Coupled effects of mechanics, geometry, and chemistry on bio-membrane behavior

Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.

We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.

We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane.

Structural and mechanistic motifs in membrane proteins: the three-dimensional modelling of rhodopsin, band 3, and the nicotinic acetylcholine receptor

Because so little is known about the structure of membrane proteins, an attempt has been made in this work to develop techniques by which to model them in three dimensions. The procedures devised rely heavily upon the availability of several sequences of a given protein. The modelling procedure is composed of two parts. The first identifies transmembrane regions within the protein sequence on the basis of hydrophobicity, β-turn potential, and the presence of certain amino acid types, specifically, proline and basic residues. The second part of the procedure arranges these transmembrane helices within the bilayer based upon the evolutionary conservation of their residues. Conserved residues are oriented toward other helices and variable residues are positioned to face the surrounding lipids. Available structural information concerning the protein's helical arrangement, including the lengths of interhelical loops, is also taken into account. Rhodopsin, band 3, and the nicotinic acetylcholine receptor have all been modelled using this methodology, and mechanisms of action could be proposed based upon the resulting structures.

Specific residues in the rhodopsin and iodopsin sequences were identified, which may regulate the proteins' wavelength selectivities. A hinge-like motion of helices M3, M4, and M5 with respect to the rest of the protein was proposed to result in the activation of transducin, the G-protein associated with rhodopsin. A similar mechanism is also proposed for signal transduction by the muscarinic acetylcholine and β-adrenergic receptors.

The nicotinic acetylcholine receptor was modelled with four trans-membrane helices per subunit and with the five homologous M2 helices forming the cation channel. Putative channel-lining residues were identified and a mechanism of channel-opening based upon the concerted, tangential rotation of the M2 helices was proposed.

Band 3, the anion exchange protein found in the erythrocyte membrane, was modelled with 14 transmembrane helices. In general the pathway of anion transport can be viewed as a channel composed of six helices that contains a single hydrophobic restriction. This hydrophobic region will not allow the passage of charged species, unless they are part of an ion-pair. An arginine residue located near this restriction is proposed to be responsible for anion transport. When ion-paired with a transportable anion it rotates across the barrier and releases the anion on the other side of the membrane. A similar process returns it to its original position. This proposed mechanism, based on the three-dimensional model, can account for the passive, electroneutral, anion exchange observed for band 3. Dianions can be transported through a similar mechanism with the additional participation of a histidine residue. Both residues are located on M10.

Techniques for strength measurement at high pressures and strain-rates using transverse waves

The study of the strength of a material is relevant to a variety of applications including automobile collisions, armor penetration and inertial confinement fusion. Although dynamic behavior of materials at high pressures and strain-rates has been studied extensively using plate impact experiments, the results provide measurements in one direction only. Material behavior that is dependent on strength is unaccounted for. The research in this study proposes two novel configurations to mitigate this problem.

The first configuration introduced is the oblique wedge experiment, which is comprised of a driver material, an angled target of interest and a backing material used to measure in-situ velocities. Upon impact, a shock wave is generated in the driver material. As the shock encounters the angled target, it is reflected back into the driver and transmitted into the target. Due to the angle of obliquity of the incident wave, a transverse wave is generated that allows the target to be subjected to shear while being compressed by the initial longitudinal shock such that the material does not slip. Using numerical simulations, this study shows that a variety of oblique wedge configurations can be used to study the shear response of materials and this can be extended to strength measurement as well. Experiments were performed on an oblique wedge setup with a copper impactor, polymethylmethacrylate driver, aluminum 6061-t6 target, and a lithium fluoride window. Particle velocities were measured using laser interferometry and results agree well with the simulations.

The second novel configuration is the y-cut quartz sandwich design, which uses the anisotropic properties of y-cut quartz to generate a shear wave that is transmitted into a thin sample. By using an anvil material to back the thin sample, particle velocities measured at the rear surface of the backing plate can be implemented to calculate the shear stress in the material and subsequently the strength. Numerical simulations were conducted to show that this configuration has the ability to measure the strength for a variety of materials.

Cooperative properties of lipid bilayers : collective director fluctuations and the effects of hydrophobic mismatch in protein/lipid membrane systems

Cooperative director fluctuations in lipid bilayers have been postulated for many years. ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements have been used identify these motions and to determine the origin of increased slow bilayer motion upon addition of unlike lipids or proteins to a pure lipid bilayer.

The contribution of cooperative director fluctuations to NMR relaxation in lipid bilayers has been expressed mathematically using the approach of Doane et al.^1 and Pace and Chan.^2 The T_2^(-1)’s of pure dimyristoyllecithin (DML) bilayers deuterated at the 2, 9 and 10, and all positions on both lipid hydrocarbon chains have been measured. Several characteristics of these measurements indicate the presence of cooperative director fluctuations. First of all, T_2^(-1) exhibits a linear dependence on S2/CD. Secondly, T_2^(-1) varies across the ^2H-NMR powder pattern as sin^2 (2, β), where , β is the angle between the average bilayer director and the external magnetic field. Furthermore, these fluctuations are restricted near the lecithin head group suggesting that the head group does not participate in these motions but, rather, anchors the hydrocarbon chains in the bilayer.

T_2^(-1)has been measured for selectively deuterated liquid crystalline DML hilayers to which a host of other lipids and proteins have been added. The T_2^(-1) of the DML bilayer is found to increase drastically when chlorophyll a (chl a) and Gramicidin A' (GA') are added to the bilayer. Both these molecules interfere with the lecithin head group spacing in the bilayer. Molecules such as myristic acid, distearoyllecithin (DSL), phytol, and cholesterol, whose hydrocarbon regions are quite different from DML but which have small,neutral polar head groups, leave cooperative fluctuations in the DML bilayer unchanged.

The effect of chl a on cooperative fluctuations in the DML bilayer has been examined in detail using ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements. Cooperative fluctuations have been modelled using the continuum theory of the nematic state of liquid crystals. Chl a is found to decrease both the correlation length and the elastic constants in the DML bilayer.

A mismatch between the hydrophobic length of a lipid bilayer and that of an added protein has also been found to change the cooperative properties of the lecithin bilayer. Hydrophobic mismatch has been studied in a series GA' / lecithin bilayers. The dependence of 2H-NMR order parameters and relaxation rates on GA' concentration has been measured in selectively deuterated DML, dipalmitoyllecithin (DPL), and DSL systems. Order parameters, cooperative lengths, and elastic constants of the DML bilayer are most disrupted by GA', while the DSL bilayer is the least perturbed by GA'. Thus, it is concluded that the hydrophobic length of GA' best matches that of the DSL bilayer. Preliminary Raman spectroscopy and Differential Scanning Calorimetry experiments of GA' /lecithin systems support this conclusion. Accommodation of hydrophobic mismatch is used to rationalize the absence of H_(II) phase formation in GA' /DML systems and the observation of H_(II) phase in GA' /DPL and GA' /DSL systems.

1. J. W. Doane and D. L. Johnson, Chem. Phy3. Lett., 6, 291-295 (1970). 2. R. J. Pace and S. I. Chan, J. Chem. Phy3., 16, 4217-4227 (1982).

Adsorption of Pb(II) and Cu(II) on α-quartz from aqueous solutions: influence of pH, ionic strength, and complexing ligands

Adsorption of aqueous Pb(II) and Cu(II) on α-quartz was studied as a function of time, system surface area, and chemical speciation. Experimental systems contained sodium as a major cation, hydroxide, carbonate, and chloride as major anions, and covered the pH range 4 to 8. In some cases citrate and EDTA were added as representative organic complexing agents. The adsorption equilibria were reached quickly, regardless of the system surface area. The positions of the adsorption equilibria were found to be strongly dependent on pH, ionic strength and concentration of citrate and EDTA. The addition of these non-adsorbing ligands resulted in a competition between chelation and adsorption. The experimental work also included the examination of the adsorption behavior of the doubly charged major cations Ca(II) and Mg(II) as a function of pH.

The theoretical description of the experimental systems was obtained by means of chemical equilibrium-plus-adsorption computations using two adsorption models: one mainly electrostatic (the James-Healy Model), and the other mainly chemical (the Ion Exchange-Surface Complex Formation Model). Comparisons were made between these two models.

The main difficulty in the theoretical predictions of the adsorption behavior of Cu(II) was the lack of the reliable data for the second hydrolysis constant(*β_2) The choice of the constant was made on the basis of potentiometric titratlons of Cu^(2+)

The experimental data obtained and the resulting theoretical observations were applied in models of the chemical behavior of trace metals in fresh oxic waters, with emphasis on Pb(II) and Cu(II).

The Get3 ATPase drives unidirectional targeting of tail-anchored membrane proteins

Efficient and accurate localization of membrane proteins is essential to all cells and requires a complex cascade of interactions between protein machineries. This is exemplified in the recently discovered Guided Entry of Tail-anchored protein pathway, in which the central targeting factor Get3 must sequentially interact with three distinct binding partners (Get4, Get1 and Get2) to ensure the targeted delivery of Tail-anchored proteins to the endoplasmic reticulum membrane. To understand the molecular and energetic principles that provide the vectorial driving force of these interactions, we used a quantitative fluorescence approach combined with mechanistic enzymology to monitor the effector interactions of Get3 at each stage of Tail-anchored protein targeting. We show that nucleotide and membrane protein substrate generate a gradient of interaction energies that drive the cyclic and ordered transit of Get3 from Get4 to Get2 and lastly to Get1. These data also define how the Get3/Tail-anchored complex is captured, handed over, and disassembled by the Get1/2 receptor at the membrane, and reveal a novel role for Get4/5 in recycling Get3 from the endoplasmic reticulum membrane at the end of the targeting reaction. These results provide general insights into how complex cascades of protein interactions are coordinated and coupled to energy inputs in biological systems.

A. An investigation of the relation between the tensile strength and (Brinell) hardness of non-ferrous alloys. B. A design of a fatigue testing machine for a college laboratory

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Chemical studies of viral entry mechanisms: I. Hydrophobic protein-lipid interactions during sendai virus membrane fusion. II. Kinetics of bacteriophage λ DNA injection.

Viruses possess very specific methods of targeting and entering cells. These methods would be extremely useful if they could also be applied to drug delivery, but little is known about the molecular mechanisms of the viral entry process. In order to gain further insight into mechanisms of viral entry, chemical and spectroscopic studies in two systems were conducted, examining hydrophobic protein-lipid interactions during Sendai virus membrane fusion, and the kinetics of bacteriophage λ DNA injection.

Sendai virus glycoprotein interactions with target membranes during the early stages of fusion were examined using time-resolved hydrophobic photoaffinity labeling with the lipid-soluble carbene generator3-(trifluoromethyl)-3-(m-^(125 )I] iodophenyl)diazirine (TID). The probe was incorporated in target membranes prior to virus addition and photolysis. During Sendai virus fusion with liposomes composed of cardiolipin (CL) or phosphatidylserine (PS), the viral fusion (F) protein is preferentially labeled at early time points, supporting the hypothesis that hydrophobic interaction of the fusion peptide at the N-terminus of the F_1 subunit with the target membrane is an initiating event in fusion. Correlation of the hydrophobic interactions with independently monitored fusion kinetics further supports this conclusion. Separation of proteins after labeling shows that the F_1 subunit, containing the putative hydrophobic fusion sequence, is exclusively labeled, and that the F_2 subunit does not participate in fusion. Labeling shows temperature and pH dependence consistent with a need for protein conformational mobility and fusion at neutral pH. Higher amounts of labeling during fusion with CL vesicles than during virus-PS vesicle fusion reflects membrane packing regulation of peptide insertion into target membranes. Labeling of the viral hemagglutinin/neuraminidase (HN) at low pH indicates that HN-mediated fusion is triggered by hydrophobic interactions, after titration of acidic amino acids. HN labeling under nonfusogenic conditions reveals that viral binding may involve hydrophobic as well as electrostatic interactions. Controls for diffusional labeling exclude a major contribution from this source. Labeling during reconstituted Sendai virus envelope-liposome fusion shows that functional reconstitution involves protein retention of the ability to undergo hydrophobic interactions.

Examination of Sendai virus fusion with erythrocyte membranes indicates that hydrophobic interactions also trigger fusion between biological membranes, and that HN binding may involve hydrophobic interactions as well. Labeling of the erythrocyte membranes revealed close membrane association of spectrin, which may play a role in regulating membrane fusion. The data show that hydrophobic fusion protein interaction with both artificial and biological membranes is a triggering event in fusion. Correlation of these results with earlier studies of membrane hydration and fusion kinetics provides a more detailed view of the mechanism of fusion.

The kinetics of DNA injection by bacteriophage λ. into liposomes bearing reconstituted receptors were measured using fluorescence spectroscopy. LamB, the bacteriophage receptor, was extracted from bacteria and reconstituted into liposomes by detergent removal dialysis. The DNA binding fluorophore ethidium bromide was encapsulated in the liposomes during dialysis. Enhanced fluorescence of ethidium bromide upon binding to injected DNA was monitored, and showed that injection is a rapid, one-step process. The bimolecular rate law, determined by the method of initial rates, revealed that injection occurs several times faster than indicated by earlier studies employing indirect assays.

It is hoped that these studies will increase the understanding of the mechanisms of virus entry into cells, and to facilitate the development of virus-mimetic drug delivery strategies.

Part I. Influence of membrane morphology on ion-exchange and charge propagation in composite polyelectrolyte electrode coatings. Part II. Dynamic surface tension measurements of polarization relaxation at mercury pool electrodes by the method of Wilhelmy.

Part I. Novel composite polyelectrolyte materials were developed that exhibit desirable charge propagation and ion-retention properties. The morphology of electrode coatings cast from these materials was shown to be more important for its electrochemical behavior than its chemical composition.

Part II. The Wilhelmy plate technique for measuring dynamic surface tension was extended to electrified liquid-liquid interphases. The dynamical response of the aqueous NaF-mercury electrified interphase was examined by concomitant measurement of surface tension, current, and applied electrostatic potential. Observations of the surface tension response to linear sweep voltammetry and to step function perturbations in the applied electrostatic potential (e.g., chronotensiometry) provided strong evidence that relaxation processes proceed for time-periods that are at least an order of magnitude longer than the time periods necessary to establish diffusion equilibrium. The dynamical response of the surface tension is analyzed within the context of non-equilibrium thermodynamics and a kinetic model that requires three simultaneous first order processes.

Strength of tantalum at high pressures through Richtmyer-Meshkov laser compression experiments and simulations

Strength at extreme pressures (>1 Mbar or 100 GPa) and high strain rates (106-108 s-1) of materials is not well characterized. The goal of the research outlined in this thesis is to study the strength of tantalum (Ta) at these conditions. The Omega Laser in the Laboratory for Laser Energetics in Rochester, New York is used to create such extreme conditions. Targets are designed with ripples or waves on the surface, and these samples are subjected to high pressures using Omega’s high energy laser beams. In these experiments, the observational parameter is the Richtmyer-Meshkov (RM) instability in the form of ripple growth on single-mode ripples. The experimental platform used for these experiments is the “ride-along” laser compression recovery experiments, which provide a way to recover the specimens having been subjected to high pressures. Six different experiments are performed on the Omega laser using single-mode tantalum targets at different laser energies. The energy indicates the amount of laser energy that impinges the target. For each target, values for growth factor are obtained by comparing the profile of ripples before and after the experiment. With increasing energy, the growth factor increased.

Engineering simulations are used to interpret and correlate the measurements of growth factor to a measure of strength. In order to validate the engineering constitutive model for tantalum, a series of simulations are performed using the code Eureka, based on the Optimal Transportation Meshfree (OTM) method. Two different configurations are studied in the simulations: RM instabilities in single and multimode ripples. Six different simulations are performed for the single ripple configuration of the RM instability experiment, with drives corresponding to laser energies used in the experiments. Each successive simulation is performed at higher drive energy, and it is observed that with increasing energy, the growth factor increases. Overall, there is favorable agreement between the data from the simulations and the experiments. The peak growth factors from the simulations and the experiments are within 10% agreement. For the multimode simulations, the goal is to assist in the design of the laser driven experiments using the Omega laser. A series of three-mode and four-mode patterns are simulated at various energies and the resulting growth of the RM instability is computed. Based on the results of the simulations, a configuration is selected for the multimode experiments. These simulations also serve as validation for the constitutive model and the material parameters for tantalum that are used in the simulations.

By designing samples with initial perturbations in the form of single-mode and multimode ripples and subjecting these samples to high pressures, the Richtmyer-Meshkov instability is investigated in both laser compression experiments and simulations. By correlating the growth of these ripples to measures of strength, a better understanding of the strength of tantalum at high pressures is achieved.

Strength, Deformation and Fracture in Metallic Nanostructures

An understanding of the mechanics of nanoscale metals and semiconductors is necessary for the safe and prolonged operation of nanostructured devices from transistors to nanowire- based solar cells to miniaturized electrodes. This is a fascinating but challenging pursuit because mechanical properties that are size-invariant in conventional materials, such as strength, ductility and fracture behavior, can depend critically on sample size when materials are reduced to sub- micron dimensions. In this thesis, the effect of nanoscale sample size, microstructure and structural geometry on mechanical strength, deformation and fracture are explored for several classes of solid materials. Nanocrystalline platinum nano-cylinders with diameters of 60 nm to 1 μm and 12 nm sized grains are fabricated and tested in compression. We find that nano-sized metals containing few grains weaken as sample diameter is reduced relative to grain size due to a change from deformation governed by internal grains to surface grain governed deformation. Fracture at the nanoscale is explored by performing in-situ SEM tension tests on nanocrystalline platinum and amorphous, metallic glass nano-cylinders containing purposely introduced structural flaws. It is found that failure location, mechanism and strength are determined by the stress concentration with the highest local stress whether this is at the structural flaw or a microstructural feature. Principles of nano-mechanics are used to design and test mechanically robust hierarchical nanostructures with structural and electrochemical applications. 2-photon lithography and electroplating are used to fabricate 3D solid Cu octet meso-lattices with micron- scale features that exhibit strength higher than that of bulk Cu. An in-situ SEM lithiation stage is developed and used to simultaneously examine morphological and electrochemical changes in Si-coated Cu meso-lattices that are of interest as high energy capacity electrodes for Li-ion batteries.

Development of Microfluidic Devices with the Use of Nanotechnology to Aid in the Analysis of Biological Systems Including Membrane Protein Separation, Single Cell Analysis, and Genetic Markers

Computation technology has dramatically changed the world around us; you can hardly find an area where cell phones have not saturated the market, yet there is a significant lack of breakthroughs in the development to integrate the computer with biological environments. This is largely the result of the incompatibility of the materials used in both environments; biological environments and experiments tend to need aqueous environments. To help aid in these development chemists, engineers, physicists and biologists have begun to develop microfluidics to help bridge this divide. Unfortunately, the microfluidic devices required large external support equipment to run the device. This thesis presents a series of several microfluidic methods that can help integrate engineering and biology by exploiting nanotechnology to help push the field of microfluidics back to its intended purpose, small integrated biological and electrical devices. I demonstrate this goal by developing different methods and devices to (1) separate membrane bound proteins with the use of microfluidics, (2) use optical technology to make fiber optic cables into protein sensors, (3) generate new fluidic devices using semiconductor material to manipulate single cells, and (4) develop a new genetic microfluidic based diagnostic assay that works with current PCR methodology to provide faster and cheaper results. All of these methods and systems can be used as components to build a self-contained biomedical device.

Strength of thin-walled elliptical cylinders supported at the minor axis

In this investigation it was found that the instability failure of curved sheet is nearly independent of the type of loading and is primarily a function of the maximum stress, radius-thickness ration and modulus of elasticity. A method of correlating the critical stress of thin sheet under several different types of loading is given. An explanation for the experimental critical stress of thin walled cylinders under bending being greater than that for pure compression is given. The strength of unstiffened thin walled circular nose sections under pure bending was found to be controlled by local instability of the section, rather than a large scale instability. The equation of local instability of curved sheet gives values which are in fair agreement with those found experimentally.

The strength of elliptical cylinders supported at the minor axis under bending plus shear loads is governed primarily by the bending strength, and is little effected by the sheer force unless the amount of shear is quite large with respect to the moment. The effect of increasing the amount of elliptically greatly reduces the bending and shear strength of nose sections. Under torsional loads the stress at buckling falls off as the ration of the major to minor axis increases but the failure stress decreases at a slower rate than the buckling stress. The length effect of semi-circular sections under torsion is similar to that of a circular tube, and can be obtained by Donnell's theoretical equation.

Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach

Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.

The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.

Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.

In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.

In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.

Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.