Dynamics of Engineered Artificial Membranes and Biosensors

Contents
Preface
List of Abbreviations
Part I Introduction and Background
	1 Motivation and Outline
		1.1 Why Membranes?
		1.2 Guided Tour of the Book
	2 Biochemistry for Engineers: A Short Primer
		2.1 Bonded and Nonbonded Molecular Interactions
		2.2 Lipids, Vesicles, and Bilayers
		2.3 Lipid Bilayers
			2.3.1 Archaebacteria and DphPC Bilayers
			2.3.2 Energetics of Lipid Bilayers
			2.3.3 Structure of Lipid Bilayers
		2.4 Peptides and Proteins
		2.5 Ion Channels
		2.6 Tethers, Spacers, and the Bioelectronic Interface
			2.6.1 Tethers
			2.6.2 Spacers
			2.6.3 Bioelectronic Interface
		2.7 How to Visualize Macromolecules
		2.8 Closing Remarks
	3 Engineered Artificial Membranes
		3.1 Membranes
		3.2 Artificial Membrane Architectures
		3.3 Engineered Artificial Tethered Membranes
		3.4 Sensing with Engineered Tethered Membranes
			3.4.1 Device 1: Ion-Channel Switch (ICS) Biosensor
			3.4.2 Device 2: Pore Formation Measurement Platform (PFMP)
			3.4.3 Device 3: Electroporation Measurement Platform (EMP)
			3.4.4 Device 4: Electrophysiological Response Platform (ERP)
		3.5 Multiphysics Dynamic Models of Engineered Tethered Membranes
			3.5.1 Ab Initio Molecular Dynamics
			3.5.2 Molecular Dynamics
			3.5.3 Coarse-Grained Molecular Dynamics
			3.5.4 Continuum Theories
			3.5.5 Reaction-Rate Theory
		3.6 Electrolyte Dynamics: Steric Effects and Double-Layer Charging
		3.7 Future Technologies: Implantable Medical Devices, Diagnostics, and Therapeutics
			3.7.1 Cochlear and Retinal Implants
			3.7.2 In Vitro Medical Diagnostics (IVDs)
			3.7.3 Molecular Therapeutics
			3.7.4 Biological Neural Networks
			3.7.5 Microeletrodes and Single-Cell Measurements
			3.7.6 Summary
		3.8 Closing Remarks
Part II Building Engineered Membranes, Devices, and Experimental Results
	4 Formation of Engineered Tethered Membranes
		4.1 Introduction
			4.1.1 Engineered Tethered Membrane: Structure
			4.1.2 Overview of Tethered Device
		4.2 Building an Engineered Artificial Membrane
			4.2.1 Solvent-Exchange Technique
			4.2.2 Evaluating the Quality of the Engineered Membrane
		4.3 Inserting Proteins and Ion Channels into Engineered Artificial Membranes
			4.3.1 Spontaneous Insertion Method
			4.3.2 Electrochemical Insertion Method
			4.3.3 Proteoliposomal Insertion Method
		4.4 Laboratory Exercise: Tethered Membranes and Spontaneous Insertion of Gramicidin Channels
			4.4.1 Prepare the Engineered Tethered Membrane for Spontaneous gA Ion-Channel Insertion
			4.4.2 Spontaneous Insertion of gA Ion Channels
			4.4.3 Measuring Membrane Conductance Response
		4.5 Complements and Sources
		4.6 Closing Remarks
	5 Ion-Channel Switch (ICS) Biosensor
		5.1 Introduction
		5.2 ICS Biosensor: Construction and Formation
		5.3 Operation of the ICS Biosensor
			5.3.1 Large and Small Analyte Detection
			5.3.2 Impedance Response of ICS Biosensor for Digoxin and b-Fab
		5.4 ICS Biosensor: Flow Velocity, Binding-Site Density, and Specificity
			5.4.1 Flow Velocity and Binding-Site Density
			5.4.2 Specificity in Complex Environments
		5.5 Detection of Influenza A in Clinical Samples
			5.5.1 ICS Biosensor Preparation and Clinical Trials for Rapid Influenza A Diagnosis
			5.5.2 Influenza A Clinical Samples
			5.5.3 Results of Influenza A Clinical Trial
		5.6 ICS for Multianalyte Detection
			5.6.1 Biosensor Arrays
			5.6.2 Multi-Analyte Detection
		5.7 Complements and Sources
		5.8 Closing Remarks
	6 Physiochemical Membrane Platforms
		6.1 Introduction
		6.2 Device 1: Pore Formation Measurement Platform (PFMP)
			6.2.1 Pore Formation Measurement Platform: Introduction
			6.2.2 Pore Formation Measurement Platform: Construction
			6.2.3 Pore Formation Measurement Platform: Operation and Experimental Measurements
		6.3 Device 2: Electroporation Measurement Platform (EMP)
			6.3.1 Electroporation Measurement Platform: Introduction
			6.3.2 Electroporation Measurement Platform: Formation
			6.3.3 Electroporation Measurement Platform: Operation and Experimental Measurements
		6.4 Device 3: Electrophysiological Response Platform (ERP)
			6.4.1 Electrophysiological Response Platform: Overview
			6.4.2 Electrophysiological Response Platform: Formation
			6.4.3 Electrophysiological Response Platform: Operation and Experimental Measurements
		6.5 Complements and Sources
		6.6 Closing Remarks
	7 Experimental Measurement Methods for Engineered Membranes
		7.1 Introduction
		7.2 Electrical Response of Engineered Membranes
			7.2.1 Electrical Impedance Measurements
			7.2.2 Time-Dependent Electrical Measurements
			7.2.3 Interpretation of Measured Current Response
		7.3 Spectroscopy and Imaging Techniques for Engineered Tethered Membranes
			7.3.1 X-Ray Reflectometry for Measuring Area per Lipid
			7.3.2 Nuclear Magnetic Resonance Measurements of the Conformation and Orientation of Gramicidin A
			7.3.3 Fluorescence Recovery after Photobleaching for Measuring Lipid Diffusion
			7.3.4 Neutron Reflectometry for Measuring Membrane Thickness and Reservoir Thickness
			7.3.5 Summary
		7.4 Complements and Sources
		7.5 Closing Remarks
Part III Dynamic Models for Artificial Membranes: From Atoms to Device
	8 Reaction-Rate-Constrained Models for Engineered Membranes
		8.1 Introduction
		8.2 Fractional-Order Macroscopic Model
			8.2.1 Fractional-Order Derivatives: Double-Layer Capacitance and Charging Dynamics
			8.2.2 Fractional-Order Macroscopic Model: Sinusoidal and Time-Varying Excitation Potential
			8.2.3 Determining the Quality of an Engineered Membrane Using the Fractional-Order Macroscopic Model
		8.3 Experimental Measurements: Fractional-Order Macroscopic Model
			8.3.1 Spacer Surface and Electrolyte Concentration
			8.3.2 Variation in Membrane Types and Tether Density
			8.3.3 Estimating the Dielectric Constant of the Membrane
		8.4 Modeling Membranes with Sterol Components
			8.4.1 Fractional-Order Model for Cholesterol in Engineered Membranes
			8.4.2 Impedance Analysis of Engineered Membranes Containing Sterol Molecules
		8.5 Complements and Sources
		8.6 Closing Remarks
	9 Reaction-Rate-Constrained Models for the ICS Biosensor
		9.1 Introduction
		9.2 Detection of Analyte Species in the Reaction-Rate Regime
			9.2.1 Aside: From Chemical Equations to Reaction-Rate Differential Equations
			9.2.2 Reaction-Rate Model of the ICS Biosensor
			9.2.3 Singular Perturbation Analysis of Dimer Concentration
			9.2.4 Detection of Human Chorionic Gonadotropin (hCG)
		9.3 Microelectrode ICS (mICS) Biosensor and Hidden Markov Model (HMM)
			9.3.1 Hidden Markov Model for mICS Biosensor
			9.3.2 Hidden Markov Model Statistical Signal Processing
			9.3.3 Detection of Monoterpene Oxidation Product (MTOP)
		9.4 Complements and Sources
		9.5 Closing Remarks
	10 Diffusion-Constrained Continuum Models of Engineered Membranes
		10.1 Introduction
		10.2 Mass Transport versus Reaction-Rate-Limited Kinetics
			10.2.1 Damköhler and Péclet Numbers
			10.2.2 Characterization of Operating Regime
		10.3 Mass-Transport-Limited Model of the ICS Biosensor Dynamics
			10.3.1 Poisson’s Equation: Electrostatics
			10.3.2 Nernst–Planck Equation: Advection and Diffusion
			10.3.3 Poisson–Nernst–Planck Equation
			10.3.4 Estimating the Reaction Rates in the ICS Biosensor
			10.3.5 Experimental Results: Streptavidin, TSH, Ferritin, and hCG
		10.4 Biosensor Arrays: Numerical Case Study
			10.4.1 Biosensor Array Model
			10.4.2 Mass-Transport Phase Diagram
			10.4.3 Sensor Array Can Mitigate Mass-Transport Limits
		10.5 Pore Formation Dynamics: Models for PGLa Antimicrobial Peptides
			10.5.1 Generalized Reaction-Diffusion Equation
			10.5.2 Analyte and Surface Reaction Mechanism of PGLa
			10.5.3 Dynamic Model of Electrolyte and Surface Diffusion of PGLa
			10.5.4 Experimental Results: Reaction Dynamics of PGLa
		10.6 Asymptotic Poisson–Nernst–Planck Model and Lumped Circuit Parameters
			10.6.1 Double-Layer Capacitance and Electrolyte Resistance for Blocking Electrode
			10.6.2 Double-Layer Capacitance for Reaction-Limited Electrode
		10.7 Complements and Sources
			10.7.1 Poisson–Nernst–Planck (PNP) Model
			10.7.2 ICS Biosensor Arrays and Multicompartment Models
			10.7.3 Parameter Estimation and System Identification
		10.8 Closing Remarks
	11 Electroporation Models in Engineered Artificial Membranes
		11.1 Introduction
			11.1.1 Applications of Electroporation
			11.1.2 What Is Electroporation?
			11.1.3 Mesoscopic Model of Electroporation
			11.1.4 Organization of This Chapter
		11.2 Smoluchowski–Einstein Equation
			11.2.1 Source Term and Energy Term of the Smoluchowski–Einstein Equation
			11.2.2 Summary
		11.3 Multiphysics (Mesoscopic) Model of Electroporation
			11.3.1 Equivalent Circuit Model of Electroporation
			11.3.2 Singular Perturbation Approximation and Electrical Dynamics
		11.4 Continuum Model of Electroporation: Aqueous Pore Conductance and Double-Layer Capacitance
			11.4.1 Continuum Model 1: Generalized Poisson–Nernst–Planck (GPNP) Equation
			11.4.2 Continuum Model 2: Poisson–Fermi–Nernst–Planck (PFNP) Equation
		11.5 Computing Engineered Tethered-Membrane Parameters from Continuum Theory
			11.5.1 Computing Pore Conductance
			11.5.2 Electrical Potential Energy for Pore Formation
			11.5.3 Computing Pore Capacitance
			11.5.4 Double-Layer Capacitance
			11.5.5 Detection Tests for Ionic Correlation Effects
		11.6 Faradic Reactions at the Bioelectronic Interface
			11.6.1 Faradic Reactions and Double-Layer Charging at the Bioelectronic Interface
			11.6.2 Faradic Reaction Boundary Conditions for the PFNP Continuum Model
		11.7 Complements and Sources
		11.8 Closing Remarks
	12 Electroporation Measurements in Engineered Membranes
		12.1 Introduction
		12.2 Aqueous Pore Conductance, Capacitance, and Electrical Energy
			12.2.1 Aqueous Pore Conductance
			12.2.2 Aqueous Pore Electrical Energy
			12.2.3 Aqueous Pore Capacitance
		12.3 Pore Radii and Membrane Conductance Dynamics
		12.4 Sensitivity of Current Response to Model Parameters
		12.5 Effect of Tether Density of Membrane Electroporation Dynamics
		12.6 Heterogeneous Membrane Mixtures
		12.7 Membranes with Sterol Inclusions
		12.8 Estimating Hydration Ion Size and Faradic Reaction Rates
		12.9 Electrical Double-Layer Charging Dynamics
			12.9.1 Spatially Dependent Dielectric Constant at the Bioelectronic Interface
			12.9.2 Voltage-Dependent Double-Layer Capacitance
		12.10 Large Excitation Potentials and Double-Layer Charging Dynamics
		12.11 Complements and Sources
		12.12 Closing Remarks
	13 Electrophysiological Response of Ion Channels and Cells
		13.1 Introduction
		13.2 Dynamic Model of Embedded Ion Channels
		13.3 Electrophysiological Response of a Voltage-Gated Ion Channel
		13.4 Dynamic Model of Electrophysiological Response of Cells
			13.4.1 Macroscopic Model of the Electrophysiological Response Platform
			13.4.2 Cellular Membrane Conductance and Charging Dynamics
		13.5 Electrophysiological Response of Skeletal Myoblasts
		13.6 Complements and Sources
		13.7 Closing Remarks
	14 Coarse-Grained Molecular Dynamics
		14.1 Introduction
		14.2 Basics of Coarse-Grained Molecular Dynamics
			14.2.1 From an Atomistic to a Mesoscopic Coarse-Grained Description of Engineered Membranes
		14.3 Atomistic-to-Observable Model of Tethered Membranes
		14.4 Aside: The Fokker–Planck Equation
			14.4.1 Kolmogorov and Fokker–Planck Equations
			14.4.2 First-Passage Time and the Arrhenius Equation
		14.5 Coarse-Grained Molecular Dynamics Model for the Bioelectronic Interface and Water
			14.5.1 Percus–Yevick Equation and Water Density at the Bioelectronic Interface
			14.5.2 Density Profile of Water at the Bioelectronic Interface
			14.5.3 Fokker–Planck Equation: Spatially Dependent Water Diffusion Coefficient
			14.5.4 Diffusion Tensor of Water in Tethering Reservoir
			14.5.5 Summary
		14.6 Tethered Membrane Dynamics and Energetics
			14.6.1 Lipid Energetics and Pore Density
			14.6.2 Line Tension and Surface Tension
			14.6.3 Deuterium Order Parameter
			14.6.4 Lipid Lateral Diffusion
			14.6.5 Geometric Properties of Tethered Membranes
			14.6.6 Summary
		14.7 Control of Tethered-Membrane Properties by Sterol Inclusions
			14.7.1 Lateral Diffusion Dynamics of Lipids and Cholesterol
			14.7.2 Biomechanics of Lipids and Cholesterol
		14.8 Molecular Diffusion and Langevin’s Equation
			14.8.1 Langevin’s Equation and Diffusion of Molecules
			14.8.2 Nonstationary Lipid Diffusion with Sterol Inclusions
		14.9 Case Study: Atomistic-to-Observable Model PGLa Pore Formation in Tethered Membranes
			14.9.1 Coarse-Grained Molecular Dynamics Simulation of Tethered Membrane Containing PGLa
			14.9.2 Diffusion of PGLa and Membrane Properties from Coarse-Grained Molecular Dynamics
			14.9.3 Surface Binding and Oligomerization of PGLa from Coarse-Grained Molecular Dynamics
		14.10 Complements and Sources
		14.11 Closing Remarks
	15 All-Atom Molecular Dynamics Simulation Models
		15.1 Introduction
		15.2 Basics of Molecular Dynamics
			15.2.1 Potential Energy Functions
			15.2.2 Macroscopic Parameters and Statistical Ensembles
			15.2.3 Numerical Methods for Molecular Dynamics
		15.3 MD Simulations for the Dynamics of Engineered Membranes
		15.4 Aqueous Pore Formation Dynamics in Tethered Membranes
		15.5 Capacitance and Dipole Potential of Tethered Membranes
		15.6 Modeling Ion Permeation and Channel Conductance
			15.6.1 Models for Ion Permeation: From Ab Initio to Reaction Rate
			15.6.2 Gramicidin Channel Conductance Estimation Using Distributional Molecular Dynamics
		15.7 Gramicidin A (gA) Dimer Dissociation and Reaction-Rate Estimation
			15.7.1 Molecular Reaction Dynamics of Gramicidin Channel Dissociation
			15.7.2 Gramicidin A Reaction Rates
		15.8 Complements and Sources
		15.9 Closing Remarks
	16 Closing Summary for Part III: From Atoms to Device
Appendices
	Appendix A Elementary Primer on Partial Differential Equations (PDEs)
		A.1 Linear, Semilinear, and Nonlinear Partial Differential Equations
		A.2 Linear Partial Differential Equations and Boundary Conditions
		A.3 Nondimensionalization of Partial Differential Equations
		A.4 Solutions of Partial Differential Equations
	Appendix B Tutorial on Coarse-Grained Molecular Dynamics with Peptides
		B.1 Constructing the All-Atom and Coarse-Grained Structure of a Peptide
		B.2 Construction of Coarse-Grained Lipid Bilayer
		B.3 How to Insert PGLa Peptides in the Transmembrane State
		B.4 Note on Publication-Quality Figures
	Appendix C Experimental Setup and Numerical Methods
		C.1 Ion-Channel Switch Biosensor
		C.2 Pore Formation Measurement Platform: PGLa
		C.3 Tethered-Membrane Parameters: Pore Conductance and Electrical Energy
		C.4 Coarse-Grained Molecular Dynamics (CGMD) Simulations
		C.5 CGMD Simulation Setup for PGLa
			C.5.1 Simulation Setup of All-Atom Molecular Dynamics
Bibliography
Index