external gating signals, the potassium channel can move reversibly through a series of structural conformations from a closed to an open state. 2D crystals of the inwardly rectifying K(+) channel KirBac3.1 from Magnetospirillum magnetotacticum have been captured in two distinct conformations, providing "snap shots" of the gating process. Analysis by electron cryomicroscopy of these KirBac3.1 crystals has resulted in reconstructed images in projection at 9 A resolution. Kir channels are tetramers of four subunits arranged as dimers of dimers. Each subunit has two transmembrane helices (inner and outer). In one crystal form, the pore is blocked; in the other crystal form, the pore appears open. Modeling based on the KirBac1.1 (closed) crystal structure shows that opening of the ion conduction pathway could be achieved by bending of the inner helices and significant movements of the outer helices.     

The pore helix is involved in stabilizing the open state of inwardly rectifying K+ channels

Ion channels can be gated by various extrinsic cues, such as voltage, pH, and second messengers. However, most ion channels display extrinsic cue-independent transitions as well. These events represent spontaneous conformational changes of the channel protein. The molecular basis for spontaneous gating and its relation to the mechanism by which channels undergo activation gating by extrinsic cue stimulation is not well understood. Here we show that the proximal pore helix of inwardly rectifying (Kir) channels is partially responsible for determining spontaneous gating characteristics, affecting the open state of the channel by stabilizing intraburst openings as well as the bursting state itself without affecting K(+) ion-channel interactions. The effect of the pore helix on the open state of the channel is qualitatively similar to that of two well-characterized mutations at the second transmembrane domain (TM2), which stabilize the channel in its activated state. However, the effects of the pore helix and the TM2 mutations on gating were additive and independent of each other. Moreover, in sharp contrast to the two TM2 mutations, the pore helix mutation did not affect the functionality of the agonist-responsive gate. Our results suggest that in Kir channels, the bottom of the pore helix and agonist-induced conformational transitions at the TM2 ultimately stabilize via different pathways the open conformation of the same gate.     

A Kv channel with an altered activation gate sequence displays both "fast" and "slow" activation kinetics

The Kv1–4 families of K⁺ channels contain a tandem proline motif (PXP) in the S6 helix that is crucial for channel gating. In human Kv1.5, replacing the first proline by an alanine resulted in a nonfunctional channel. This mutant was rescued by introducing another proline at a nearby position, changing the sequence into AVPP. This resulted in a channel that activated quickly (ms range) upon the first depolarization. However, thereafter, the channel became trapped in another gating mode that was characterized by slow activation kinetics (s range) with a shallow voltage dependence. The switch in gating mode was observed even with very short depolarization steps, but recovery to the initial "fast" mode was extremely slow. Computational modeling suggested that switching occurred during channel deactivation. To test the effect of the altered PXP sequence on the mobility of the S6 helix, we used molecular dynamics simulations of the isolated S6 domain of wild type (WT) and mutants starting from either a closed or open conformation. The WT S6 helix displayed movements around the PXP region with simulations starting from either state. However, the S6 with a AVPP sequence displayed flexibility only when started from the closed conformation and was rigid when started from the open state. These results indicate that the region around the PXP motif may serve as a "hinge" and that changing the sequence to AVPP results in channels that deactivate to a state with an alternate configuration that renders them "reluctant" to open subsequently. voltage-gated potassium channel     

Molecular dynamics simulation of the M2 helices within the nicotinic acetylcholine receptor transmembrane domain: structure and collective motions

Multiple nanosecond duration molecular dynamics simulations were performed on the transmembrane region of the Torpedo nicotinic acetylcholine receptor embedded within a bilayer mimetic octane slab. The M2 helices and M2-M3 loop regions were free to move, whereas the outer (M1, M3, M4) helix bundle was backbone restrained. The M2 helices largely retain their hydrogen-bonding pattern throughout the simulation, with some distortions in the helical end and loop regions. All of the M2 helices exhibit bending motions, with the hinge point in the vicinity of the central hydrophobic gate region (corresponding to residues alphaL251 and alphaV255). The bending motions of the M2 helices lead to a degree of dynamic narrowing of the pore in the region of the proposed hydrophobic gate. Calculations of Born energy profiles for various structures along the simulation trajectory suggest that the conformations of the M2 bundle sampled correspond to a closed conformation of the channel. Principal components analyses of each of the M2 helices, and of the five-helix M2 bundle, reveal concerted motions that may be relevant to channel function. Normal mode analyses using the anisotropic network model reveal collective motions similar to those identified by principal components analyses.