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Assessing the Structure and Stability of Transmembrane Oligomeric Intermediates of an α‑Helical Toxin Rajat Desikan,† Prabal K. Maiti,‡ and K. Ganapathy Ayappa*,†,§ †

Department of Chemical Engineering, ‡Centre for Condensed Matter Theory, Department of Physics, and §Centre for Biosystems Science and Engineering, Indian Institute of Science, Bengaluru, India 560012 S Supporting Information *

ABSTRACT: Protein membrane interactions play an important role in our understanding of diverse phenomena ranging from membrane-assisted protein aggregation to oligomerization and folding. Pore-forming toxins (PFTs) are the primary vehicle for infection by several strains of bacteria. These proteins which are expressed in a water-soluble form (monomers) bind to the target membrane and conformationally transform (protomers) and self-assemble to form a multimer transmembrane pore complex through a process of oligomerization. On the basis of the structure of the transmembrane domains, PFTs are broadly classified into β or α toxins. In contrast to β-PFTs, the paucity of available crystal structures coupled with the amphipathic nature of the transmembrane domains has hindered our understanding of α-PFT pore formation. In this article, we use molecular dynamics (MD) simulations to examine the process of pore formation of the bacterial α-PFT, cytolysin A from Escherichia coli (ClyA) in lipid bilayer membranes. Using atomistic MD simulations ranging from 50 to 500 ns, we show that transmembrane oligomeric intermediates or “arcs” form stable proteolipidic complexes consisting of protein arcs with toroidal lipids lining the free edges. By creating initial conditions where the lipids are contained within the arcs, we study the dynamics of spontaneous lipid evacuation and toroidal edge formation. This process occurs on the time scale of tens of nanoseconds, suggesting that once protomers oligomerize, transmembrane arcs are rapidly stabilized to form functional water channels capable of leakage. Using umbrella sampling with a coarse-grained molecular model, we obtain the free energy of insertion of a single protomer into the membrane. A single inserted protomer has a stabilization free energy of −52.9 ± 1.2 kJ/mol and forms a stable transmembrane water channel capable of leakage. Our simulations reveal that arcs are stable and viable intermediates that can occur during the pore-formation pathway for ClyA.

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and infection propagation.5,6 The water-soluble PFT proteins expressed by the organism (referred to as monomers) spontaneously recognize and bind to the target plasma membrane or to specific protein or lipid receptors.2,5 Upon binding to the membrane, monomers undergo a conformational change into a membrane-bound form (termed a protomer). The assembly-competent membrane-bound protomer spontaneously undergoes membrane-assisted oligomeriza-

INTRODUCTION

The eukaryotic cellular plasma membrane, composed mainly of amphipathic lipid molecules, serves as a semipermeable barrier compartmentalizing the cytosolic cellular contents from the extracellular environment and is vital for life. Pore-forming toxins (PFTs) are an ubiquitous class of lytic proteins that primarily undermine the structural integrity of the plasma membrane and cause cell death by disrupting the osmotic and ionic gradients across the cellular plasma membrane.1−5 The pathogenesis of several bacterial infections in humans caused by Vibrio cholerae, Listeria monocytogenes, Bacillus anthracis, Escherica coli, and Staphylococcus aureus is primarily PFTmediated; transmembrane pore formation causes unregulated transport across the cell membrane, thus leading to cell death © XXXX American Chemical Society

Special Issue: Tribute to Keith Gubbins, Pioneer in the Theory of Liquids Received: July 1, 2017 Revised: September 19, 2017 Published: September 20, 2017 A

DOI: 10.1021/acs.langmuir.7b02277 Langmuir XXXX, XXX, XXX−XXX

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Figure 1. Schematics of the widely accepted prepore pathway and the growing pore pathway for PFTs, using ClyA as the model PFT, are illustrated (top view of the membrane). The various membrane-bound pore-forming intermediates of the dodecameric ClyA pore (single protomers, trimers, hexamers, and nonamers) are shown in red and are derived from the crystal structure of ClyA (PDB ID 2WCD), the membrane lipids are represented as green circles, and water molecules in the pore lumen are represented as blue circles. In the prepore pathway, none of the intermediates apart from the fully formed pore are capable of leakage.

transmembrane partially oligomerized pores or arcs that are lined by a lipid edge.1,11,12 The paucity of high-resolution structures of membrane-inserted PFT pores and pore-forming intermediates impedes our understanding of pore-forming mechanisms. Although water-soluble monomeric structures of several PFTs have been resolved, the resolution of membranebound intermediates, such as the protomeric and intermediate oligomeric states, and of the final transmembrane pores is challenging. In addition, tracking PFT oligomerization on membranes is a formidable challenge since pore-forming proteins lie well below the optical resolution limit, and the dynamics are typically complete on time scales of hundreds of microseconds.13 Ionic conductance and vesicle leakage experiments provide indirect evidence of the underlying pore kinetics and morphology.14,15 Hence, proposed mechanisms are either derived from indirect observations of pore assembly or reconstructed from the few available crystal structures of the PFT monomers and the membrane-inserted pores.1,16 While pore structures and assembly mechanisms of β-PFTs such as Staphylococcus aureus α-hemolysin,17 Staphylococcus aureus γ-hemolysin,18 and Vibrio cholerae cytolysin19 have been extensively studied, molecular mechanisms of α-PFT oligomerization and lipid reorganization during pore formation are poorly understood.1,2,4,14,20−23 Intrinsic participation of the membrane lipids along with the inserted transmembrane helices to form the pore complex is a recurring theme for α-PFTs.14,24 Escherichia coli cytolsin A (ClyA) is currently one of only two α-helical PFTs with available crystal structures of both the water-soluble monomer25 and the membrane-inserted pore complex.16 Thus, ClyA can be conveniently used to decipher the assembly mechanism for the class of α-helical PFTs.16,20,26 The crystal structure of the pore reveals the formation of a dodecameric homo-oligomeric complex having a total length of 13 nm, with the inner channel diameter varying from 7 nm at the extracellular end to 4 nm at the transmembrane or cytosolic end.16 The current understanding and challenges regarding the pore-forming pathway of ClyA are detailed below.

tion with other protomers to form higher-order oligomeric pore intermediates. The process of oligomerization is terminated upon formation of the final multimeric transmembrane pore complex, whose diameters typically range from a few to tens of nanometers.2 PFTs are primarily classified as α- and β-PFTs, depending on whether the transmembrane domains of the pore assume amphiphilic α-helices or β-sheets as the dominant secondary structures.2 Unlike protein aggregation, which is driven primarily by misfolded states, the transmembrane pores formed by the PFTs have a definite oligomeric structure implying the underlying stability and robustness associated with this process of membrane-assisted self-assembly. In contrast to PFTs, integral host membrane proteins (especially those with α-helical transmembrane domains) are partitioned into the lipid membrane by the translocon protein complex, an active process that requires energy supply by GDP−GTP exchange and multiple cellular machineries to work in tandem.7,8 Therefore, PFTs are unique from a membrane−protein perspective because the toxins are originally secreted in a water-soluble form but eventually sample the membrane environment to form multimeric integral transmembrane channels.1,2 Many mechanisms for understanding protomer oligomerization on the target membrane have been proposed. According to the widely accepted prepore paradigm (illustrated in Figure 1), protomers oligomerize on an intact membrane into a fully formed prepore, and transmembrane pore formation occurs with the insertion of the prepore assembly into the plasma membrane. This transition can be accompanied by a large conformational change as in the case of cholesterol-dependent cytolysins such as pneumolysin.9 The prepore pathway has been experimentally verified for many members of the class of β-PFTs such as α-hemolysin and γ-hemolysin or the cholesterol-dependent cytolysins such as perfringolysin O.10 Alternately, in the growing pore paradigm (illustrated in Figure 1), membrane-inserted pore intermediates also known as arcs grow by oligomerization to form the pore complex. This pathway is supported for some PFTs by the observation of B


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Figure 2. Top and front views of starting configurations of the ClyA arcs (6-mer to 10-mer and the 12-mer) are illustrated here. The pink portion of the arcs corresponds to the solvent-exposed domain, and cyan represents the transmembrane domain. The n-mer complexes were formed by simply removing the required number of pore subunits from the 12-mer. During the course of all atomistic simulations, the arc structures do not deviate significantly from the initial configurations shown here (discussed later).

ClyA pore as well as ClyA arcs at various levels of oligomerization (6-mer to 10-mer). In both atomistic and coarse-grained simulations, we observe that the 1-mer is stable and creates a transmembrane water channel. Coarse-grained simulations using the MARTINI force field (with polarizable water44 and PME electrostatics) and umbrella sampling are used to obtain the free energy of protomer−membrane binding. These simulations show that a single membrane-inserted protomer is a thermodynamically favorable state. To address the issue of partially oligomerized intermediates, we performed to our knowledge for the first time extensive all-atom molecular dynamics simulations of 6-mer to 10-mer arcs in both saturated DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) and unsaturated POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid membranes. In all simulations carried out over 50−500 ns, the proteolipid arclike structures retain their structural integrity, indicating that these purported structures are stable. We observe that lipids initially present in the arc spontaneously evacuate the arc interior, leading to the formation of a transmembrane water channel, and we discuss the possible biological implications of our observations.

The water-soluble ClyA monomer initially binds to the target membrane, which contains cholesterol that acts as a lipid receptor for ClyA,5 and subsequent membrane-assisted oligomerization results in the formation of the transmembrane pore complex. Surprisingly little is known about ClyA’s oligomerization pathways, the molecular role for cholesterol, and the fate of lipids during pore formation.20,21 ClyA pore intermediates (termed arcs) in electron micrographs have been observed upon inducing pore formation in detergent,27,28 in planar lipid monolayer films,29 and in single-molecule experiments in detergent.30 Combined experimental and modeling studies have shown that these ClyA arcs (1-mer to 11-mer) mostly oligomerize in a reversible and sequential manner on the membrane,15,31 though nonsequential oligomerization has been shown in detergents.30,32 While ClyA was previously assumed to follow the prepore pathway16 where only the 12-mer causes leakage, an experimental and modeling study (performed in our laboratory) of ClyA-induced calcein dye leakage from small unilamellar vesicles15 has shown that 5-mer to 12-mer ClyA arcs cause leakage. An unlikely noncanonical pathway, where intact ClyA prepores oligomerize in the absence of membranes and directly insert into intact target membranes upon contact, had previously been proposed,33 but this mechanism has been challenged34 and is not considered in this study. Several questions which require a molecular understanding of pore formation remain unanswered in this extended paradigm of ClyA pore formation. Two of them are the following: (i) Is a membrane-inserted protomer a favorable state, and can it form a water channel? (ii) How do the membrane-inserted arcs clear the central lipids corresponding to the pore lumen to form stable water channels capable of leakage? Because experiments are often resolution-limited on spatiotemporal scales, we attempt to answer these questions in this article with evidence from fully atomistic and coarse-grained molecular dynamics simulations. Fully atomistic MD simulations of PFTs enable us to observe equilibrium configurations of these large membrane−protein complexes at molecular resolution and have been used to study the structure and properties of the ClyA pore,35−37 the mechanism of conformational transition from the soluble ClyA monomer to the membrane-bound protomer,38 and transport properties of various molecules through the pore lumen of the β-PFT, α-hemolysin.39−43 In this article, we carry out MD simulations of the single transmembrane ClyA protomer (1-mer) and the full 12-mer

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COMPUTATIONAL METHODS

All-Atom MD Simulations. The dodecameric crystal structure of the ClyA pore channel (PDB ID 2WCD) has unresolved N-terminal residues 1−7 and C-terminal residues 293−303, and these residues were added to the crystal structure as described previously.35 Standard residue protonation states according to the force field definitions have been assumed for all protein molecules in this study. Coordinates of the ClyA protomer as well as that of partial n-mer pore intermediates or arcs were obtained from the reconstructed crystal structure. The implicit assumption here is that in the absence of further structural information on these elusive pore intermediates it is reasonable to assume that the protomers’ structure and assembly in the arcs are not drastically different from those of the protomers in the crystal structure of the ClyA pore. As mentioned in the Introduction, multiple studies have observed ClyA arcs, and combined experimental and kinetic modeling studies have predicted their existence.15,27−32,34 Even if the structures were slightly different, molecular dynamics simulations enable conformational sampling and thus often yield energetically relaxed equilibrium structures at molecular resolution, which can be utilized to deduce the mechanism and energetics of pore formation. The 6-mer to 10-mer complexes and the 12-mer are illustrated in Figure 2 and are obtained by deleting the requisite number of protomers from the pore crystal structure. All of the MD simulations presented in the main text of this article were performed using C


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Langmuir GROMACS software version 4.6.4 (www.gromacs.org),45 and some simulations in the Supporting Information were performed using GROMACS software version 2016.3 (see the Supporting Information for details). Visualization of the initial and final configurations obtained from the simulations was performed with VMD version 1.9.3.46 Additional analyses were carried out using self-written tools in MATLAB version R2017a. The single ClyA protomer as well as the n-mer arcs were inserted into pre-equilibrated DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) or POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) membranes by deleting the overlapping lipids between the protein and membrane. The lipid−protein complex was solvated using TIP3P47 water molecules, with adequate solvent buffers on both the solventexposed side and the cytosolic side of the ClyA arcs. Each ClyA protomer carries a positive charge of 7, hence a sufficient number of Na+ counterions (42, 49, 56, 63, 70 for the 6-mer, 7-mer, 8-mer, 9-mer, and 10-mer, respectively) were added to create charge-neutral initial configurations. The 12-mer simulations performed previously35 and the 1-mer simulations were carried out at 0.15 M NaCl concentration. Upon solvent and ion addition, the solvent molecules in contact with the lipid core in the bilayer−protein interstices were removed. The AMBER 99SB-ILDN force field48 with ϕ corrections,49 which was shown to perform well for proteins,50 was used to describe the intraand intermolecular interactions of the protein and ions. The AMBER force field-compatible Slipid parameters51 were used to model the DMPC and POPC lipids. Electrostatic interactions were computed using the particle mesh Ewald method52 with a 1.0 nm real space cutoff, and the van der Waal’s interactions were computed with a 1.0 nm cutoff. All bonds were constrained using the LINCS algorithm.53 A leapfrog integrator with a 2 fs integration time step was used along with Verlet buffered lists (target energy drift of 0.005 kJ/mol/ns per atom). Neighbor lists were updated every 10 steps; three-dimensional periodic boundary conditions were used. For the single solvated protomer simulations in the absence of a membrane, simulations were carried out with the above parameters but in the NVT ensemble without pressure coupling. A synopsis of all simulations performed along with relevant detail is shown in Table 1. All systems were energy minimized for 10 000−100 000 steps using the steepest-descent method (step size 0.01 nm). Initially, 200−500 ps runs in the NPT ensemble with harmonic restraints on the protein atoms were performed. Subsequently, 50- to 500-ns-long runs in the NPT ensemble were performed for the ClyA protomer and all arcs in DMPC and POPC membranes as well the 12-mer pore in a DMPC membrane (Table 1). We used the Nosé−Hoover thermostat54,55 or the velocity-rescale thermostat56 to control the system temperature at 310 K by using a time constant of 0.5 or 0.1 ps, respectively. System pressure corresponding to 1 bar was maintained in the plane of the membrane as well as in the direction normal to the membrane by using the semi-isotropic Parrinello−Rahman pressure-coupling scheme57 (isothermal compressibilities of κxy = κz = 4.5 × 10−5 bar−1, time constant of 10 ps). PMF of ClyA Protomer Membrane Binding from MARTINI Simulations with Polarizable Water. The single ClyA protomer in a DMPC membrane was set up using the MARTINI force field (Elnedyn 2.2) with a polarizable water model44 and PME in order to capture the electrostatics accurately, especially at the complex protein−membrane−water interfaces. Upon equilibrating the ClyA protomer in the DMPC membrane for 100 ns, the steered MD feature of GROMACS was used to create 24 initial configurations along the reaction coordinate ζ (defined as the distance between the centers of mass of the membrane and protomer) such that each window was separated at intervals of Δζ = 0.2 nm. The phosphate atoms of the membrane were restrained in the Z coordinate using harmonic restraints of 100 000 kJ mol−1 nm−2. Solvent and unit-cell equilibration simulations for 2 ns and umbrella sampling simulations for 100 ns per window were carried out with a weak restraining harmonic force at that particular value of ζ. A spring constant of 10 kJ mol−1 nm−2 was used for all windows (see Figure S2 for the rationale behind choosing this value), except windows 11 and 12 which were simulated again

Table 1. Complete List of All of the Production Simulations Performeda NaCl concentration (M)

protein

membrane

ensemble

simulation time (ns)

ClyA protomer (1mer) solvated ClyA protomer ClyA arc (6mer) ClyA arc (6mer) ClyA arc (6-mer, CHARMM36, SI) ClyA arc (7mer) ClyA arc (7mer) ClyA arc (8mer) ClyA arc (9mer) ClyA arc (9mer) ClyA arc (9-mer, CHARMM36, SI) ClyA arc (10mer) ClyA arc (10mer) ClyA pore (12-mer) ClyA protomer (MARTINI, PMF) ClyA protomer (MARTINI, Figure S2)

DMPC

NPT

500

0.15

NVT

300

0.15

DMPC

NPT

224

charge-neutral

POPC

NPT

50

charge-neutral

POPC

NPT

20

0.15

DMPC

NPT

50

charge-neutral

POPC

NPT

50

charge-neutral

POPC

NPT

50

charge-neutral

DMPC

NPT

50

charge-neutral

POPC

NPT

50

charge-neutral

POPC

NPT

20

0.15

DMPC

NPT

289

charge-neutral

POPC

NPT

50

charge-neutral

DMPC

NPT

100

0.15

DMPC

NPT

2400

charge-neutral

DMPC

NPT

200

charge-neutral

a

All of the simulations were carried out with explicit solvent and at 310 K. For charge-neutral simulations, only Na+ counterions are present to ensure charge neutrality. with spring constants of 100 kJ mol−1 nm−2. This is because windows 11 and 12 correspond to the water−bilayer interface and exhibit large fluctuations in ζ for weak harmonic restraints. All simulations were performed in the NPT ensemble, and the simulation parameters and choice of algorithms are similar to that used in the all-atom simulations (described above). Briefly, a leapfrog integrator with a 20 fs integration time step was used, PME electrostatics were employed with an effective dielectric constant of ϵr = 2.5 and a cutoff of 1.2 nm, the velocity-rescale thermostat56 was used to set the system temperature at 310 K with a time constant of 0.1 ps, and the semi-isotropic Parrinello−Rahman pressure coupling scheme57 with a time constant of 12 ps was utilized to equilibrate the unit cell. To ensure that the protein’s internal conformation is at equilibrium at each window during umbrella sampling, we examine the RMSD of the full protein and helix αA1 from the 100-ns-long unrestrained equilibrium simulations of window 24 (described in Figure S2). We find that the conformational change of the N-terminus is complete by 20 ns (Figure S3), and a final snapshot after 100 ns is illustrated in Figure S4. Hence, the first 20 ns of each window is censored, and the resulting PMF and associated binding energy are reported in Figure 5. The effect of varying the censoring threshold on the PMF is reported in Figure S5, where we find that the PMF is relatively insensitive to the censoring threshold. The potential of mean force along the reaction coordinate was obtained by using the weighted histogram analysis method (WHAM; implemented in the g_wham58 tool in GROMACS version 4.6.4.) on histograms from the umbrella sampling trajectories, and the final PMF was generated by dividing histograms along the reaction coordinate into 200 bins. The error bars on the PMF were D


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Figure 3. (A) Initial and final snapshots of a single ClyA protomer and the ClyA pore inserted into DMPC membranes (the N-terminal helix αA1 is colored green, the C-terminal helix αG is colored blue, and the β-tongue consisting of residues 177−203 is colored magenta). (B) RMSD traces of the various conformations of ClyA show structural differences. (C) Comparison of the equilibrium RMSFs of the single transmembrane ClyA protomer (averaged over various blocks of time) with a protomer subunit in the transmembrane ClyA pore. (D) Axial tilts of helices αA1 and αB with respect to the Z axis are plotted as a function of simulation time for the single protomer and are compared with the tilts averaged over all protomer subunits in the ClyA pore. The axes for helices αA1 and αB are defined as vectors passing through the center of mass of residues 11 and 33 and residues 38 and 99 (shown as labeled yellow beads in the protomer on the right), respectively. (E) Temporal trend in the radius of gyration (Rg) of the single protomer. time of λCOM(t), estimated by fitting a single exponential to the 6-mer and 10-mer trajectories, was found to be τ6 = 1.13 ns and τ10 = 2.04 ns, respectively. Subsequently, λCOM(t) from the 6-mer and 10-mer trajectories was divided into blocks of length τ6 and τ10 after discarding the first 50 ns of both trajectories, and k and F were computed for every block from eq 5. The mean k and F values were computed by averaging over all of the blocks, and error bars were computed by 1deletion block-jackknife resampling.59,60 From this method, the mean values of k and F for the 6-mer were calculated to be 39.68 ± 10.56 pN/nm and 306.06 ± 81.42 pN, respectively, and for the 10-mer, 11.39 ± 3.78 pN/nm and 76.61 ± 25.03 pN, respectively.

computed by generating 2000 bootstrapped trajectories from the obtained histogram such that the new random trajectories had similar converged histograms and autocorrelation times. Spring Constant and Force between the Edge Protomers from Atomistic MD Simulations. If the distance between the edge protomers in the arcs is normally distributed around a mean, then these edge protomers can be assumed to be connected by a virtual harmonic spring with a spring constant k and a restoring force F. Assuming a classical Hamiltonian for the spring in the canonical ensemble, the equation for the spring constant (in kJ mol−1 nm−2) at a temperature of 310 K can be derived as shown below. The Hamiltonian of a one-dimensional harmonic oscillator is given as

p2 kr 2 /(p , r ) = + 2m 2

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RESULTS Membrane-Bound ClyA Protomer Retains Structural Integrity and Stabilizes a Continuous Transmembrane Water Channel. A key factor in the pore-formation process of PFTs such as ClyA is the conformational transformation from a water-soluble monomer to an assembly-competent protomer. To the best of our knowledge, experimental data pertaining to the energetics of membrane binding of ClyA is absent in the literature. First, we determine if the single transmembrane protomer is structurally stable relative to a protomer bound in the fully oligomeric pore. To contrast the structural attributes of ClyA in these two conformations (single transmembrane protomer and bound protomer in the pore complex), a 500-nslong all-atom MD simulation of a single transmembrane ClyA protomer and a 100-ns-long all-atom simulation of the transmembrane ClyA pore were performed. The initial and final simulation snapshots are illustrated in Figure 3A. The RMSD traces with respect to the initial simulation structures of the single membrane-inserted protomer and the pore are contrasted (illustrated in Figure 3B). The single membrane-inserted protomer has a RMSD with larger fluctuations when compared to that of the pore. A comparison of the per-residue root-mean-square fluctuations (RMSFs) between the single transmembrane ClyA protomer in comparison to protomer subunits in the dodecameric pore (RMSF averaged over all 12 protomer subunits) is illustrated in Figure 3C. The fluctuations of all of the residues in the single protomer are consistently higher than the residues in the pore, and this is attributed to the absence of stabilizing protein− protein interactions for the single protomer. Changes in the orientation of the single transmembrane protomer with respect

(1)

where r is defined as the normally distributed Euclidean distance between the center of mass of the two edge protomers. The variance in the mean position can be calculated as

∬ r 2e(−β /(p , r)) dp dr ⎛⎜ ∬ r e(−β /(p , r)) dp dr ⎞⎟ ⟨r ⟩ − ⟨r ⟩ = −⎜ (−β /(p , r )) dp dr ⎟ ∬ e(−β /(p , r))dp dr ⎠ ⎝ ∬e 2

2

2

(2)

⟨r 2⟩ − ⟨r ⟩2 =

∫ e(−βp

2

/2m)

dp ∫ r 2e(−βkr

2

(−βp /2m)

∫e

/2)

2

(−βkr /2)

dp ∫ e

⎛ (−βp /2m) ⎞ dp ∫ r e(−βkr /2) dr ⎟ ∫e −⎜ 2 ⎜ (−βp2 /2m) ⎟ dp ∫ e(−βkr /2) dr ⎠ ⎝∫e 2

2

2

dr

dr

2

(3)

Because these are Gaussian integrals, we get

⟨r 2⟩ − ⟨r ⟩2 =

(

κBT 1 −

2 π

) (4)

k

Hence,

k=

(

κBT 1 − 2

2 π 2

⟨r ⟩ − ⟨r ⟩

) and F =

(

κBT 1 −

2 π

)⟨r⟩

2

⟨r ⟩ − ⟨r ⟩2

(5) −1

where magnitude of the force (F) is in pN molecule . Because we report only single-molecule results, we write the units of force simply as pN. From now onward, r(t) is referred to as λCOM(t). Results for the 6-mer and the 10-mer are calculated as follows. The autocorrelation E


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Langmuir to the membrane are illustrated by a comparison of the helix tilts of helices αA1 and αB, as shown in Figure 3D. It can be seen that the helix tilts of the single protomer exhibits drift as well as large fluctuations from the initial value, while a protomer in the pore is stable. This is consistent with previous Go-model simulations of the ClyA protomer in the presence of an explicit model membrane,38 where the protomer samples a large number of helix tilt angels in the membrane-inserted state. The temporal trend of the radius of gyration (Rg) of the single protomer is shown in Figure 3E, and we observe stable trends by the end of the 500-ns-long simulation. Overall, these results confirm that the protomer in the pore is a more favorable state because of protein−protein interactions with neighboring protomers, but the single protomer does not lose its structural integrity in the absence of the other protomers. The all-atom MD simulations of the single membraneinserted protomer (described above) also show for the first time to our knowledge that a stable and continuous membranespanning water column is stabilized by the hydrophilic face of the amphipathic transmembrane N-terminal helix (Figure 4A; also see Figure S1). Transmembrane amphipathic helix αA1 is cleanly separated into hydrophobic and hydrophilic surfaces, thus resembling a Janus surface (illustrated in Figure 4A). The

hydrophobic surface interacts with the hydrophobic lipid acyl chains, whereas the hydrophilic surface stabilizes the spontaneously formed transmembrane water channel. Because the equilibration of lipids and solvent around the protein is crucial, we carried out simulations with an alternate equilibration protocol and a completely different force field, CHARMM36.61,62 The single protomer was inserted into a POPC membrane using the CHARMM-GUI membrane builder63−65 (http://www.charmm-gui.org/), ensuring that lipids were completely packed around the protein, with extensive unit cell and solvent equilibration simulations (details in Supporting Information). Using this initial configuration, 20 ns simulations revealed the formation of the water channel as discussed above, indicating that the formation of the water channel is a robust phenomenon (Figure S6). From this finding, it is conceivable that the oligomerization of the protomers in the noninserted state extends this transmembrane domain into a Janus surface, with the alkyl lipid tails stabilized by the hydrophobic outer surface and the aqueous channel in the pore lumen stabilized by the inner hydrophilic surface, as described in the growing pore mechanism (Figure 1). Another α-PFT fragaceatoxin C also possesses an amphipathic N-terminal helix with a Janus surface topography which forms the transmembrane domain of the membrane-inserted pore.24 These findings for ClyA indicate that oligomerization and membrane leakage can be initiated by a single membrane-inserted protomer. We next assess the binding free energy of a single ClyA protomer to a DMPC membrane by employing coarse-grained simulations (MARTINI force field with polarizable water and full electrostatics) with the umbrella sampling technique. We point out that although it is desirable to obtain the PMF using an all-atom description, complete umbrella sampling, given the size of the protein and the corresponding simulation box, is computationally prohibitive. Furthermore, MARTINI force fields have been know to capture protein membrane interactions quite accurately.66,67 The free-energy profile is shown in Figure 5. It can be clearly seen that membrane binding by ClyA is thermodynamically favorable, with a freeenergy gain of ΔE = −52.9 ± 1.2 kJ/mol, or ∼ −12.6 ± 0.3 kcal/mol, at ζ ≈ 6.0 nm for membrane-inserted conformations relative to completely solvated conformations (configurations illustrated in Figure 5). This is similar to a previous estimate of −46 kJ/mol for ClyA.38 The membrane-inserted protomer (from the initial window) of the coarse-grained simulations also stabilizes a transmembrane water channel as shown in Figure 4B. In addition to this, the protomer is completely solvated in the final windows of the umbrella sampling simulations and is seen to undergo significant structural distortions in the N-terminus and helix αA1. The final snapshot after 100 ns from umbrella sampling simulations of configuration 24 is magnified in Figure S4, and structural distortions such as unfolding of the Nterminus and helix αA1 (colored orange) can be observed. Fully Solvated Protomer Is Structurally Unstable Compared to a Membrane-Inserted Protomer. To analyze the structural distortions of the fully solvated protomer in detail, fully atomistic simulations of the transmembrane vs solvated protomer conformations were compared, and the initial and final snapshots of the protomer in both solvated and transmembrane configurations are shown in Figure 6A−F. The evident distortion in the N-terminus and helix αA1 (residues 1−34) is due to the exposure of hydrophobic residues in this

Figure 4. (A) Instantaneous snapshot at 300 ns of the transmembrane protomer from an all-atom MD simulation shows the transmembrane water channel. Final snapshots at 500 ns are shown in Figure S1. Transmembrane residues 1 to 36, which comprise the N-terminus and the amphipathic helix αA1, are depicted below with the hydrophobic residues colored green, hydrophilic residues colored red, and proline 36 colored purple. (B) Snapshots (100 ns each) of the transmembrane protomer from the first window of the MARTINI umbrella sampling simulations (also illustrated in Figure 5) show that the single protomer forms a water channel in coarse-grained simulations as well. Note that the center-of-mass distances between the protomer and the membrane are restrained by a weak harmonic force in MARTINI, but all-atom simulations are not. F


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Figure 5. Free energy of the protomer binding to the membrane is shown using the potential of mean force (PMF) along reaction coordinate ζ (distance between the center of mass of the membrane and the center of mass of the protomer). The PMF was obtained by simulating 24 configurations of the transmembrane protomer, with overlapping histograms at intervals of Δζ = 0.2 nm for 100 ns each (Methods). These simulations were carried out using the MARTINI coarse-grained force field with polarizable water and full electrostatics. Snapshots (100 ns) from the 1st window, 13th window, and last window are illustrated along with the value of ζ at 100 ns. The protein residues corresponding to the N-terminus and helix αA1 and the rest of the protein are represented by orange and red vdW spheres, respectively. PO4 membrane beads are shown as green vdW spheres.

amphipathic domain to the aqueous environment (also see Figure S4). This is corroborated by the time traces of the backbone root-mean-square deviations (RMSD) of this domain (shown in Figure 6G) which plateau at a higher value for the solvated protomer as well as the decreased helicity of these residues in the solvated protomer as compared to that of the membrane-inserted protomer. The loss of structural integrity in the putative transmembrane domain of the solvated protomer (illustrated in Figure 6G) suggests that the membrane-bound protomer conformation with the N-terminus residues bound to the membrane is structurally favorable. The protomer can be in a noninserted state with the amphipathic N-terminus and helix αA1 bound to the upper leaflet, or the protomer may span the membrane and create a membrane channel as shown in Figure 4. Similar evidence for membrane insertion of the N-terminal helix prior to oligomerization has been shown for other αhelical pore-forming proteins such as Equinatoxin II68 and Bax.69 Spontaneous Formation of Membrane-Permeabilizing Proteolipid ClyA Arcs. In the previous section (Figure 4), we observed that a single membrane-inserted protomer stabilizes a transmembrane water channel. In this section, we investigate the stability of larger transmembrane arcs to displace central lipids and form stable water channels in the membrane. To observe the spontaneous formation of water channels, the transmembrane arcs were initially inserted into previously wellequilibrated DMPC lipid bilayers with the lipids initially present in and around ClyA arcs. No water defect was present at the start of simulations, and the membrane was intact except for the inserted protein complexes. Representative simulation

Figure 6. (A−F) Initial and final simulation snapshots of the fully solvated protomer compared to the transmembrane protomer show that the structure of residues 1−34 comprising the N-terminus and helix αA1 is significantly distorted when the protomer is away from the membrane, and these residues are completely exposed to the solvent. The ClyA protomer is colored red except for transmembrane residues 1−34, which are colored orange, and phosphate beads in the membrane colored green. The solvent is omitted for clarity. (G) Final snapshots (all-atom) of the membrane-inserted protomer and the completely solvated protomer without a membrane highlight the structural distortions at the N-terminus. Corroboratively, the RMSD of residues 1−34 is significantly higher for the fully solvated protomer than for the transmembrane protomer, indicating the greater stability of the transmembrane state. Secondary structural analysis (% helicity) shows the loss of helical structure for the stretch of residues 1−34 in the solvated protomer but not for the membrane-inserted protomer.

snapshots of the initial and final configurations (50 ns) of the 6mer and 9-mer ClyA arcs in DMPC bilayers and 6-mer to 10mer arcs in POPC bilayers are shown in Figure 7A,C. By 50 ns for all arcs, the lipids initially present in the hydrophilic arc interior were spontaneously displaced into the surrounding membrane, with a transmembrane water channel replacing the displaced lipids. The displacement sequence for the lipids over the 50-ns-long simulation for the 7-mer arc in the DMPC membrane is illustrated in Figure 7B. This indicates that the favorable configuration for transmembrane ClyA arcs is the formation of a transmembrane water channel that solvates the inner hydrophilic surface of the transmembrane domain. Results from all-atom simulations of the 6-mer and 10-mer arcs in DMPC with longer run times (up to 289 ns) show that G


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Figure 7. (A) Rapid lipid evacuation from the interior of the transmembrane ClyA pore intermediates (6-mer and 9-mer; water and ions removed for clarity) into the plane of the surrounding DMPC membrane occurs within 50 ns. (B) A timeline of lipid evacuation is shown for the 7-mer. (C) Fully atomistic simulations of ClyA arcs inserted into POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) membranes show rapid lipid evacuation within 50 ns for the 6-mer to the 10-mer (water and ions removed for clarity). Corresponding lipid survival probabilities for all n-mer arcs in DMPC and POPC membranes are shown in Figure 8.

Figure 8. A line connecting residue 189 on chain A and residue 11 on chain G of a 7-mer (colored green) defines the boundary between the interior and the exterior of the pore. The continuous survival probability (CSP) of DMPC and POPC lipids within the 6-mer, 7-mer, 9-mer, and 10-mer ClyA arcs captures the probability that a lipid resides in the interior of an arc for a specific length of time.

the lipids within the arc. The definition of the arc boundary is assumed to be a line joining residues 11 and 189 in the edge protomers of the arc as shown in Figure 8. For the ith lipid, the instantaneous probability Pi(t) is either 1 if the lipid is inside the arc or 0 otherwise. The lipid position is tracked by the coordinates of its phosphorus atom. The survival probability for N lipids at time t is given as

the water channel and the proteolipid arc complexes on longer time scales are stable (discussed subsequently). Using a similar CHARMM-GUI protocol for lipid packing in the arc interior (without water) as implemented for the single protomer, 20 ns simulations with the CHARMM36 force field for the 7-mer arc revealed rapid lipid evacuation and the formation of a transmembrane water channel, similar to the results presented above, reinforcing the observation of lipid evacuation and water channel formation (Figure S7). Kinetics of Lipid Evacuation from the Atomistic MD Simulations. Because lipids are displaced from the hydrophilic arc interior within a period of 50 ns, we computed the continuous survival probability (CSP) of the lipids originally present in the arcs (illustrated in Figure 7) to quantify the kinetics of lipid evacuation. CSP defines the residence time of

N

S(t ) =

to + t

∑ ∏ Pi(tk) i=1

tk = to

(6)

where the angular brackets represent shifted time averages. The normalized CSP, ⟨S(t)/S(0)⟩, is calculated over 50 ns H


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Figure 9. (A) Front view of a 9-mer (red) with the stable transmembrane water channel (blue) in a membrane (transparent green slab) illustrating that the stable ClyA arcs are functional membrane-permeabilizing entities. A cross-section across the bilayer of the 9-mer arc in DMPC reveals the toroidal orientation of the lipids at the edge of the bilayer facing the arc interior (lipid choline headgroups colored red and phosphate groups colored green). (B) An analysis of the lipid tilts in the arc vicinity: the distribution of the angle subtended by the lipid vector with the z axis is shown. Two peaks corresponding to the upper and lower lipid leaflets can be seen for lipids in the bulk membrane (blue). However, in the lipid shell immediately surrounding the 9-mer (green), θ assumes intermediate values which correspond to toroidal lipids lying nearly perpendicular to the z axis. (C) Toroidal lipids participate in a larger number of hydrogen bonds in both 7-mer and 9-mer arcs in comparison with lipids away from the proteolipidic edge. (D) Water radial distribution functions (g(r)) around the phosphorus atoms of the toroidal and free lipids for 7-mer and 9-mer arcs are shown.

mechanism, assembly first occurs on the membrane surface to form a prepore which subsequently inserts into the membrane. The fate of the lipids during this stage is largely unknown. Recent AFM images70−72 show the presence of inserted arcs at different stages of oligomerization for the cholesterol-dependent toxins, listeriolysin O and suilysin, which are known to follow a prepore pathway. In this scenario, partially assembled pores (or prearcs) on the membrane surface undergo a conformational change resulting in membrane insertion and the formation of a transmembrane pore. Our simulations shed light on a possible lipid displacement pathway to stabilize the transmembrane arcs. Recent work in our laboratory15 suggests that ClyA leakage on small unilamellar vesicles occurs predominantly through membrane-inserted arcs formed by the stochastic insertion of prearcs. Here again, rapid lipid displacement dynamics would lead to the formation of a stable arc. However, it must be noted that while the lipid reorientational dynamics has been observed in our simulations to be typically complete within tens of nanoseconds, the actual displacement of lipids from the arc interior on complex cellular membranes with an underlying cytoskeleton may be significantly slower. Molecular Analysis of the Toroidal Lipid Edge. An important property of the lipid bilayer membranes is the propensity to form an edge defect, characterized by the line tension of the edge (Λ). This tension causes the reorientation of lipids at the edge of membranes in ribbon configurations into configurations similar to the reorientation of lipids observed at the mouth of the arcs.73 The formation of the toroidal lipid edge shields the hydrophobic lipid acyl tails from solvent exposure, locally offsets the energy penalty due to missing protomers, and stabilizes the partially formed arcs and may

(sampling frequency of 10 ps, 5000 snapshots over each 50 ns trajectory) and fit to the following biexponential function: S (t ) S(0)

⎛ t⎞ ⎛ t⎞ = A exp⎜ − ⎟ + B exp⎜ − ⎟ + k ⎝ τf ⎠ ⎝ τs ⎠

(7)

In the above equation, constant B = 1 − A − k from initial conditions. Two distinct time constants are observed in the CSP fits: τf describes the fast component of lipid evacuation, and τs describes the slower component. Because the survival probabilities have decayed to almost zero for most of the cases as shown in Figure 8, τs describes the residence time of the lipids inside the arc. We attribute the fast component ( 0.5, as illustrated in Figure

10. Assuming that the curvature of the arcs is similar to that of

Figure 10. Top-view schematics of two arc complexes where n n ≤ 0.5 and n > 0.5 are illustrated (protomers illustrated in n max

max

blue). The length of the lipid edge, L(n), the angle subtended by the nmer arcs, θ(n), and the radius of the pore, Rpore, are also depicted. The energetic penalty for the formation of the lipid edge given by eq 9 is plotted for the 1-mer to 12-mer arcs for Λ = 10 and 46.1 pN. Λ depends on the length of the lipid acyl chains and whether the lipid is saturated or unsaturated, and the above range encompasses various lipid bilayers as reported previously.73

the fully formed pore, we can extend the argument that the protomers in a partially oligomerized arc also subtend the same angle in the center of the pore. Because the ClyA pore has a tapering transmembrane region, we use an average value of the upper and lower pore radii (Ru and Rl, respectively) to obtain the edge length L(n). Figure 9A depicts the upper and lower leaflets in the context of the arcs. The edge penalty for the transmembrane n-mer arc complex can be expressed as ⎛ θ(n) ⎞ [Fn]toroidal lipid = Λ(Ru + Rl)sin⎜ ⎟ ; n = 1, ..., nmax ⎝ 2 ⎠ (9)

The typical value of Λ for the lipid membrane edge formation lies in the range of 10−46.1 pN,73 and for the DMPC lipids, the value is 19.2 ± 2.8 pN. Using this range for Λ and values of Ru = 7 nm and Rl = 4 nm,16,37 we obtain the variation in [Fn]toroidal lipid as illustrated in Figure 10. The energetics are proportional to L(n), reaching a maximum at θ = 90 or n = 6. For the dodecameric ClyA pore where n = nmax = 12, the J


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Figure 11. (A) RMSD time traces and corresponding histograms for the 6-mer and 10-mer arcs in DMPC membranes, simulated for 224 and 289 ns, respectively. (B) Superposition of the initial (cyan) and final (red) snapshots of the 6-mer and 10-mer arcs shows that the arc geometry is undistorted as the simulation proceeds. (C) Stable Rg (radius of gyration) time traces and histograms (inset) of the 6-mer and 10-mer arcs further corroborate the notion of arc stability. (D) Time traces and distributions of the axial tilts of helices αA1 and αB (as illustrated in Figure 3D) averaged over all of the protomer subunits in the 6-mer and 10-mer arcs are shown. (E) The time trace of the center-of-mass distance between the edge protomers (λCOM(t)) is shown; the inset illustratates λCOM for the 6-mer.

the simulated unit cell is illustrated for both the 6-mer and the 10-mer in Figure S8, and the trends are observed to be stable. Time traces of the Euclidean center-of-mass distance between the edge protomers (λCOM(t), illustrated schematically for a 6-mer in the inset of Figure 11E) are analyzed for both the 6-mer and 10-mer arcs (Figure 11E). Stable λCOM(t) trends can be used to evaluate the tendency of the arcs to close and form n-mer pores where n < nmax. Furthermore, the edge-protomer center-of-mass distances can be used to compute the spring constant (k) between the edge protomers (which gives a rough measure of the arc stiffness) and the equilibrium harmonic force (F) between the arc edges (eq 5 of Methods). The mean values of k and F for the 6-mer are 39.68 ± 10.56 pN/nm and 306.06 ± 81.42 pN, respectively, which are ∼4 times greater than that of the 10-mer (11.39 ± 3.78 pN/nm and 76.61 ± 25.03 pN, respectively). Intuitively, smaller oligomers have a higher spring constant due to lower arcbackbone fluctuations. However, as oligomerization proceeds and additional protomers are added to the arcs, the flexibility of n-mer arc-backbones increases as a result of the increasing arc length and attractive forces between the edge protomers, which also become progressively proximal as oligomerization proceeds. This renders flexibility to the arcs and increases edge-protomer fluctuations (Figure 11E), thus leading to a net decrease in arc stiffness as evidenced by lower spring constants and forces for the 10-mer. However, the 10-mer arc does not close and form a full pore on the simulated time scales, and this is consistent with the notion that the 12-mer is the predominant pore stoichiometry observed experimentally.16,32

penalty is zero when pore formation is complete. The estimate for forming the toroidal edge which lies in the range of 10−150 kJ/mol must be overcome for the n-mer arcs to be stable in the membrane as our MD simulations suggest. Thus, stabilization of the arc must be driven by protomer−protomer and protomer−membrane interactions which offset the cost of forming the edge. Evaluating these energetic contributions to derive a complete free-energy landscape for the oligomerization process is outside the scope of this article, and we are currently pursuing these computations. Structural Stability of the 6-mer and 10-mer Proteolipidic ClyA Arcs from Longer Atomistic MD Simulations. The fully atomistic 50-ns-long 6-mer and 10-mer ClyA arc simulations in DMPC membranes were extended to 224 and 289 ns, respectively, in order to verify the structural stability of the arcs at longer time scales (Figure 11). The RMSDs of both arcs (Figure 11A) show small deviations from initial structures, as confirmed by the superposition of initial and final structures (Figure 11B) and the mostly constant radius of gyration (Rg, Figure 11C). These observations imply that the 6-mer and 10-mer arcs are stable and reveal no propensity to disassociate over simulation time scales of hundreds of nanoseconds. RMSD and Rg histograms appear to be normally distributed as shown in Figure 11A,C. The orientation of the arcs measured by averaging helix tilts of helices αA1 and αB over all protomer subunits in the arcs is shown to be stable over the simulation time scales in Figure 11D and similar to the observations of the 12-mer (Figure 3D). Fluctuations in the orientation of the 6-mer are marginally higher than that of the 10-mer. The time trace of the length of K


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DISCUSSION AND CONCLUSION We have carried out extensive molecular dynamics simulations in an effort to shed light on the state of the oligomeric intermediates that could form during pore formation for the αPFT, ClyA. Fully atomistic MD simulations show that the transmembrane ClyA pore intermediates or arcs are structurally stable with toroidal lipids forming the part of the water channel where proteins are missing. Initial conditions with lipids present within the arc interior illustrate the dynamics of lipid evacuation and reorientation to form toroidal lipid edges bordering the water channel. While the lipid reorientational dynamics is typically complete within tens of nanoseconds, it must be noted that lipid evacuation time scales on actual cellular membranes with an underlying cytoskeleton may be significantly slower. Other studies on melittin81 and actinoporins14,24 have suggested that lipid participation is essential in stabilizing the transmembrane pore. Toroidal lipid topologies observed in our MD simulations, lining the free edges of the ClyA arcs, are similar to the reoriented lipids observed during electroporation82 and X-ray reconstructions of lipid toroids in transmembrane pores of α-PFTs.79 Our study suggests that ClyA proteolipidic arcs (Figure 7) could potentially form the oligomerization intermediates in the pore-forming pathway of ClyA, similar to the growing-pore paradigm proposed for PFTs (illustrated in Figure 1). We provide molecular details about the single transmembrane protomer conformation, about which no experimental details are currently known. Recent structurebased models have been used to study the conformational change from a water-soluble monomer to a membrane-inserted protomer, 38 where membrane-bound intermediates are sampled during the transition into the membrane. Here we show that the membrane-inserted protomer is a relatively stable state with a favorable free energy of binding to the membrane (estimated using umbrella sampling). Surprisingly, the existence of a stable water channel seen in both the atomistic and MARTINI simulations of the single membrane-inserted protomer shows its membrane-permeabilizing ability (Figure 4). We briefly comment on the existence of arcs within the framework of two pore-forming paradigms. In the prepore model, protein oligomerization occurs at the membrane interface until a prepore complex is assembled. Subsequently concerted membrane penetration of the prepore completes the formation of the transmembrane pore complex (Figure 1). In this regard, β-PFTs have been experimentally studied and pore formation is found to occur with the formation of a prepore in several cases.9,17,78,83,84 In the growing pore model, as oligomerization proceeds, lipid evacuation and the formation of transmembrane water channels are assumed to occur simultaneously. This phenomenon has not been observed or characterized at molecular resolution and remains an open problem. In addition, lipid evacuation during the formation of the transmembrane α-helical barrel in α-PFTs such as ClyA remains unanswered20 because the oligomerization pathways and kinetics are not fully determined. Multiple models have been proposed where arcs have been implicated to play a critical role in PFT-mediated lysis pathways,1,75 specifically in the case of ClyA.15,30 Semicircularized arcs have been shown to cause ion leakage in various membranes.4,12 The release of calcium and potassium ions by these arcs can instigate several downstream cellular processes that can enhance the lytic ability of PFTs even at sublytic concentrations,4,85−88 and our study

supports this view. Identifying the presence of partially oligomerized intermediates akin to the arclike structures investigated in this study supports the growing pore pathway. A nuance to this pathway is that noninserted arcs can oligomerize on the membrane surface (prepore pathway) and can stochastically insert to form transmembrane arcs.15 Finally, we point out that the process of unregulated pore formation on a membrane surface accompanied by lipid displacement from the pore lumens could drive membrane buckling and tension generation. The number of ClyA arcs and pores required to lyse erythrocytes31 has been shown to be ∼105 at the onset of lysis, thus leading to a maximum estimated coverage of 7% of the erythrocyte cell surface. Note that in our simulations the protein to lipid ratio is significantly higher. Because the actual scenario is an extremely dilute regime, the manner in which membrane mechanical properties are modulated by ClyA pores is still an open question. The situation is further complicated by the multicomponent cell membrane and the presence of an actin cytoskeleton, embedded sugars, and integral membrane proteins. In summary, the combined observations provide strong in silico evidence at molecular resolution for simultaneous lipid evacuation from the central pore lumen as oligomerization proceeds and the ability of all membrane-inserted n-mers including the single transmembrane protomer to spontaneously form stable water channels capable of leakage. We speculate that modulating ClyA arc distributions by operating in the appropriate concentration regimes in suitably packed membranes may prove useful for selective membrane permeabilization and size-based analyte separations using ClyA nanopores and arcs.89

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b02277.

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All-atom simulations, spring constants in MARTINI sampling, protein confirmational changes, and simulations set up using CHARMM-GUI protocols (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91 (80) 2293 2769. Fax: +91 (80) 2360 8121. ORCID

Rajat Desikan: 0000-0002-0785-8187 Prabal K. Maiti: 0000-0002-9956-1136 K. Ganapathy Ayappa: 0000-0001-7599-794X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Department of Science and Technology (DST), Government of India, for a grant under which this work was carried out. The authors thank Sandhya S. Visweswariah, J. K. Basu, Narendra M. Dixit, Rahul Roy, and Pranesh Padmanabhan for extensive discussions. L


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