# Gramicidin Lateral Distribution in Phospholipid Membranes: Fluorescence Phasor Plots and Statistical Mechanical Model

^{1}

^{2}

^{*}

## Abstract

**:**

_{cr}including 0.143). Rigid clusters form aggregates in which gramicidin dimers are regularly distributed, in some cases, even to superlattices. At X

_{cr}, the size of cluster aggregates and regular distributions reach a local maximum. Before a similar model was developed for cholesterol/DMPC mixtures (Sugar and Chong (2012) J. Am. Chem. Soc. 134, 1164–1171) and here the similarities and differences are discussed between these two models.

## 1. Introduction

_{2}CH

_{2}OH) contains four tryptophans whereas gramicidin B and C have the tryptophan at position 11 replaced by phenylalanine and tyrosine, respectively. The N-terminus of the gramicidin polypeptide chain contains a formyl moiety (-HCO) and the C-terminus is linked to aminoethanol (-NHCH

_{2}CH

_{2}OH). Gramicidin is very hydrophobic and able to spontaneously insert into lipid bilayers. The peptide may span half of the liposomal membrane bilayer or form a head-to-head dimer of single helices, spanning the whole membrane and serving as a channel (diameter ~4 Å) passing monovalent cations across the membrane [3,4,5,6]. Gramicidins in phospholipid bilayers have been used as a valuable model system for studying membrane insertion and lipid-protein interactions of membrane-spanning channels [7]. In the present study, we used this model system to explore how channel peptides are distributed laterally in membranes, an area that has drawn increasing attention in recent years [8,9].

^{6.3}-helix, in oriented DMPC liquid crystalline bilayers has been reported [3,4,5]. Differential scanning calorimetry (DSC) [10,11] showed that small quantities of gramicidins totally remove the pre-transition endotherm of DMPC and broaden the lipid main phase transition. The enthalpy of the main phase transition decreases linearly with increasing gramicidin content until 0.05 gramicidin mole fraction and levels off at about 0.16 gramicidin mole fraction. Below 0.16 gramicidin mole fraction in DMPC, several interesting studies are noticed. Polarized attenuated total reflection infrared and spin-label electron spin resonance revealed that at a peptide/lipid molar ratio of 1:10, three to four lipids per monomer are motionally restricted by interaction with gramicidin A, probably via the association with the four tryptophans, which are located at the membrane-water interface [11]. Nuclear magnetic resonance (NMR) studies performed in the range of 0–0.05 gramicidin mole fraction pointed out that in gramicidin/DMPC mixtures each gramicidin molecule was surrounded by approximately one layer of bound lipids [12]. Earlier molecular dynamics simulations also indicated the presence of a layer of bound DMPC molecules around a gramicidin molecule [13]. More recent molecular dynamics simulations by Kim et al. [14] revealed the radial distribution of DMPC molecules both around a monomer and a dimer of gramicidin A. They found that the bilayer thickness strongly depends on the lateral distance from the gramicidin dimer. The membrane hydrophobic thickness changes non-monotonically from a value of 28 Å (gel state), with an initial decrease in the thickness within 4–5 Å from the dimer then an increase within the next 2.0–2.5 Å, followed by a monotonic decrease until it levels off at the thickness of fluid DMPC bilayer (25 Å). In contrast, the DMPC bilayer thickness around the gramicidin monomer remains at 25 Å unchanged with lateral distance. Based on NMR [3] and flash photolysis studies [15], Harroun et al. concluded that, at the gramicidin/DMPC molar ratio of 1:10, virtually all the gramicidin molecules (close to 100%) are in dimeric form [16]. These studies imply that, in gramicidins/DMPC mixtures, the lipid molecules around the peptide form the liquid ordered phase and the lipids away from the peptide are in liquid disordered phase.

## 2. Results

#### 2.1. Phasor Plots of Intrinsic Protein Fluorescence in Gramicidins/DMPC Mixtures

#### 2.2. Generalized Polarization of Laurdan Fluorescence in Gramicidin A/DMPC Mixtures

#### 2.3. Model

#### 2.3.1. On the Condensing Effect of Gramicidin

^{−2}is the lateral density of DMPC far from the gramicidin dimer (62 Å

^{2}is the cross-sectional area of a DMPC in a one component fluid bilayer [25]) and ${R}_{g}=7.5$Å [14] is the radius of the gramicidin dimer.

#### 2.3.2. Modeling Gramicidin/Phospholipid Mixture—Qualitative Description

^{2}$=({A}_{12}-{7.5}^{2}\xb7\pi )/6$ where the cross-sectional area of a rigid cluster at M = 12 is ${A}_{12}=520.1$ Å

^{2}(see Figure 7). The cross-sectional area of a fluid DMPC is 62 Å

^{2}[25]. Since 11.1 < 12, if each of the fluid lattice units would contain two gramicidin monomers in Figure 8A, ${X}_{g}$ would be larger than ${X}_{cr}^{12}$, i.e.: ${X}_{g}=0.1432\gtrsim {X}_{cr}^{12}=0.143$. Actually, in Figure 8A most of the fluid lattice units contain two gramicidin monomers but there are two fluid lattice units with one gramicidin monomer in each. Since in each of these two fluid lattice units (each containing one gramicidin monomer) the number of DMPC molecules is more than 12 thus ${X}_{g}=0.1427\lesssim {X}_{cr}^{12}=0.143$. In Figure 8B most of the lattice units contain fluid DMPCs and zero gramicidin monomers and thus ${X}_{g}=0.0077\ll {X}_{cr}^{12}=0.143$. (In Figure 8B there are 25 gramicidin dimers and 1 gramicidin monomer, i.e., the total number of gramicidins is 51. Since ${X}_{cr}^{12}=0.143$ is the lower limit of critical mole fraction, at X

_{g}< 0.143, no more than 12 DMPC can condense to each gramicidin dimer and we assume that, at X

_{g}< 0.143, 12 DMPC molecules are condensed to each gramicidin dimer. In the 25 rigid clusters there are 25 × 12 = 300 DMPCs. At the lattice unit containing the gramicidin monomer there are 13.93 fluid DMPCs. In the remaining 400 − 25 − 1 = 374 fluid lattice units there are 374 × 16.78 = 6275.7 fluid DMPCs. Thus the gramicidin mole fraction is ${X}_{g}$ = (51/(51 + 300 + 13.93 + 6275.7)) = 0.0077.)

_{reg}= 0.965 and 0.0625, respectively. (In Figure 8A out of 400 lattice units there are 400−14 rigid clusters, thus A

_{reg}= (400−14)/400 = 0.965. In Figure 8B out of 400 lattice units there are 25 rigid clusters, thus A

_{reg}= 25/400 = 0.0625)

#### 2.3.3. Modeling Gramicidin/Phospholipid Mixture—Statistical Mechanical Description

#### Calculating ${N}_{u}$

#### Free Energy of the Lattice

#### On the Solubility Limit of Gramicidin

#### 2.3.4. Results of the Theoretical Model

_{reg}only slightly depends on the value of the model parameter ${\epsilon}_{g}^{s}-{\epsilon}_{g}^{u}$ (see Figure S2).

## 3. Discussion

#### 3.1. On Measured and Predicted Critical Mole Fractions

#### 3.2. On the Upper and Lower Limit of Critical Mole Fractions

_{reg}, is expected to be measured at the solubility limit of gramicidin in DMPC bilayers. According to our experiments (Figure 5) the critical mole fraction, ${X}_{cr}^{11}=0.154$, represents the solubility limit (Figure 10). Note that in this case the calculated maximum of A

_{reg}at mole fraction 0.154 should be a half-maximum because the gramicidin starts to precipitate from the phosphatidylcholine lipid matrix above this critical mole fraction. Thus the actual solubility limit marks the upper limit of the applicability of our model. On the other hand, with increasing M, the predicted critical mole fractions become closer to each other and their reliable detection becomes increasingly difficult. Also, the condensing effect of the gramicidin should be weaker on phospholipid molecules that are farther away. Once the condensing energy at the perimeter of a rigid cluster is comparable with the thermal energy unit we reach the upper bound of the size of a rigid cluster, and the respective gramicidin mole fraction marks the lower limit of the applicability of our model. Since we could not detect a biphasic behavior of gramicidin fluorescence phasor dots at M > 12, the lower limit of critical mole fractions is ${X}_{cr}^{12}=0.143$. This could be the case because at M > 12 not only nearest neighbor but also next nearest neighbor DMPC molecules would belong to the rigid clusters and according to the molecular dynamics simulations [14] the next nearest neighbor DMPC molecules are in fluid state.

_{g}< 0.143 almost 100% of the gramicidins are part of rigid clusters and these rigid clusters may form aggregates. Since ${X}_{cr}^{12}=0.143$ is the lower limit of critical mole fraction at X

_{g}< 0.143 no more than 12 DMPC can condense to each gramicidin dimer and we assume that at X

_{g}< 0.143 12 DMPC molecules are condensed to each gramicidin dimer. As an example, a possible arrangement of the rigid clusters for X

_{g}= 0.0077 is shown in Figure 8B. With decreasing gramicidin concentration, the total area of the aggregates linearly decreases in the membrane, while the surface area of fluid DMPC linearly increases, i.e., A

_{reg}linearly decreases from 1 to 0 as X

_{g}decreases from 0.143 to 0 (blue line in Figure 10, which shows only part of this linear decrease of A

_{reg}from 1 to 0.98). The decrease is linear because the cross-sectional area of DMPC (located in the fluid phase) is the same no matter how close it is to the rigid aggregates.

#### 3.3. Comparing the Results of the Model with Other Experimental Data

_{reg}is practically equal to 1 (Figure 10), i.e., at these mole fractions, there are only rigid clusters. Since in a rigid cluster the gramicidin is in dimeric form, there are only gramicidin dimers in the membrane at the critical mole fractions. Also, according to the model result, next to the critical mole fractions A

_{reg}is between 0.98 and 1. These results of our model, without any parameter fitting, are in agreement with the NMR [3] and flash photolysis studies [15], based on which Harroun et al. concluded that, at the 1:10 gramicidin/DMPC molar ratio, close to 100% of the gramicidin is in dimeric form [16].

#### 3.4. Similarities and Differences between Gramicidin/DMPC and Cholesterol/DMPC Mixtures

_{reg}(Figure 10) was calculated at a critical mole fraction 0.143. Similar biphasic changes were found at critical mole fractions of sterol/phosphatidylcholine (PC) mixtures (reviewed in [19]); and (ii) at the critical mole fractions, both the gramicidin near the Trp/Tyr residues (Figure 1, Figure 2, Figure 3, Figure 4, Figure 5 and Figures S3 and S4) and the sterol in DMPC [32] report a tighter membrane local environment.

_{reg}values are in the range of 0.98–1.0 (Figure 10), while in the case of cholesterol/DMPC mixtures, the A

_{reg}values are in the range of 0.65–0.90 [17,18,19]. A possible reason of this difference is that the surface area of the side of a gramicidin is about 1.8–1.9 times larger than the surface area of the side of a cholesterol and that the gramicidin dimer, that is present only in the rigid clusters, spans the membrane, while cholesterol spans only one layer of the bilayer. Thus, in gramicidin/DMPC mixtures, the lipid molecules are able to condense to a larger surface. To calculate the surface areas, we used the following data: the length and radius of a gramicidin is 13.75 and 7.5 Å, respectively [3,14,36], while the length and radius of a cholesterol molecule is 16.3 and 3.29–3.48 Å, respectively [37,38].

#### 3.5. On Gramicidin/DMPE Mixtures

#### 3.6. Biophysical and Functional Implications

## 4. Materials and Methods

#### 4.1. Preparation of Gramicidin/DMPC Mixtures

^{−1}cm

^{−1}[48], respectively. The stock solution of DMPC (Avanti Polar Lipids, Alabaster, AL, USA) was made in chloroform, with the phospholipid concentration determined as previously described [49]. Gramicidins and DMPC mixed in organic solvents were first dried under a stream of nitrogen gas and then subjected to high vacuum (1 × 10

^{−3}mbar) for ~12 h using a Labcono freeze-dry system (Freezone 4.5, Kansas City, MO, USA). The dried DMPC/gramicidins were hydrated using a pre-warmed buffer (50 mM Tris, 10 mM EDTA, 0.02% NaN

_{3}, pH 7.15), followed by vortexing for 2–3 min at 40 °C to make multilamellar vesicles (MLVs) and annealing through three heating (40 °C for 0.5 h)/cooling (4 °C for 0.5 h) cycles. Unilamellar vesicles (LUVs) were made from MLVs by passing the vesicles 10 times through two stacked 400-nm Nucleopore polycarbonate membranes under nitrogen gas pressure at 40 °C using an extruder (Lipex Biomembranes, Vancouver, BC, Canada). The accuracy of the determination of gramicidin content in DMPC is estimated to be ~0.001–0.002 mole fraction, and the procedures to achieve such a high mole fraction accuracy have been described previously [50,51]. The particle size and polydispersity index (PDI) of the MLVs and LUVs were measured on a Malvern Nano ZS spectrometer (Worcs, UK).

#### 4.2. Fluorescence Lifetime Measurements

#### 4.3. Measurements of Generalized Polarization (GP) of Laurdan Fluorescence

_{ex}= (I

_{435}− I

_{500})/(I

_{435}+ I

_{500})) [56] was then calculated from the spectral readings. Here I

_{435}and I

_{500}are the fluorescence intensities at 435 nm and 500 nm, respectively. The sample was excited at 340 nm.

## 5. Concluding Remarks

_{reg}values are in the range of 0.98–1.0 (Figure 10), while in the case of cholesterol/DMPC mixtures, the A

_{reg}values are in the range of 0.65–0.90 [17,19]. Otherwise, compared to sterols/PC mixtures, gramicidins/PC mixtures have the same thermodynamic tendency to form condensed complexes and subsequently ordered cluster aggregates and superlattices, in coexistence with the fluid phase.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Phasor plot of intrinsic gramicidin fluorescence in various gramicidin D (gD)/DMPC multilamellar vesicles (MLVs) measured at 37 °C using 15 different modulation frequencies: (from left to right) 200.00, 143.94, 103.59, 74.55, 53.65, 38.61, 27.79, 20.00, 14.39, 10.36, 7.46, 5.37, 3.86, 2.78, and 2.00 MHz. The semi-circular arc is called the “universal circle” [21]. Inlet: enlarged phasor data measured at 200.00 and 143.94 MHz; the relative errors of G (=M cosφ) and S (=M sinφ) are: ΔG = 0.00098–0.00101 (200 MHz) and 0.00139–0.00141 (143.9 MHz), and ΔS = 0.00096–0.00099 (200 MHz) and 0.00096–0.00099 (143.9 MHz).

**Figure 2.**Phasor plot of gramicidin fluorescence lifetime in gD/DMPC MLVs with varying gD mole fractions ranging from 0.139–0.147. Samples were measured at 45 °C using 15 different modulation frequencies: (from left to right) 200.00, 143.94, 103.59, 74.55, 53.65, 38.61, 27.79, 20.00, 14.39, 10.36, 7.46, 5.37, 3.86, 2.78, and 2.00 MHz. The semi-circular arc is called the “universal circle” [21]. Inlet: enlarged phasor data measured at 200.00 and 143.94 MHz; the relative errors of G (=M cosφ) and S (=M sinφ) are: ΔG = 0.00097–0.001 (200 MHz) and 0.0013–0.00143 (143.9 MHz), and ΔS = 0.00097–0.00101 (200 MHz) and 0.00099–0.00101 (143.9 MHz).

**Figure 3.**Phasor plot of gramicidin fluorescence lifetime in gramicidin A (gA)/DMPC MLVs. In this sample set, gA mole fraction was varied from 0.141 to 0.149 with an increment of 0.02. Samples were measured at 37 °C using 15 different modulation frequencies (from left to right) 200.00, 143.94, 103.59, 74.55, 53.65, 38.61, 27.79, 20.00, 14.39, 10.36, 7.46, 5.37, 3.86, 2.78, and 2.00 MHz. The semi-circular arc is called the “universal circle” [21]. Inlet: enlarged phasor data measured at 200.00 and 143.94 MHz; the relative errors of G (=M cosφ) and S (=M sinφ) are: ΔG =0.00101–0.00102 (200 MHz) and 0.00146–0.00150 (143.9 MHz), and ΔS = 0.00099–0.00101 (200 MHz) and 0.00101–0.00102 (143.9 MHz).

**Figure 4.**Effect of gA mole fraction on the phasor dots of gramicidin fluorescence lifetime in gA/DMPC large unilamellar vesicles (LUVs). In this sample set, five gA mole fractions (0.141, 0.143, 0.145, 0.147, 0.149) were examined. Samples were measured at 37 °C using 3 different modulation frequencies (from left to right) 200.00, 143.94, and 103.59 MHz. The semi-circular arc is called the “universal circle” [21]. Inlet: enlarged phasor data measured at 143.94 and 103.59 MHz; the relative errors of G and S are: ΔG = 0.00136–0.00145 (143.9 MHz) and 0.00184–0.00192 (103.59 MHz), and ΔS = 0.00097–0.00103 (143.9 MHz) and 0.00091–0.00095 (103.59 MHz).

**Figure 5.**Phasor plot of gramicidin fluorescence lifetime in a sample set of gD/DMPC MLVs with gD content centered around the theoretically predicted critical mole fraction 0.154. Samples were measured at 37 °C using 3 different modulation frequencies (from left to right) 200.0, 143.9 and 103.6 MHz; the relative errors of G and S are: ΔG = 0.000824–0.015405 (200 MHz), 0.001269–0.002807 (143.9 MHz), and 0.002025–0.031970 (103.6 MHz) and ΔS = 0.000632–0.000815 (200 MHz), 0.000879–0.000949 (143.9 MHz), and 0.000849–0.000902 (103.6 MHz). The semi-circular arc is called the “universal circle” [21]. At every modulation frequency the phasor dots were measured at the following mole fractions: gD mole fraction: (

**A**) 0.147, 0.149, 0.151, 0.154, 0.156, 0.158, 0.160; (

**B**) 0.147, 0.149, 0.151, 0.154.

**Figure 6.**Laurdan’s generalized polarization (GP) versus gramicidin A mole fraction in gramicidin A/DMPC MLVs. Temperature = 37 °C. Error bars are the standard deviations of GP values obtained from three independently prepared samples.

**Figure 7.**Condensing effect of gramicidin dimer. Red and blue curves are the radius, R and cross-sectional area, ${A}_{M}={R}^{2}\pi $, respectively, of a rigid cluster as a function of the number of hydrocarbon chains, within a layer of the bilayer, condensed to a gramicidin dimer, M (=2 N). These curves were calculated from Equation (1) by using parameter values Rg = 7.5 Å [14]. R and ${A}_{M}$ are given in Å and Å

^{2}, respectively.

**Figure 8.**Lattice model of gramicidin/DMPC membrane. The bilayer is represented by hexagonally arranged units of squares. The surface area of a unit is equal with the surface area of a rigid cluster, ${A}_{M}$ (see Figure 7). A unit represents either a rigid cluster (green unit with black dot at the center) or part of the fluid phase (white unit with randomly distributed black and red circles). Black dot: gramicidin dimer. Green square: phospholipid molecules condensed to the central gramicidin dimer. Red and black circle: gramicidin monomer in the upper and lower layer of the bilayer, respectively. (

**A**) ${X}_{g}=0.1427\approx {X}_{cr}^{M}=0.143$; (

**B**) ${X}_{g}=0.0077\ll {X}_{cr}^{M}=0.143$ where M = 12; (

**C**) Gramicidin dimers (black hexagons) may be regularly distributed into superlattices in the aggregated rigid clusters. This is an illustration of an aggregate of 3 rigid clusters where 12 phospholipids (green trapezoids) are condensed to each gramicidin dimer (6 located at the upper and 6 at the lower layer of the bilayer, i.e., this is the case when M = 12).

**Figure 9.**Aggregate of rigid clusters at ${X}_{g}\cong {X}_{cr}^{M}=0.154$ where M = 11. Gramicidin dimers (black hexagons) may be regularly distributed into superlattices in the aggregated rigid clusters. This is an illustration of an aggregate of 8 rigid clusters where 11 phospholipids (green trapezoid: lipid condensed to one gramicidin dimer; green parallelogram: lipid condensed to two nearest neighbor gramicidin dimers) are condensed to each gramicidin dimer (5.5 located at the upper and 5.5 at the lower layer of the bilayer).

**Figure 10.**Proportion of regularly packed membrane area. Regular area fraction, ${A}_{reg}$ is plotted against the gramicidin mole fraction, ${X}_{g}$. Green lines: the curves of regular area fractions calculated around the critical gramicidin mole fractions, by Equation (4). Green dashed lines are theoretically calculated but not experimentally supported. At ${X}_{g}<0.143$ the theoretically predicted peaks would appear experimentally if more than 12 DMPC’s were able to condense to a gramicidin dimer. Green solid lines are theoretically calculated and experimentally supported. One of the red arrows is at the measured lower limit of critical mole fractions, (Figure 1, Figure 2, Figure 3 and Figure 4). The other red arrow is at the measured upper limit of the critical mole fractions, (Figure 5) which is also the solubility limit of gramicidin in DMPC bilayer. Gramicidin precipitates from the gramicidin/DMPC bilayer above this mole fraction (see explanation to Figure 5). The blue line is the assumed change of ${A}_{reg}$ if there is no critical gramicidin mole fraction below 0.143. If the vertical axis started from ${A}_{reg}=0$ and the horizontal axis from ${X}_{g}=0$, then the blue line would go from (${A}_{reg}=1$, ${X}_{g}=0.143$ ) to (${A}_{reg}=0$, ${X}_{g}=0$ ). The model parameters are listed in Table S1 and the energy difference was: ${\epsilon}_{g}^{s}-{\epsilon}_{g}^{u}=0$ cal/mol.

M | $\text{}{\mathit{X}}_{\mathit{c}\mathit{r}}^{\mathit{M}}\text{}$ | w (cal/mol) | w (cal/mol) |
---|---|---|---|

$\text{}{\mathit{\epsilon}}_{\mathit{g}}^{\mathit{s}}-{\mathit{\epsilon}}_{\mathit{u}}^{\mathit{s}}=0\text{}$ | $\text{}{\mathit{\epsilon}}_{\mathit{g}}^{\mathit{s}}-{\mathit{\epsilon}}_{\mathit{u}}^{\mathit{s}}=-1000\text{}$ | ||

9 | 0.182 | 489.2 | 447.0 |

10 | 0.166 | 486.8 | 444.1 |

11 | 0.154 | 485.2 | 442.3 |

12 | 0.143 | 484.1 | 441.5 |

13 | 0.133 | 483.7 | 441.4 |

14 | 0.125 | 483.8 | 442.0 |

15 | 0.118 | 484.3 | 443.2 |

16 | 0.111 | 485.3 | 444.9 |

17 | 0.105 | 486.6 | 447.0 |

18 | 0.100 | 488.3 | 450.0 |

19 | 0.0952 | 490.2 | 452.4 |

20 | 0.0909 | 492.4 | 455.5 |

21 | 0.0870 | 494.8 | 459.0 |

22 | 0.0833 | 497.4 | 462.5 |

23 | 0.0800 | 500.3 | 466.4 |

24 | 0.0769 | 503.3 | 470.4 |

25 | 0.0741 | 506.4 | 474.5 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Sugár, I.P.; Bonanno, A.P.; Chong, P.L.-G.
Gramicidin Lateral Distribution in Phospholipid Membranes: Fluorescence Phasor Plots and Statistical Mechanical Model. *Int. J. Mol. Sci.* **2018**, *19*, 3690.
https://doi.org/10.3390/ijms19113690

**AMA Style**

Sugár IP, Bonanno AP, Chong PL-G.
Gramicidin Lateral Distribution in Phospholipid Membranes: Fluorescence Phasor Plots and Statistical Mechanical Model. *International Journal of Molecular Sciences*. 2018; 19(11):3690.
https://doi.org/10.3390/ijms19113690

**Chicago/Turabian Style**

Sugár, István P., Alexander P. Bonanno, and Parkson Lee-Gau Chong.
2018. "Gramicidin Lateral Distribution in Phospholipid Membranes: Fluorescence Phasor Plots and Statistical Mechanical Model" *International Journal of Molecular Sciences* 19, no. 11: 3690.
https://doi.org/10.3390/ijms19113690