Gramicidin Lateral Distribution in Phospholipid Membranes: Fluorescence Phasor Plots and Statistical Mechanical Model
"> Figure 1
<p>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” [<a href="#B21-ijms-19-03690" class="html-bibr">21</a>]. 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).</p> "> Figure 2
<p>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” [<a href="#B21-ijms-19-03690" class="html-bibr">21</a>]. 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).</p> "> Figure 3
<p>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” [<a href="#B21-ijms-19-03690" class="html-bibr">21</a>]. 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).</p> "> Figure 4
<p>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” [<a href="#B21-ijms-19-03690" class="html-bibr">21</a>]. 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).</p> "> Figure 5
<p>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” [<a href="#B21-ijms-19-03690" class="html-bibr">21</a>]. At every modulation frequency the phasor dots were measured at the following mole fractions: gD mole fraction: (<b>A</b>) 0.147, 0.149, 0.151, 0.154, 0.156, 0.158, 0.160; (<b>B</b>) 0.147, 0.149, 0.151, 0.154.</p> "> Figure 6
<p>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.</p> "> Figure 7
<p>Condensing effect of gramicidin dimer. Red and blue curves are the radius, R and cross-sectional area, <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>M</mi> </msub> <mo>=</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> <mi>π</mi> </mrow> </semantics></math>, 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 [<a href="#B14-ijms-19-03690" class="html-bibr">14</a>]. R and <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>M</mi> </msub> </mrow> </semantics></math> are given in Å and Å<sup>2</sup>, respectively.</p> "> Figure 8
<p>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, <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mi>M</mi> </msub> </mrow> </semantics></math> (see <a href="#ijms-19-03690-f007" class="html-fig">Figure 7</a>). 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. (<b>A</b>) <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo>=</mo> <mn>0.1427</mn> <mo>≈</mo> <msubsup> <mi>X</mi> <mrow> <mi>c</mi> <mi>r</mi> </mrow> <mi>M</mi> </msubsup> <mo>=</mo> <mn>0.143</mn> </mrow> </semantics></math>; (<b>B</b>) <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo>=</mo> <mn>0.0077</mn> <mo>≪</mo> <msubsup> <mi>X</mi> <mrow> <mi>c</mi> <mi>r</mi> </mrow> <mi>M</mi> </msubsup> <mo>=</mo> <mn>0.143</mn> <mo> </mo> </mrow> </semantics></math> where M = 12; (<b>C</b>) 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).</p> "> Figure 9
<p>Aggregate of rigid clusters at <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo>≅</mo> <msubsup> <mi>X</mi> <mrow> <mi>c</mi> <mi>r</mi> </mrow> <mi>M</mi> </msubsup> <mo>=</mo> <mn>0.154</mn> </mrow> </semantics></math> 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).</p> "> Figure 10
<p>Proportion of regularly packed membrane area. Regular area fraction, <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math> is plotted against the gramicidin mole fraction, <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>g</mi> </msub> </mrow> </semantics></math>. 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 <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo><</mo> <mn>0.143</mn> </mrow> </semantics></math> 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, (<a href="#ijms-19-03690-f001" class="html-fig">Figure 1</a>, <a href="#ijms-19-03690-f002" class="html-fig">Figure 2</a>, <a href="#ijms-19-03690-f003" class="html-fig">Figure 3</a> and <a href="#ijms-19-03690-f004" class="html-fig">Figure 4</a>). The other red arrow is at the measured upper limit of the critical mole fractions, (<a href="#ijms-19-03690-f005" class="html-fig">Figure 5</a>) 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 <a href="#ijms-19-03690-f005" class="html-fig">Figure 5</a>). The blue line is the assumed change of <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>g</mi> </mrow> </msub> </mrow> </semantics></math> if there is no critical gramicidin mole fraction below 0.143. If the vertical axis started from <math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and the horizontal axis from <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, then the blue line would go from (<math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo>=</mo> <mn>0.143</mn> </mrow> </semantics></math> ) to (<math display="inline"><semantics> <mrow> <msub> <mi>A</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> ). The model parameters are listed in <a href="#app1-ijms-19-03690" class="html-app">Table S1</a> and the energy difference was: <math display="inline"><semantics> <mrow> <msubsup> <mi>ε</mi> <mi>g</mi> <mi>s</mi> </msubsup> <mo>−</mo> <msubsup> <mi>ε</mi> <mi>g</mi> <mi>u</mi> </msubsup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> cal/mol.</p> ">
Abstract
:1. Introduction
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
2.3.2. Modeling Gramicidin/Phospholipid Mixture—Qualitative Description
2.3.3. Modeling Gramicidin/Phospholipid Mixture—Statistical Mechanical Description
Calculating
Free Energy of the Lattice
On the Solubility Limit of Gramicidin
2.3.4. Results of the Theoretical Model
3. Discussion
3.1. On Measured and Predicted Critical Mole Fractions
3.2. On the Upper and Lower Limit of Critical Mole Fractions
3.3. Comparing the Results of the Model with Other Experimental Data
3.4. Similarities and Differences between Gramicidin/DMPC and Cholesterol/DMPC Mixtures
3.5. On Gramicidin/DMPE Mixtures
3.6. Biophysical and Functional Implications
4. Materials and Methods
4.1. Preparation of Gramicidin/DMPC Mixtures
4.2. Fluorescence Lifetime Measurements
4.3. Measurements of Generalized Polarization (GP) of Laurdan Fluorescence
5. Concluding Remarks
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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M | w (cal/mol) | w (cal/mol) | |
---|---|---|---|
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 |
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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
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 StyleSugár, 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