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Free energy analyses of cell-penetrating peptides using the weighted ensemble method

Seungho Choe∗

Department of Energy Science & Engineering, Daegu Gyeongbuk Instituteof Science & Technolgy (DGIST), Daegu 42988, South Korea andEnergy Science & Engineering Research Center, Daegu Gyeongbuk

Institute of Science & Technolgy (DGIST), Daegu 42988, South Korea

Cell-penetrating peptides (CPPs) have been widely used for drug-delivery agents; however, ithas not been fully understood how they translocate across cell membranes. The Weighted En-semble (WE) method, one of powerful and flexible path sampling techniques, can be helpful toreveal translocation paths and free energy barriers along those paths. Within the WE approachwe show how Arg9 (nona-arginine) and Tat interact with a DOPC/DOPG (4:1) model membrane,and we present free energy (or potential mean of forces, PMFs) profiles of penetration, although atranslocation across the membrane has not been observed in the current simulations. Two differentcompositions of lipid molecules were also tried and compared. Our approach can be applied to anyCPPs interacting with various model membranes, and it will provide useful information regardingthe transport mechanisms of CPPs.

I. INTRODUCTION

Cell-penetrating peptides(CPPs) have been exten-sively studied for a long time since they are capableof transporting various cargoes(e.g., proteins, peptides,DNAs, and even small drugs) into cells [1]. Various fac-tors, including the concentration of CPPs and the prop-erties of the membrane affect the transport mechanismsof CPPs [2, 3]. It has been known that the transloca-tion mechanisms of different families of CPPs are notthe same, and most CPPs can have more than a singlepathway depending on the experimental conditions suchas a concentration of CPPs [4].Arginine (R)-rich peptides have been extensively stud-

ied because of their effectiveness in translocation [3, 5].One of the possible scenarios for the insertion of R-richpeptides into the lipid bilayer is a strong interaction withnegatively charged phospholipid heads.Molecular dynamics (MD) simulations have been used

to investigate functional properties of various CPPs andtheir interactions with many different lipids; however,the mechanism of translocation of CPPs and interactionswith lipids are still under debate. Herce et al. [6, 7]showed in their MD simulations that the attractive in-teractions between the Arg9 (or Tat) peptides and thephosphate groups of the phospholipids results in signifi-cant local distortions of the bilayer, and these distortionslead to the formation of a toroidal pore. However, Herceet al.’s simulation was criticized by Yesylevskyy et al. [8]that the spontaneous translocation of CPPs in MD sim-ulations is not expected within a short time scale (100∼ 200 ns). It is believed that the time required for thetranslocation of CPP is on the order of minutes [9].It is unclear that we can observe the translocation of

CPPs across the membranes using conventional all-atomMD simulations. However, an MD simulation is still one

∗ schoe@dgist.ac.kr

of valuable tools to study protein-lipid interactions, andit can provide us with detailed information such as thecontribution of electrostatic energy between CPPs andthe membranes, effects of water molecules, etc. In ourprevious work [10], we found that the electrostatic in-teraction between Arg9 and a DOPC/DOPG(4:1) mem-brane plays a role at the initial stage of translocation.We also quantitatively showed that a number of watermolecules coordinated by Arg9 was increased during thepenetration, and this led to a membrane thinning and adecreased bending rigidity of the membrane. However,we couldn’t find a translocation of Arg9 across the mem-brane within a 1 µs time scale.

Due to the short time scale achieved in current MDsimulations, people have been using biased simulations(e.g., umbrella sampling [11–13], steered MD simulations[14]) to study CPPs and their interactions with mem-branes. The umbrella sampling is very popular to obtainfree energy barrier between CPPs and membranes. How-ever, people have noticed that there could be an artifactin the free energy analysis due to a short simulation timein each window.

In this study, we implement a weighted ensemble (WE)method [15] in our MD simulations (see more in theMethods section). The WE method is one of very flexiblepath sampling techniques and it is easy to implement. Adetailed review was given by Zuckerman and Chong [15].We use the WESTPA software [16, 17], which has beenwidely applied to various systems, ranging from atom-istic to cellular scale. It turns out that the WE methodis very effective for studying interactions between CPPsand membranes and for getting free energy barriers inthe current study.

First, we apply the WE method to Arg9 with aDOPC/DOPG(4:1) membrane used in the previousstudy [10] as well as Tat with identical lipids. Onlya few simulations used mixtures of lipids(e.g., a mix-ture of DOPC/DOPG or DOPC/DOPE) so far, and itis still unclear whether the surface charge of a mem-brane affects the translocation of CPPs. For example, a

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DOPC/DOPG(1:1) membrane appeared the better hostfor the translocation of KR9C in experiments [18] and thefluorescence probe carboxyfluorescein-labeled R9 (CF-R9) translocates continuously across the lipid membraneof single DOPG/DOPC (2/8), DOPG/DOPC (4/6), andDLPG/ DTPC (2/8) giant unilamellar vesicles (GUVs)and enters these GUVs without pore formation [19].However, Herce et al. showed in their experiments thatDOPG lipids are not necessary for the Arg9 peptides topenetrate bilayers [7]. Thus, we also simulate two differ-ent lipid compositions, DOPC/DOPE(4:1) and DOPClipids, respectively, to see if the surface charge of modelmembranes affects the penetration of CPPs. Then, thefree energy barriers between CPPs and model membranescan be obtained using the WE simulation data, and thesefree energy calculations will be helpful to understand thetransport mechanisms of CPPs.

II. METHODS

A. Equilibrium simulations

All simulations were performed using the NAMD pack-age [20] and CHARMM36 force field [21]. The followingsystems were well equilibrated before starting the WEsimulations: 4 Arg9 with a DOPC/DOPG(4:1) mem-brane (System I), 4 Tat with a DOPC/DOPG(4:1) mem-brane (System II), 4 Arg9 with a DOPC/DOPE(4:1)membrane (System III), and 4 Arg9 with a DOPCmembrane (System IV). CHARMM-GUI [22] wasused to setup a DOPC/DOPG(4:1) membrane, aDOPC/DOPE(4:1) membrane, a DOPC membrane andTIP3P water molecules. The DOPC/DOPG(4:1) mix-ture consists of 76 DOPC and 19 DOPG lipids in eachlayer in System I. The same model membrane was usedin System II. System III has a DOPC/DOPE(4:1) mix-ture which consists of 80 DOPC and 20 DOPE lipids ineach layer. System IV has 95 DOPC lipids in each layer.K and Cl ions were added in each system to make a con-centration of 150 mM. All Arg9 (in System I, III, andIV) or Tat (in System II) peptides were initially locatedin the upper solution, and they were bound to the upperlayer during the equilibration.The NPT simulations were performed at T = 310K.

Temperature and pressure were kept constant usingLangevin dynamics. An external electric field(0.05V/nm) was applied in the negative z-direction(fromCPPs to the membrane) as suggested in previous work[7, 23] and also in our previous simulations [10] to accountfor the transmembrane potential [24]. The particle-meshEwald(PME) algorithm was used to compute the electricforces, and the SHAKE algorithm was used to allow a 2fs time step during the whole simulations.In the case of System I, we use a pre-equilibrated struc-

ture in the previous study [10], which was equilibratedup to 1 µs. System II was also equilibrated for at least1µs. The other two systems (System III and IV) were

equilibrated for 100 ns before starting the WE simula-tions. This time scale is enough for CPPs to close tomodel membranes. Fig. S1 (see Supplementary Infor-mation) shows both an initial setup and a snapshot afterequilibration for each system, and Fig. S2 presents ra-dial distribution functions of the followings: phosphorusatoms vs. water, phosphorus atoms vs. oxygen in wa-ter, ester oxygen vs. oxygen in water. These plots showthat the quality of hydration of membranes is very sim-ilar to each other. During the equilibration, CPPs wereconfined in the upper water box so that there is no in-teraction between CPPs and the lower leaflet of modelmembranes. Whenever a CPP is leaving the upper waterbox, a small force was applied to pull that CPP inside thebox. All CPPs in each system were well contacted withthe lipid molecules after the equilibration, and then theWE simulations were performed using those equilibratedsystems.

B. Weighted Ensemble (WE) simulations

We use the WESTPA (The Weighted Ensemble Simu-lation Toolkit with Parallelization and Analysis) softwarepackage [16, 17] to enable the simulation of rare events,for example, translocation of CPPs across a model mem-brane. WESTPA is an open source, and its utility hasbeen proved for a broad range of problems. All WE tra-jectories are unbiased and hence used to calculate condi-tional probabilities or transition rates.To use the WE method in MD simulations, we need to

define a progress coordinate, a number of bins, a numberof walkers (child simulations) in each bin, and a time in-terval for splitting and combining trajectories [16]. Wedefine the progress coordinate as a distance in z-directionbetween the center of mass of phosphorus atoms in theupper leaflet and that of a CPP (Arg9 or Tat). Afterequilibration of each system, an initial distance betweenphosphorus atoms and a CPP was measured, and bound-aries were set using this initial position and the positionof the center of the membrane, for example, [- 18 A (thecenter of membrane), 3 A (the initial distance)]. Each binsize was 0.25 A and, the number of walkers in each binwas 5. The time interval for splitting and combining thetrajectories was set 5 ps during all the WE simulations.The progress coordinate was calculated using MDAnaly-sis [25]. The potential mean of force (PMF) profiles wereobtained from each WE simulation data using ”w pdist”and ”plothist” codes in the WESTPA package [16, 17].

III. RESULTS

A. WE simulations show much-enhancedpenetration within a short amount of time

We observe that both Arg9 and Tat penetrate throughthe middle of the model membrane during the WE simu-

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lations; however, translocation across the membrane hasnot been observed in the current simulations.Fig. 1 shows the penetration depth of both Arg9 and

Tat vs. the number of iterations of each WE simulation.Here, we define the penetration depth as a distance be-tween the center of mass of CPP and that of phosphorusatoms of the upper leaflet. The penetration depth ofArg9 in the previous equilibrium simulation was about−6 ∼ −7 A[10], and the current WE simulation shows−17.6 A and −17.7 A for Arg9 and Tat, respectively.The initial positions of Arg9 and Tat after equilibrationare different from each other; however, they quickly pene-trate the DOPC/DOPG(4:1) membrane. Note that theseplots show only one of the trajectories of each simulationwhich shows the maximum penetration depth. Multi-ple trajectories can not reach the middle of the mem-brane. As one can see in the figure, the penetration depthchanges a lot within a very short time scale. As describedin the Methods section, each iteration corresponds to 5ps and the figure shows that both CPPs reach their max-imum penetration depth within a very short time scale(3 ∼ 5 ns) after the WE simulation started. Therefore,the WE method provides us with a very effective tool toovercome potential energy barriers.Fig. 2 presents snapshots of both Arg9 and Tat, which

show the maximum penetration depth during the WEsimulation. The yellow shows each CPP, and gray is thelipids. The blue and red are phosphorus atoms of theupper and the lower leaflets. Water molecules, ions, andthe other three CPPs are omitted for clarity. As one cansee in Fig. 2, the membrane is deformed a lot when Arg9or Tat penetrates the middle of the membrane. Fig. S3in Supplementary Information shows membrane curva-ture more clearly. As shown in the previous simulation[10], a number of water molecules around a CPP is in-creased when the CPP penetrates the membrane, and amembrane thinning is also observed in the current WEsimulations.

B. Electrostatic energy between a CPP and amodel membrane plays a role during the

translocation

In our previous equilibrium simulation of Arg9 with aDOPC/DOPG(4:1) membrane, we showed that electro-static energy between Arg9 and the membrane is stronglycorrelated with the penetration depth of Arg9[10]. Thisproved that electrostatic interaction between a CPP anda membrane is essential at the early translocation stage[26].We calculate the same electrostatic energy between

Arg9 (or Tat) and the membrane. We want to see if thereis still a strong correlation between electrostatic energyand penetration depth during the WE simulations. Weuse two trajectories in Fig. 1 to calculate electrostaticenergy.Fig. 3 presents the penetration depth (left axis, black

line) vs. electrostatic energy (right axis, blue line) be-tween Arg9 and the lipid molecules within 15 A of Arg9.The red dotted line is an average over every 30 itera-tions. The figure shows that an absolute magnitude ofelectrostatic energy becomes smaller when Arg9 rapidlypenetrates inside the membrane (e.g., between 450th ∼

550th iterations). Therefore, one can expect that thepenetration increases as the magnitude of electrostaticenergy becomes smaller.We find similar behavior in the case of Tat. Fig. 4

shows the same energy calculation for Tat. The red dot-ted line is an average over every 30 iterations as before.The penetration increases gradually as the magnitude ofelectrostatic energy becomes getting smaller.At the initial stage of translocation, it is well known

that the interaction between positive charges of CPPsand a negative part of lipid molecules is essential forbinding. The current simulations show that electrostaticinteraction between CPPs and membranes still plays arole during the translocation of CPPs. In System I &System II Arg9 and Tat strongly interact with DOPGlipids, and the translocation seems not easy. However,our simulations show that the translocation of CPPs ispossible even in this strong electrostatic interaction. Dur-ing the translocation, the electrostatic interaction shouldbe diminished. We conjecture that water molecules playa role to make electrostatic energy weaker. As shownin the previous work [10], a number of water moleculesaround CPPs is increased during the translocation.

C. The free energy profiles based on the WEsimulation data show that Arg9 penetrates througha DOPC/DOPG(4:1) model membrane much easier

than Tat does

This section presents the potential mean of force(PMF) profiles of Arg9 and Tat along the penetrationpaths shown in Fig. 1. Another advantage of usingthe WE method is that it provides a free energy anal-ysis without any biased sampling (e.g., umbrella sam-pling) [16]. Therefore, these PMF profiles will tell us howmuch potential energy barriers exist along those pathsand which CPP can penetrate the membrane more effi-ciently.Fig. 5 shows the PMF profiles of both Arg9 and Tat

as a function of a progress coordinate (or reaction co-ordinate). We use a penetration depth as the progresscoordinate. The progress coordinate becomes negativewhen Arg9 and Tat penetrate below the upper leaflet ofthe membrane. The blue line is the PMF profile for Arg9and the red line for Tat. One can notice that the freeenergy of Arg9 is much lower than that of Tat. Fig. 5shows that a free energy barrier is about 100 kT for Arg9to reach the middle of the membrane while it is about280 kT for Tat to reach a similar position. This meansthat Arg9 penetrates the DOPC/DOPG(4:1) membranemuch easier than Tat does. However, these analyses can

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FIG. 1. The penetration depth of Arg9 (blue line) and Tat(red line) vs. a number of iterations

FIG. 2. Snapshots of Arg9 (left) and Tat(right) with a DOPC/DOPG(4:1) model membrane (yellow: CPP, gray: lipids, blueand red: phosphorus atoms of DOPC and DOPG, respectively).

depend on the type of model membranes, and we can notconclude that Arg9 is always more efficient for penetrat-ing membranes than Tat regardless of membrane types.The order of magnitude of free energy for Arg9 (∼ 100kT) is very similar to a previous result [27], which usedumbrella samplings. On the other hand, Tat’s order ofmagnitude of free energy is much higher than those ofprevious simulations [8, 13]. Note that most of the pre-vious free energy analyses were done with a single lipidmolecule (e.g., DOPC or DPPC), while we use a mixedcomposition of lipid molecules (DOPC/DOPG(4:1)) inour simulations. Although the magnitude of free energycan depend on systems studied, the observed tendencybetween Arg9 and Tat is consistent with experimentalresults [28, 29] which showed more efficient cellular up-take of Arg9 than Tat.

D. Different lipid compositions slightly affect thePMF profiles of Arg9

It is interesting to see whether a different lipidcomposition can affect the penetration depth and thePMF profile. Fig. 6 presents the PMF profiles ofArg9 with DOPC/DOPG(4:1) lipids, DOPC/DOPE(4:1)lipids, and DOPC lipids, respectively. The blue line isfor Arg9 with DOPC/DOPG(4:1) lipids shown already inFig. 5. The red one is for Arg9 with DOPC/DOPE(4:1)lipids and the orange for Arg9 with DOPC lipids. DOPCand DOPE lipids are neutral, while DOPG lipids are neg-atively charged. We want to see if the translocation ofCPPs strongly correlates with the lipid types, e.g., thecharge of membranes.

The minimum point in each plot is different from eachother because the initial position of each CPP after equi-libration is not the same. Although the initial positionsare different from each other, the slope of each plot looksvery similar to each other. Although Arg9 in System III

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FIG. 3. The penetration depth of Arg9 (left axis, black line) vs. electrostatic energy between Arg9 and lipids molecules within15 A of Arg9 (right axis, blue line). The red dotted line is an average over every 30 iterations.

FIG. 4. Same as in Fig. 3 , but for Tat.

(with DOPC/DOPE(4:1) lipids) and Arg9 in System IV(with DOPC lipids) have not reached the final position asof System I (with DOPC/DOPG(4:1)), the similar slopemeans similar variations in free energy. Based on theseplots, we can conjecture that the penetration of Arg9 isnot much dependent on the lipid composition, and theeffect of surface charge is minimal.

IV. DISCUSSION

Both Arg9 and Tat don’t show any translocation acrossthe model membranes during the WE simulations. How-ever, the WE method can be helpful to identify thetransport mechanisms of CPPs and interactions betweenCPPs and lipid molecules because conventional equilib-rium MD simulations have difficulty in sampling. Freeenergy (potential mean of force, PMF) profiles can beobtained without any biased simulation (e.g., umbrella

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FIG. 5. Comparison of potential mean of force (PMF) between Arg9(blue line) and Tat(red line).

FIG. 6. Comparison of potential mean of force (PMF). Arg9 with a DOPC/DOPG(4:1) (blue line), a DOPC/DOPE(4:1) (redline), and a DOPC (orange line), respectively.

sampling) within the WE approach. The WE simulationand its free energy analyses can be used to study theefficiency of penetration of CPPs.

Is it possible to observe the translocation if we simulatemuch longer? Currently, both Arg9 and Tat are stuck inthe hydrophobic core. They can stay in the hydropho-bic core for a long time even if we simulate much longer.They can move up and down a little, but it is not likelyto move in either direction, moving back or forward. Avisual inspection shows that they are trapped inside the

hydrophobic core. The lipids make a small cage aroundCPPs so that CPPs cannot move easily. It seems thata single CPP cannot cause further deformation of themembrane at the current stage, and thus it is difficult tomove. There is a possibility that the free energy barri-ers along the downward direction are much higher thanthose along the upward direction. In that case, it is eas-ier for CPPs to go back to the hydrophilic region wherethey started. It will be interesting to try the WE simula-tions from the current positions of both Arg9 and Tat to

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the hydrophilic area outside, i.e., the positive z-direction.Then, we will obtain another free energy profiles for bothArg9 and Tat, and these profiles will give us a clue.There are still some limitations in our WE simulations.

First, a time scale of each trajectory shown in Fig. 1 isless than 10 ns. Note that the total simulation time foreach CPP simulation is about 5 ∼ 10 µs, which includesall the walkers (child simulations) in each bin and all theiterations. This time scale of a single trajectory mightbe too short to observe a water pore mentioned in theprevious results [8, 13, 27, 30]. Second, our PMF profilesare incomplete because we don’t find any translocationof CPPs and PMF profiles spanned only from the top tothe middle of the model membranes. It has been knownthat free energy barriers between CPPs and membranesare changed in the presence of a water pore. For example,Huang et al.[27] reported that the free energy becomeslower in the presence of a water pore. This confirms theprevious results from MD simulations and a continuummodeling which calculate the free energy of a single argi-nine residue for translocating across a membrane [31–34].We need moreWE simulation data points to complete thefree energy profiles, which include translocation of CPPacross the membranes and the effect of the water pore.Third, we haven’t attached any cargo to Arg9 (or Tat)in the current study. We expect that the conformationalchanges both in CPP and the model membranes dependon a type of cargo. CPPs are commonly used with at-taching negatively charged molecules and thus the totalcharge of the system decreases or gets closer to neutral.It is not clear whether the overall charge of the whole sys-tem or only the charge of CPP is essential for the inter-nalization. Most electronic neutral CPPs are usually farless powerful than cationic or amphiphilic CPPs. How-ever, the electronic neutral cyclic peptide cyclosporin A(CsA) can have stronger (5-fold or 19-fold) penetratingcapacity than other neutral peptides and its penetratingcapacity was as strong as Tat [35]. On the other hand,in the case of oligoarginine (Rn: n=4,8,12,16) R12 andR16 showed more efficient uptake than R4 and R8 [36].If only the charge of CPP is essential during the translo-cation, we can compare the free energy barriers of theseoligoarginine within the WE method and identify theirpenetration efficiency.It has been known that it is difficult for a single CPP

to make a pore and to make a translocation across themembrane [8]. One of the key factors which makes the

water pore is a concentration of CPPs. In our WE simu-lations, the P(protein)-L(lipids) ratio was 0.042 or 0.05,and these concentrations maybe not be enough to observethe translocation across the membrane. Another criticalfactor for translocating CPPs is pH dependence. Experi-mental results showed the uptake of CPPs depends on pHvalues[37, 38], and the uptake of CPPs is enhanced at lowpH. It is worth trying MD simulations at low pH to seeif any changes in conformational changes both in CPPsand in the model membranes. There has been significantprogress in the development of constant pH moleculardynamics (pHMD) techniques [39, 40] and this approachwith the WE method would be good to reveal the pHdependence in interactions between CPPs and the modelmembranes.

Our simulations show characteristics of both thecarpet-like model [41] and the membrane thinning model[42]. It is interesting to note that an orientation (a di-rection from the N-terminal to the C-terminal) of CPPs(Arg9 or Tat) in our simulations is almost parallel to themembrane, and its orientation is changed a little duringthe entire simulation. This could be one of the reasonsthat it is difficult for a single CPP to make a water pore.In this work, the progress coordinate was set for a singleCPP, and it was difficult to observe aggregation of CPPsin a local area. To make a water pore, a collective be-havior between CPPs seems to be essential, and a highconcentration of CPPs would be needed. It is worth usingan increased concentration of CPPs and implementing aprogress coordinate as a distance between the center ofmass of the phosphorus atoms of the upper leaflet andthat of more than a single CPP (e.g., two Arg9 or twoTat). However, the penetration of two CPPs seems muchslower than using a single CPP [43].

ACKNOWLEDGMENTS

This work was supported by the Faculty start-up fundfrom DGIST and by the DGIST R&D Program of theMinistry of Science and ICT (21-BRP-12)

The author would like to thank the DGIST Supercom-puting Big Data Center for computing resources and theNational Supercomputing Center with supercomputingresources including technical support (KSC-2021-CRE-0296).

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1

Supplementary Information

Free energy analyses of cell-penetrating peptides using the

weighted ensemble method

Seungho Choe∗

Department of Energy Science & Engineering,

Daegu Gyeongbuk Institute of Science & Technolgy

(DGIST), Daegu 42988, South Korea and

Energy Science & Engineering Research Center,

Daegu Gyeongbuk Institute of Science & Technolgy (DGIST), Daegu 42988, South Korea

∗ schoe@dgist.ac.kr

1

I. SYSTEM SETUP

System I and System II were equilibrated for at least 1 µs, while System III and IV

were equilibrated for 100 ns. As for System I, we use a pre-equilibrated structure in the

previous study [1]. Fig. S1 shows snapshots of both the initial and the final structure after

finishing equilibration. Each row corresponds to each system (e.g., System I, II, III, and

IV). The first and second columns present the initial setup of each system (both a side view

and a top view, respectively). Four Arg9 (or Tat) were initially placed in the upper water

box and stayed in the upper water box during equilibration. The third and fourth columns

show the final structure after equilibration (both a side view and a top view). A 100ns-long

equilibration may be short to fully equilibrate the system (System III and IV); however, a

visual inspection shows that four Arg9 were contacted with the lipid molecules. We also plot

radial distribution functions to check the hydration profiles of each system Fig. S2 presents

radial distribution functions g(r) (a) phosphorus vs. water (b) phosphorus vs. oxygen in

water (c) easter oxygen vs. oxygen in water. The radial distribution function of each system

is quantitatively very similar to each other, and the structures in System III and IV can be

used as initial structures for the WE simulations.

II. MEMBRANE CURVATURE

Fig. S3 shows membrane curvature from System I & II simulations, respectively (left: a

side view, right: top view). It indicates significant deformation when Arg9 or Tat penetrates

the DOPC/DOPG(4:1) membrane. Each layer (the upper and the lower) consists of only

phosphorus atoms in the lipid molecules in this figure. The colored dots on the upper layer

depict the Cαs of each Arg9 or Tat.

[1] S. Choe, Molecular dynamics studies of interactions between arg9(nona-arginine) and a

dopc/dopg(4:1) membrane, AIP Advances 10, 105103 (2020).

2

FIG. S1. The initial setup and a snapshot after equilibration (first low: System I; second low:

System II; third low: System III; fourth low: System IV). The yellow is Arg9 (System I, III, IV) or

Tat (System II). The blue dots depict phosphorus atoms of DOPC lipids, while the red (orange)

dots are those atoms of DOPG(DOPE) lipids. The gray line shows lipid molecules, and water

molecules are shown as licorice

3

0 2 4 6 8 10Distance [Å]

0

0.5

1

1.5

2g

(r)

P-w

ate

r

System ISystem IISystem IIISystem IV

0 2 4 6 8 10Distance [Å]

0

0.5

1

1.5

2

2.5

3

g(r

) P

-Ow

ate

r

System ISystem IISystem IIISystem IV

0 2 4 6 8 10Distance [Å]

0

0.2

0.4

0.6

0.8

g(r

) O

-Ow

ate

r

System ISystem IISystem IIISystem IV

FIG. S2. Radial distribution function g(r) of (a) phosphorus atoms in lipids vs. water (b) phos-

phorus atoms vs. oxygen atoms in water molecules (c) ester oxygen in lipids vs. oxygen atoms in

water.

4

FIG. S3. Membrane curvature (a) System I (4 Arg9 with DOPC/DOPG(4:1) lipids) (b) System II

(4 Tat with DOPC/DOPG(4:1) lipids)

5