Line tension assisted membrane permeation at the transition temperature in mixed phase lipid bilayers Open Access

Yang, Lewen (2016)

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This dissertation is focused on molecular dynamics simulation and the theoretical analysis of coarse-grain lipid models. The permeability of lipid bilayers to a variety of permeants shows a peak at the transition temperature, when melting from an ordered gel phase to a disordered fluid phase. To explore this anomalous behavior, a five-site lipid membrane model that exhibits a phase transition upon expansion or compression was studied to determine how the permeation rate of a simple particle depends on the phase composition in the two-phase region and on particle size. For large permeants and system sizes, an anomalous behavior is found where permeability increases upon compression of the bilayer. By tracking the environment of each permeation event, and by normalizing the statistics to each phase's area fraction, we found that the permeation rate is not enriched in the interfacial regions, contradicting the prediction from the "leaky interface" hypothesis. However, as the ratio of the fluid phase went down, its local permeation rate was increased with a corresponding increase in the area per lipid. This result motivated a model for the decrease in effective permeability barrier through fluid phase domains arising from a decrease in the length of the gel/fluid interface at the midpoint of a permeation event. A specially-designed large permeant moving through the DPPC bilayer (represented by the MARTINI 2.0 model) was used to study the effect of line-tension-assisted membrane permeation. The umbrella sampling method has been used to evaluate the free energy profile for these permeation processes. At the lipid phase transition temperature, the permeation barrier for passage through an enclosed fluid domain embedded in a patch of gel was significantly lower than for passage through a fluid stripe domain. This difference in free energy barrier was produced from the interfacial free energy as there is a significant change in interfacial length due to the lipids' phase shift. The permeation through a fluid domain in a stripe geometry has a free energy barrier nearly identical to that of a gel-free fluid bilayer, when the phase shift is not accompanied by a change in the interfacial length. The interfacial line tension can be estimated to be between 10 and 13 pN from these two different systems. The permeation barrier was shown to drop even further in simulations performed at temperatures below the transition temperature. The results suggest a mechanism to explain the experimentally observed anomalous peak in the temperature-dependent permeability of lipid bilayers near their transition temperatures. The contribution of this mechanism toward the permeability of a gel phase containing a thermal distribution of fluid-phase domains is estimated using a simple statistical thermodynamic model. The dynamics of the pore closure was studied under the permeant-free condition while using the same forcefield. The melting rate constant of the lipids at the transition temperature was estimated from a stripe system with approximately equal amount of the gel and fluid lipids, upon which the temperature is set to slightly deviated from the phase transition temperature. For the system of the fluid domain surrounded by gel, the pore size at a certain time can be shown to behave consistently with that of uniform fluid systems, by using the estimated melting rate constant and the value of interfacial line tension.

Table of Contents

Chapter 1 General Introduction 15

1.1 Lipid membranes and lipid bilayers 15

1.2 Outline of this thesis 16

1.3 Thermodynamics of lipid phase transitions 19

1.4 Line tension of lipid bilayers 21

1.5 Critical domain size 22

1.6 The permeability of lipid bilayers 23

1.7 Liposome technology in drug delivery 26

1.8 Permeability anomaly during phase transition 26

1.9 The approach of this thesis 28

1.10 Simulation methods 30

1.10.1 Stochastic Langevin dynamics 30

1.10.2 Temperature coupling method 30

1.10.3 Pressure coupling methods 32

1.10.4 Free-energy calculations 33

Chapter 2 The five-site lipid model 35

2.1 Backgrounds 36

2.2 Simulation methods 39

2.2.1 Two-phase system construction 39

2.2.2 Calculating the permeation rate 44

2.2.3 Quantifying the phase composition 45

2.2.4 Calculating the total area and area per lipid of the fluid phase 49

2.3 Results 49 2.3.1 Evidence for a phase transition 50

2.3.2 Permeability across the phase transition 50

2.3.3 Quantitative test of the "leaky interface" hypothesis 51

2.3.4 Area per lipid of the fluid phase 53

2.3.5 Permeant size effect 55

2.3.6 System size effect 56

2.4 Discussion 57

2.4.1 Model to understand gel-fluid coexisting phase 57

2.4.2 Interpreting the simulation results 58

2.4.3 Comparison of simulation model to true lipid bilayers 62

2.5 Conclusions 67

Chapter 3 The line-tension-assisted membrane permeation at the transition temperature in mixed gel-fluid bilayers 69

3.1 Backgrounds 70

3.2 Simulation Methods 73

3.2.1 Construction of the system 73

3.2.2 Quantifying the phase composition and its corresponding area per lipid 77

3.2.3 Determining the phase transition temperature (Tm) 78

3.2.4 Calculation of the free energy barrier of the permeant 78

3.2.5 Dynamics of release of the permeant from the center 80

3.2.6 The correlation between the fractional ratio of gel phase and position 80

3.2.7 Calculation of Δh 81

3.3 Results 81

3.3.1 Pinpointing the phase transition temperature (Tm) 81

3.3.2 The free energy comparison 84

3.3.3 Phase change during permeation 85

3.3.4 Temperature dependence 86

3.3.5 The dynamics of the permeant leaving the bilayer 87

3.4 Discussions 88

3.4.1 Phase transition temperature 89

3.4.2 Response of phase composition to permeant insertion 89

3.4.3 The origin of difference in free energy barrier 90

3.4.4 Implications for permeability through a single fluid domain 97

3.4.5 Implications for permeability through an ensemble of domains 99

3.4.6 Statistical thermodynamic model for distribution of domain sizes 99

3.4.7 Calculation of permeability from domain size distribution 102

3.4.8 Predictions from statistical thermodynamic theory 103

3.4.9 Complicating factors 105

3.5 Conclusions 106

Chapter 4 The 2d-umbrella sampling of a sodium ion across the bilayer 108

4.1 Backgrounds 108

4.2 Simulation methods 110

4.2.1 Simulation system set up 110

4.2.2 2d-umbrella sampling 111

4.3 Results and discussions 113

4.3.1 1d-umbrella sampling 113

4.3.3 The reverse process sampling 117

4.4 Conclusions 119

Chapter 5 The pore closure dynamics of lipid membranes 120

5.1 Backgrounds 120

5.2 Simulation methods 123

5.2.1 system construction 124

5.2.2 Pore generation and pore radius estimation 124

5.2.3 The size-dependent study 125

5.2.4 Other simulation details 125

5.3 Results 126

5.3.1 The size-dependent study 126

5.3.2 The pore closure of a uniform fluid bilayer 127

5.3.3 The pore closure of an enclosed fluid bilayer surrounded by gel 129

5.4 Discussion 131 5.4.1 Understanding the pore closure of uniform fluid systems 131

5.4.2 Understanding the pore closure of enclosed fluid systems 132

5.4.3 Calculating the melting rate constant 136

5.4.4 Self-consistent check 138

5.5 Conclusion 140

References 142

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