Elasticity and Structure of Self-Assembled Systems with Defects and Inclusions Open Access

Abstract

We study the manner in which topological defects and inclusions alter the dynamics, the elasticity, and the structural conformation of three self-assembled molecular systems.

System 1: Protein hydrogels are responsive biomaterials formed upon mixing natural/engineered peptides. We designed a model of divalent "linkers" and "junctions" and evaluated how defects affect the long-time relaxation of shear stress and resulting viscosity. Junction multiplicities from three to nine are considered. A stoichiometric mismatch of ~1% in mixing peptides showed a sharp decrease in shear relaxation time (τshear). The rate of stress relaxation per bond rearrangement event is ~2-3 times increased than assumed in previous theories. The magnitudes of shear plateau moduli, (G^o) strongly deviate from predictions of Gaussian chain model. A phenomenological theory is developed to connect findings of various simulation instances. Material properties such as G^o and τshear are related to the bond lifetime, τbond.

System 2: Evaluating the lipid membrane elasticity is essential to understanding cell membrane function. Here we investigate the edge tension of bilayer edges from having pores in the membrane. Values reported from experiments vary greatly with method of investigation and techniques of edge tension detection are still emerging. Simulations of DOPC yielded edge tensions of ~45 pN, over 50% greater than the latest value reported from experiment. Edge tensions obtained for a series of phosphatidylcholine ribbons with saturated acyl tails of length 12-16 carbons and with mono-unsaturated acyl tails of length 14-18 carbons is correlated with the excess area associated with forming the edge, through a two-parameter fit.

System 3: Quantum dots (QDs) are highly sought optical probes in biomedical imaging. Experiments showed increased photoluminescence-stability and selective ligand exchange when CdSe-QDs were embedded in unimellar vesicles composed of different phase lipid. The molecular details of resulting lipid-ligand interface are unknown. We implemented UA-simulations where 2.6 nm diameter QD and 3.4 nm diameter QD capped with oleic acid ligands are embedded in DLPC, DOPC, DMPC, and DSPC bilayers. The ligand density and the QD orientation are also varied. More ordered lipid tails are observed for smaller size QDs, at lower ligand density. Lipid tail mobility correlates with lipid Tm independently of nanocrystal size/ligand density.

Table of Contents

1 Simulation . . . . . . . . . . . . 1
1.1 Foundational Statistical Mechanics Related Concepts . . . . . . . . . . 2
1.2 Selected Details of Molecular Dynamics (MD) Simulation . . . . . . . . 6
1.3 Metropolis Monte-Carlo (MMC) Sampling . . . . . . . . . . . . . . . . . 10
References . . . . . . . . . . . . 12

2 An Introduction to Self-assembled Responsive Biomaterials . . . . . . . . . . . . . . . . . . 14
2.1 Protein Networks in Experiments . . . . . . . . . . . . . . . . . . . . . 14
2.2 Background Elasticity Theory and Simulations . . . . . . . . . . . . . . 19
2.3 This Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
References . . . . . . . . . . . . . . . . . . 30

3 Effects of defects on the shear stress relaxation in self-assembled protein networks . . . . . . . 36
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.1 Key Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.2 Model details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.3 Monte Carlo algorithm for bond-rearrangement moves . . . . . . 44
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.1 Rate of defect migration . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.1 Rate of defect migration . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.2 Effect of defect migration on stress relaxation . . . . . . . . . . 56
3.4.3 Relevance to other regimes . . . . . . . . . . . . . . . . . . . . . 61
3.4.3.1 Linker excess vs. linker deficit . . . . . . . . . . . . . . 62
3.4.3.2 Time-dependent defect levels during approach to equilibrium . . . . . . . . . . . . . . . . . 65
3.4.4 Relevance to single-component networks . . . . . . . . . . . . . . 67
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
References. . . . . . . . . . . . . . . . . . 70

4 Simulation study of stress relaxation rates in transient network . . . . . . . . . . . .75
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.1 Network structure: multiple bonds and loops . . . . . . . . . . . 83
4.3.2 Defect migration probability . . . . . . . . . . . . . . . . . . . . 83
4.3.3 Plateau Storage Modulus G⁰ . . . . . . . . . . . . . . . . . . . . 85
4.3.4 Stress relaxation rate . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4.1 Network structure . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4.2 Defect migration rate . . . . . . . . . . . . . . . . . . . . . . . . 90
4.4.3 Trends in plateau modulus G⁰ . . . . . . . . . . . . . . . . . . . 91
4.4.4 Trends in shear stress relaxation time . . . . . . . . . . . . . . . 94
4.4.5 Implications of equation 4.1 . . . . . . . . . . . . . . . . . . . . . 99
4.4.6 Assumptions underlying eq. 4.1 . . . . . . . . . . . . . . . . . . . 99
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.6.1 Affine deformation approximation for shear modulus of center-force Hookean network . . . . . . . . . . . . . 103
References . . . . . . . . . . . . . . . . 105

5 Introduction to elasticity of lipid bilayer edge work . . . . . . . . . . . .109
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References . . . . . . . . . . . . . .115

6 Simulation Studies of Structure and Edge Tension of Lipid Bilayer Edges: Eects of Tail Structure and Force-Field . . . . . . .120
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.2.1 Intact Bilayer Simulations . . . . . . . . . . . . . . . . . . . . . . 123
6.2.2 Ribbon simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.2.3 Bilayers with Pores in Constant Area Simulations . . . . . . . . 127
6.3 Results AND Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.3.1 General observations on ribbon structures . . . . . . . . . . . . . 128
6.3.2 Edge tension of DOPC: dependence on force-field . . . . . . . . . 130
6.3.3 Edge tension of DOPC: comparison with experiment . . . . . . . 131
6.3.4 Lipid tail dependence of edge tension . . . . . . . . . . . . . . . . 132
6.3.5 Effects of the edge environment on lipid conformation and packing. . . . . 133
6.3.6 Correlation between structure and edge tension . . . . . . . . . . 135
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
References . . . . . . . . . . 142

7 Oleic acid (OA) capped CdSe quantum dots embedded in the lipid bilayer- A united-atom simulation description . . . . . . 149
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.2.1 Oleic acid capped-nanocrystal preparation- . . . . . . . . . . . . 155
7.2.2 Combining the capped nanocrystals with lipid bilayers, MD Parameters. . . . . . . . . . 156
7.2.3 Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.4.1 Embedded Nanocrystal Trajectory Descriptions . . . . . . . . . 164
7.4.2 Lipid Tail Disorder . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.4.3 Lipid Tail Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.4.4 Other Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
References . . . . . . . . . . . 175

About this Dissertation

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School	Laney Graduate School
Department	Chemistry
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Chemistry, Physical Chemistry, Polymer
Keyword	quantum dots, lipid-ligand interface dynamics and elasticity of reversible protein networks edge tension of lipid bilayers
Committee Chair / Thesis Advisor	Kindt, James, Emory University
Committee Members	Weeks, Eric, Emory University Lian, Tim, Emory University Bowman, Joel M, Emory University

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