Collective microparticle adhesion on fluid lipid bilayer membranes driven by multivalent interactions leads to particle aggregation

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Master Thesis

Collective microparticle adhesion

on fluid lipid bilayer membranes

driven by multivalent interactions

leads to particle aggregation

by

Edo Vreeker

August 4, 2020

Student Number Daily Supervisors

11879815 Prof. Pietro Cicuta

Dr. Lorenzo di Michele Ph. D. student Roger Rubio Sanchez Dr. Roberta Lanfranco

Assessed by

Host Institute dhr. dr. T.J. Mooibroek

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Acknowledgements

I would like to thank Prof. Pietro Cicuta and Dr. Lorenzo Di Michele for giving me the opportunity to work on my Master’s research project in their research groups at the University of Cambridge. During my project I enjoyed their committed guidance and training that helped me to grow as a researcher. I am also grateful to them for allowing me to follow lectures and a summer school beside my project, that made me more complete as a science student. Special thanks to my friend and Ph. D. student Roger Rubio Sanchez, for his daily supervision, which he did with great amount of patience and dedication in order to educate me during every aspect of my research project and writing of my thesis. I would also like to thank Dr. Roberta Lanfranco, for teaching me everything related to the microparticles that were used during this project. Furthermore, a big thanks to my friend and Ph. D. student Michal Walczak, who was always available for fruitful discussions, useful advice or for much needed relaxation after long days at the lab. Thanks for the amazing gesture to let me stay at your place during the last weeks of my project, you helped me out with your amazing hospitality and for that I am extremely grateful.

Thanks to all the other first year students at the Biological and Soft Systems group for the good chats and laughs during the work day. And finally a big thank you to the other lovely people at BSS, for the good atmosphere within the research groups which made me feel so comfortable and made me go to the lab with a great enthusiasm each and every day!

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Abstract

The plasma membrane is a vital interface for cellular processes such as signalling, intercellular communications and particle transport. These processes require the adhesion of particles on the membrane surface. The membrane undulates and its deformation is known to affect how particles or complexes such as proteins interact with the membrane. Elucidating the dynamics of adhering particles on plasma membranes is highly valuable, but a systematic approach to study this is hindered by the vast complexity of biological systems. A useful alternative is to investigate synthetic models that mimic biological systems with a minimal amount of elements. This work uses a model system containing vesicles and colloids to investigate particle adhesion on lipid bilayer membranes. Adhesion between the interfaces was driven by multivalent interactions induced by mobile DNA linkers, resembling cellular particle uptake via passive endocytosis. The aim is to elucidate how membrane deformations affect the adhesion of particles and how the collective behaviour of adhered particles will take shape.

A new experimental set-up was established contanining an epifluorescence microscope, optical tweezers and a microcapillary aspiration technique. This novel combination of equipment enabled to aspirate a vesicle and introduce individual particles to the membrane surface in a controllable fashion. First, particles were optically trapped and placed on top of a vesicle resting on the bottom of the experimental chamber. The traps would then be deactivated and particles would sediment to the bottom while adhering to the vesicle. When 3 μm microparticles were introduced to the vesicle membrane a repetitive tendency to form aggregates was observed. This aggregation is thought to be driven by membrane deformation rather than non-specific interactions. Larger amounts of adhering particles of different sizes (2 and 3 μm) were observed to form nar-row aggregates. Individual particles of 3 μm aggregating with a nearest particle were found to obtain an inter-particle distance ranging between 3.8 and 4.6 μm upon aggregation (from centre point to centre point). For 2 μm particles, this was found to be 2.2 μm on average. This would mean that aggregation would leave 0.8-1.6 and 0.2 μm of free membrane space between a pair of 3 μm and 2 μm particles, respectively. Although narrow aggregates were an interesting ob-servation, as theoretical models predict anisotropic formations, the state of the vesicle shape was thought to play a predominant role. Therefore, vesicles were lifted from the surface to elucidate the shapes of aggregates without this factor. It was observed that, despite gravitational forces, particles do not seem to form closely packed conformations. This study demonstrates a feasible method to study colloidal interactions with lipid bilayer membranes experimentally. While it was previously considered challenging to investigate membrane adhesion of partially wrapped particles, it is shown how this state is achieved with mobile linkers and particles of sizes 2 and 3 μm.

The results herein presented could help to elucidate why proteins reacting to membrane deformations aggregate and show that particle aggregation is a factor that needs to be taken into account when colloids are used as local drug vehicles to the lipid membrane.

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CONTENTS

1 Introduction

1.1 Biomimetic and minimal systems

The cells found in any eukaryotic organism on this planet are vast in variety and overwhelming in complexity, with for example the human body containing more than 1013 _{cells [1]. Each cell functions as a highly complicated reaction}

vessel, constructed from a rich variety of biomolecules, capable to accommodate a myriad of simultaneous biochemical processes. There is a lot of interest to rationally modify biological processes, in order to harness them for new appli-cations in e.g. the pharmaceutical industry or technological devices. As it is not feasible to replicate these complex biological systems in the lab, systems are designed that entail a simplified artificial model. These models are designed to mimic cellular features, for example by using an artificial lipid bilayer to replace the plasma membrane. It is desirable to create biomimetic systems containing a minimal amount of elements. This allows to systematically study the underly-ing physics and chemistry of biological processes. For example, to elucidate the effects of high pressure on the adaptation and structural behaviour of biological membranes in deep-sea creatures, a synthetic model has been built with a new high-pressure microscopy cell to apply pressure on synthetic membranes [2]. A lot of effort has also been done in the development of new soft materials inspired by biology. For example, in the area of tissue engineering, artificial scaffold-like constructs are designed from biomaterials in order to replace damaged tissue or organs [3]. Other biomimetic systems are used in advanced drug and gene deliv-ery [4]. These examples of completely different studies into biomimetic systems show how diverse this field of research is and that it is worthwhile to inves-tigate fundamental biological processes to tackle challenges in modern science and engineering.

1.2 Properties and elements of the membrane

1.2.1 The plasma membrane

The interface of the cell that separates the cytoplasm from the extracellular environment is known as the plasma membrane. The plasma membrane is semi-permeable, and constructed from a bilayer of lipid molecules. Embedded in the membrane, proteins and protein complexes can be found that perform particular functions for the cell. Membrane proteins are for example involved in transmembrane particle transport, signal transduction, or the provision of struc-tural support in cellular compartments [5]. A schematic drawing of a typical cell membrane can be observed in Figure 1, which is adapted from [1].

1.2.2 Lipids in the plasma membrane

The three classes of lipids that shape the eukaryotic membrane are glycerophos-pholipids, sphingolipids and sterols [1]. Glycerophospholipids have a diacylglyc-erol moiety that connects the polar head group to two fatty acid tails. These

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1.2 Properties and elements of the membrane

Figure 1: Schematic drawing of a typical cell membrane in which the 5 nm thick lipid bilayer and several proteins incorporated in the membrane are shown. Image adapted from [1].

fatty acid tails can be of variable chain lengths and be in a saturated state (only single covalent bonds) or in a cis-unsaturated state (a double bond where the two adjacent hydrogen atoms are at the same side of the double bond). The most common glycerophospholipid is phosphatidylcholine, which predominantly has one unsaturated fatty acyl chain [6] (see Figure 2, which is obtained from [1]). Another class of lipids present in the plasma membrane of eukaryotic cells are the sphingolipids. The hydrophobic part of a sphingolipid is ceramide, consisting of sphingosine and a fatty acid. The tails of sphingolipids are saturated, increasing the flexibility of the chain and enabling sphingolipids to pack tails closer than glycerophospholipids, which lose their flexibility due to the bulky unsaturated tail. The other major class of lipids are the non-polar sterols, with cholesterol the most common sterol in mammalian cells [6]. It is reported that membrane active sterols like cholesterol have a handful of properties that optimise the membrane [7]. First of all, they seem to have an effect on the intramembrane short-range order and long-range lateral organisation. Cholesterol reduces the fluidity of phospholipid layers (by occupying the spaces between neighbouring phospholipids created by the kinks in the unsaturated lipid tails, as described by [8]). Additionally, its presence minimises the free volume within the membrane, reducing the permeability through the lipid bilayer. Furthermore, cholesterol tends to decrease the presence of water molecules on the lipid/water interface in the membrane. This effect increases the contact and Van der Waals inter-actions between adjacent lipid molecules, reducing membrane permeability and increasing chemical stability to oxidation or hydrolysis of the lipid molecules. The presence of cholesterol in the plasma membrane is also reported to enable the possible formation of lipid rafts, domains in the membrane that could play an important role in fundamental biological processes and in which the lipids behave according to the so-called liquid-ordered state [9, 10]. Biological mem-branes are fluid, meaning that the lipids within the interface behave according to the smectic-A phase, in which the lipids have a translational order in one dimension but behave in a liquid-like order in the other two dimensions [11].

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1.3 Self-assembly of lipid molecules in aqueous solutions

Figure 2: Schematic representations of one of the most common phosphoglyc-erides in the membrane, phosphatidylcholine. In (A) a schematic drawing of the phospholipid is shown, projecting the different moieties within a phosphatidyl-choline molecule. Portrayed are the hydrophilic head group (with its glycerol, phosphate and choline moiety) and the hydrophobic tails. (B) shows the molec-ular formula of each moiety in the lipid. One fatty acid tail is saturated while the other fatty acid tail has a cis-double bond. Image obtained from [1].

1.3 Self-assembly of lipid molecules in aqueous solutions

To analyse how a cell membrane should be mimicked in our artificial model, it is important to understand some fundamental aspects of lipid systems. Why do lipid molecules in solution self-assemble into larger supramolecular complexes? What factors come into play that decide the eventual shape of these supramolec-ular complexes? And what membrane features should we assess to make sure that our artificial model membrane contains the mechanical characteristics that are reminiscent of a plasma membrane?

1.3.1 Solvation energy

The hydrophilic head group and hydrophobic aliphatic tails in a lipid make the molecule amphiphilic. Self-assembly of lipid molecules in aqueous environments, and amphiphilic molecules in general, are driven by the minimisation of the total solvation free energy [12]. The stability of these aggregates in solutions are related to both the hydration of the hydrophilic polar head groups and the isolation of the hydrophobic lipid tails from the aqueous environment. The prior minimises the solvation free energy due to an enthalpic gain by the formation of hydrogen bonds, while the latter increases the entropy of the bulk water molecules by creating more configuration space for the water molecules to form

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1.3 Self-assembly of lipid molecules in aqueous solutions

hydrogen bonds [12, 13].

1.3.2 Packing parameter of amphiphilic molecules

To understand why the lipids shape into a bilayer, it is helpful to look at the dimensions of the lipid molecules that are included in the membrane. The shape of the interface is partly driven by the spatial dimensions of the lipids within the membrane. A convenient measure that can help to predict how an assembly of amphiphiles will form is known as the packing parameter. The packing parameter p is a dimensionless number expressed by

p = v a0lc

(1) in which v is the volume of the hydrocarbon chain(s), a0 the optimal area of

the head group and lc the critical chain length, which is the maximum effective

length the chain(s) can obtain [14]. Various values of the packing parameter are known to make distinctive structures. For example, if an amphiphile has p ≤ 1

3, its self-assembly will be in favour of a spherical micelle. However, if an amphiphile has 1

2 ≤ p ≤ 1 it will be driven to shape like a vesicle and, if p ≈ 1, it will shape like a flat bilayer. Figure 3 shows a schematic drawing describing how assemblies of amphiphiles with a packing meter of p ≤ 1

3, that has a more conical shape, and with 1

2 ≤ p ≤ 1, with a more cylindrical shape, will assemble in aqueous media [1].

1.3.3 Generation of membrane curvature via symmetry breaking Although the packing parameter might be a useful guide to indicate what shape the aggregate could form, it has to be noted that generally a lipid bilayer has the tendency to adopt a flat shape. This flat shape is a consequence of a homo-geneous lipid distribution among the monolayers to maximise entropy, causing symmetry between both leaflets and hence no preference to curve in any di-rection. Therefore, work has to be performed to induce membrane curvature in a biological membrane. In cells this membrane curvature can be generated via two approaches. The first approach is to break the symmetry of the mem-branes by rearranging particular lipids with peptides to a restricted domain in the membrane, while the second approach is the creation of local membrane deformations (and thus asymmetry) by the formation of peptide domains into one of the monolayers [15]. The first approach is reported to induce asymmetry between the two leaflets of the plasma membrane, affecting the compositions and lipid packing of the leaflets, and ultimately causing asymmetry in trans-membrane protein conformations [16]. Additionally, it is argued that any asym-metrical distribution of solutes across the bilayer, such as ions or water soluble macromolecules, will already induce spontaneous membrane curvature [17].

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1.4 Cellular particle transport through endocytosis

Figure 3: Schematic representation of how detergent (upper panels) and lipid molecules (lower panels) behave in water. (A) shows on the left how a deter-gent and a lipid differ in shape, with a deterdeter-gent (containing only one apolar tail) approximating a conical shape and a lipid (containing two apolar tails) a cilindrical shape. In the middle it is shown how these amphiphiles aggregate in an aqueous environment. The cone-shaped surfactants assemble into a micelle while the cilindrical lipids assemble into a bilayer. (B) shows how the micelle and lipid effectively shield of the hydrophobic core from the aqueous environment. Image adapted from [1].

1.4 Cellular particle transport through endocytosis

One of the cellular methods to transport extracellular particles or volumes of solutes into the cytoplasm is known as endocytosis. Endocytosis is a process in which a part of the plasma membrane, including its membrane proteins, is internalised. Endocytosis is capable of internalising particles from a range of sizes smaller than 200 nm to sizes larger than 500 nm through multiple, distinct mechanisms [18]. There are generally two types of endocytosis, known as ’active’ and ’passive’ endocytosis.

1.4.1 Active endocytosis

In active endocytosis, internalisation is aided by a biochemical pathway. A well known example of an active pathway in eukaryotic cells is clathrin-mediated endocytosis, in which clathrin proteins temporarily coat the membrane to ini-tiate vesicle formation through series of protein complexes [19]. Within this pathway, dynamin is the protein responsible for the breaking of the vesicle from the plasma membrane. This means that dynamin breaks the continuity of the membrane to form the vesicle and consecutively actively reseals the separated membrane. The energy that is required for this process is obtained from the hydrolysis of GTP.

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1.4 Cellular particle transport through endocytosis

Figure 4: Schematic example of passive endocytosis. Here, a nanoparticle (NP) decorated with ligands approaches a membrane featuring receptors. When the NP is in close proximity to the membrane, initial ligand-receptor bond formation takes place. The number of bonds with the diffusive receptors increase over time, making the membrane to wrap around the NP. This will eventually lead to the formation of an endosome carrying the NP in the cytoplasm. Image adapted from [23].

1.4.2 Passive endocytosis

Passive endocytosis does not involve the mediation of a signaling pathway nor require an external energy source - it solely depends on the binding of ligands with receptors. Receptor-ligand interactions can occur between mobile-mobile and mobile-immobile linkers. While receptors (and proteins in general) are mo-bile entities able to diffuse along the plasma membrane [20], ligands on target particles can both be mobile [21] and immobile [22]. An example of passive endocytosis is shown in Figure 4, adapted from [23]. Figure 4 shows how a nanoparticle (NP) decorated with ligands approaches the membrane of a cell covered with freely diffusing receptors. When the NP reaches close proximity, the ligands bind to the receptors and the nanoparticle becomes engulfed by the membrane. Full membrane wrapping of the NP finally results in the creation of an endosome after budding from the membrane, carrying the NP in the cyto-plasm. In plasma membranes, membrane budding can either be protein driven or membrane driven [24]. Similarly, viruses are creative in their methods to penetrate a cell. After adhesion to the membrane surface, one of the methods to initiate endocytosis is to diffuse along the surface and look for preformed protein structures which are then hijacked and used to mediate the endocytosis [25]. However, some viruses are also known to use passive endocytosis. These viral particles are able to randomly walk across the membrane after initial bond

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1.5 Important properties of vesicles for model membranes

formation, binding more receptors as they diffuse along the surface [26]. This gradually increases the degree of membrane wrapping, engulfing the viral par-ticle, which ultimately results in endocytosis. Passive endocytosis can also be applied to deliver synthetic matter to a cell, which has been studied for years with for example NPs and liposomes [27, 28].

1.4.3 Applications of endocytosis

An application in which endocytosis is being exploited to transport synthetic matter into cells is the research into targeted drug delivery [29]. There are several benefits of conjugating drug molecules with low molecular weights to carriers with high molecular weights, which are stable and biocompatible in vivo [30]. Conjugation can prevent the passive diffusion of drug molecules through tissue in the body. Additionaly, preventing passive diffusion lowers the toxicity as the distribution of the drugs through the body is lowered. Finally, drugs that would benefit from this conjugation are molecules that are poorly absorbed in the body’s system on their own, but have an improved absorption when bound to an effective macromolecule.

1.5 Important properties of vesicles for model membranes

1.5.1 Size range of vesicles

Model substrates such as supported bilayer lipids or vesicle membranes have become a popular tool to study chemical and physical processes naturally occur-ring on the plasma membrane. Within these model systems, the self-assembling property of lipids is harnessed to create an interface with properties similar to biological membranes. During this project, a system is studied where cells are mimicked by synthetic vesicles with unilamellar bilayer membranes. These vesi-cles can be categorised by size. Vesivesi-cles are generally divided into three size classes: 1) small unilamellar vesicles (SUVs), with a size range of 20-100 nm. 2) large unilamellar vesicles (LUVs), with a size range of 100-1000 nm. 3) giant unilamellar vesicles (GUVs), with a size range of 1-200 μm (see figure 5) [31]. The thickness of the bilayer generally ranges between 3 − 5 nm, depending on the lipids that comprise them. Generally, GUVs are used to mimic cells as they are on a similar size scale [1].

1.5.2 Membrane bending energy and Helfrich surface free energy However, size and thickness are not the only features to be looked at when a cell is mimicked. Despite having a fixed geometry of a spherical shape, the cell membrane is soft and can be deformed easily, causing undulations. To make sure that the model system response similarly to external forces, this deforma-bility has to be taken into account. It is helpful to look at mechanical aspects of the membrane that define how rigid the bilayer is and how susceptible it is to deformations. One mechanical aspect is the bending resistance of a lipid bilayer [32]. The bending of the membrane invokes a resistance as it entails the

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Figure 5: Schematic drawing of a vesicle. Vesicles are generally divided into three size classes: 1) small unilamellar vesicles (SUVs), with a size range of 20-100 nm. 2) large unilamellar vesicles (LUVs), with a size range of 100-1000 nm. 3) giant unilamellar vesicles (GUVs), with a size range of 1-200. The thickness of a vesicle membrane is typically 3-5 nm, dependent on the lipids in the membrane. Image adapted from [31].

stretching of one array of lipids (leaflet) within the membrane, while simultane-ously the opposite leaflet is compressed. This is energetically unfavourable as the hydrophobic tails in the stretched leaflet are then more exposed to the aque-ous phase while the compressed leaflet experiences more repulsive interactions between the charged head groups.

The energy per unit surface area (or energy density) needed to bend a bilayer increases with the curvature of the membrane. The curvature energy density for a spherical membrane is described by the Helfrich free energy term

fc= κb/2

2H − C0

2

+ κGK (2)

with the material specific parameters κband κGbeing the bending rigidity and

the Gaussian bending rigidity respectively (both parameters in units of energy), C0the spontaneous curvature of the membrane (which equals to 0 when the two

leaflets in the bilayer are identical) and H and K being the mean and Gaussian curvature of the membrane surface [33]. If the surface of a sphere is taken into account, an expression can be made for the bending energy compared to a flat surface:

E = 4π 2κb+ κG

(3) [32]. The determination of κband κG of a synthetic bilayer membrane is

there-fore an important aspect in order to assess whether the membrane bends simi-larly to external forces as a biological membrane.

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1.5.3 Membrane bending rigidity

Two different approaches have been made to determine κband κG. The bending

rigidity κb is a quantity that has been determined widely by analysing the

bilayer’s thermal undulations, in which numerical methods are used to determine the shape of the membrane fluctuations from which the bending modulus is obtained. A different approach that has been used takes the in-plane area of a membrane into account. This quantity is reduced by thermal fluctuations. Therefore, if a tension would be applied to the membrane, these fluctuations would first be ironed out before the true area of the bilayer would be increased. The resistance of a bilayer to be stretched or compressed in the elastic range is expressed by the apparent area compression modulus KA,app and is given by

KA,app=

KA

1 + KA 8πβκbτ

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where KA is the area compression modulus, β the inverse of the product of the

Boltzmann constant and the absolute temperature (kBT )−1, κb the bending

rigidity and τ the applied tension [32]. At small tension, KA,app ∼ 8πβκbτ and

thus κbcan be extracted from KA,appfrom a stress/strain curve at small stress.

The Gaussian bending rigidity however, is a quantity that has not been as widely reported as κb and which is not experimentally measured. Instead, theoretical

models have been made to calculate κG. Calculations show that κG is actually

a negative value. In this project, synthetic membranes have been made from 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). It is estimated that the ratio between κG and κb in a monolayer of DOPC equals −0.5, and that it may be

assumed that for a bilayer this equals −1.0 [34]. Now that κG can be expressed

in terms of κb, the latter becomes leading to look at to determine whether

the membrane reacts accordingly to fluctuations. For DOPC membranes, the bending rigidity is reported to be 1.08 ± 0.1 × 10−19 J at 23 oC [35]. This is in the same order of magnitude as the bending rigidity of plasma membranes at temperatures between 20 − 30o_{C, which is reported to have values between}

0.2 − 4.3 × 10−19 J [32]. As both values are in the same order of magnitude, it may be assumed that it is acceptable to use DOPC lipids as a model membrane to study deformations in membrane curvature, in terms of bending rigidity. 1.5.4 Membrane tension and its determination with the

microcapil-lary aspiration technique

One of the approaches to investigate the mechanical reaction of the membrane to external forces is by assessing the generated membrane tension. Membrane tension is for example generated by the cytoskeleton and is thought to have an impact on cellular processes such as endocytosis, exocytosis and myosin contrac-tion [36, 37]. Membrane tension is defined as ’the force per unit length acting on a cross-section of the membrane’ and there are multiple available techniques to measure membrane tension, such as micropipette aspiration or membrane

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Figure 6: Bright-field images of a GUV aspirated to a microcapillary. From this image the radius of the vesicle Rv, the radius of the micropipette Rp and

the length of the membrane tube in the capillary L can be obtained. Frame B shows how an increase of L compared to Frame A relates to a higher calculated membrane tension. Image adapted and modified from [39].

tethering [38]. Micropipette aspiration is a common technique in which the membrane tension can be deduced from geometrical observables of the vesicle and the micropipette. Figure 6 shows how a GUV is aspirated to a microcap-illary [39]. A GUV in an aqueous solution rests on a glass surface such that it can be observed by an optical microscope. The microcapillary enters the batch and approaches the vesicle in close proximity. A pressure difference is applied which causes a net flow of the bulk into the microcapillary. The vesicle is sucked into the capillary to become aspirated. The domain of the vesicle outside the microcapillary is considered to be spherical after aspiration has taken place. Frame B in Figure 6 shows how the length of the membrane domain inside the microcapillary is increased from length L in frame A to L + ∆L. This is a consequence of an increased pressure difference. The increase of ∆L leads to an increase of the membrane area according to:

∆A = π 2Rp∆L 1 − Rp Rv +4∆V πDv (5) where ∆A represents the change in membrane area, Rp the diameter of the

micropipette, ∆L the change in length of the aspirated membrane tube, Rv

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1.6 Interactions of colloidal particles with membranes

equation can be simplified by assuming that the change of vesicle volume can be neglected, which has been justified by Kwok et al. in [40]. At mechanical equilibrium, the isotropic membrane tension is constant among the complete surface of the area. When the applied pressure difference is known, and the radius of the vesicle and micropipette can be obtained via analysis, it is possible to calculate the generated membrane tension via:

τ = ∆P Rp 2 1 − Rp Rv (6)

where τ represents the isotropic membrane tension [40].

Applying a controllable pressure on a vesicle is feasible by using a manome-ter set-up. Controlling the membrane tension within the vesicle enables the control of the area-to-volume ratio of a vesicle. When the area-to-volume ratio approaches 1 (e.g. by increasing the membrane tension of a vesicle with a mi-crocapillary), the shape of the membrane surface becomes spherical (using the definition as in [41]). The ability to control the membrane tension can be viewed as a valuable asset, as this parameter is thought to affect processes that involve particle induced deformations, such as the aggregation of proteins on plasma membranes driven by membrane deformation [42] or the curvature-driven mi-gration of colloidal particles on vesicles [43].

1.6 Interactions of colloidal particles with membranes

One of the motivations to study interactions between lipid bilayer membranes and colloidal particles is the fact that several viruses are known to use passive endocytosis in order to invade a host cell [44]. Additionally, colloidal particles can be applied as controlled drug delivery devices to cells [45]. An example of one of these devices is mesoporous silica nanoparticles, where the focus of research has mainly been on its drug delivery mechanisms and biocompatability [46]. One of the aspects of nano- and microparticles that has not been fully elucidated yet is their behaviour on lipid bilayer membranes after adhesion has taken place. Adhesion of particles on the membrane is caused by attractive interactions between the two surfaces, creating local membrane deformations that induce an extra curvature in the membrane. Studying the fundamental principles of these membrane curvature effects could additionally improve the understanding of protein aggregation mechanisms on biological membranes, as it is reported that membrane curvature can mediate interactions between pro-teins and drive them into aggregates [47]. One of the aspects that has been studied regarding particle adhesion is the degree of membrane wrapping around the adhering particle and how multiple adhering particles behave collectively on a membrane. Aggregation mechanisms for particles that are completely en-gulfed by the membrane have already been explored. For vesicles containing an excess membrane area, it is reported that wrapped particles tend to aggregate to decrease the bending energy in the membrane [48]. Wrapped particles were

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measured to create an interaction streng of −3.3kBT , with an interparticle

at-traction range that exceeded 2.5 times the particle diameters. It is important to mention that, experimentally, mainly microparticles are studied due to opti-cal limitations of studying nanoparticles. The degree of membrane wrapping in passive endocytosis has been shown to be dependent of particle size [49, 50]. 1.6.1 Key parameters and relevant energy contributions for particle

adhesion on membranes

Substantial effort has been done to study adhesion theoretically. In Lipowsky’s contribution to the book ’Physics of Biological Membranes’, it is discussed how the global interaction of the particle with the membrane can be described by a handful of parameters belonging to the membrane and particle [51]. The relevant parameters are the mean membrane curvature M of the membrane segment that interacts with the particle, the particle size Rpaand a parameter

described as the adhesion length RW. The adhesion length is defined as:

RW ≡

s 2κb

|W | (7)

where κb represents the bending rigidity and |W | the adhesive strength

gener-ated by the interactions between the membrane and the particle. The particle is then expected to be only partially wrapped by the membrane if the mean curvature is between: − 1 RP a < M < Mf r= − 1 RP a + 1 RW (8) in which Mf ris a threshold value for the membrane curvature, which indicates

that adhesion will not occur if M ≥ Mf r[51].

A study by Deserno on adhesion of microparticles used the Helfrich Hamil-tonian of the membrane as a basis [52]. In this study a length scale λ was introduced, determined by:

λ =r κ

σ (9)

with κ describing the bending modulus and σ the membrane tension. For typical biological values, it was determined that λ was approximately 64 nm. Consec-utively it was stated that membrane deformations smaller than this scale are mainly controlled by bending energy, while tension tends to be a key factor at larger scales. The ability to control membrane tension during adhesion of mi-croparticles is therefore thought to be a valuable asset when studying the effects of membrane deformation.

The relevant energetic contributions that come into play upon particle bind-ing and membrane wrappbind-ing are the elastic energy contributions of the mem-brane and the adhesion energy between the surface and the particle. These contributions can be summed up as:

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in which Ebeand Eteare part of the elastic energy contributions that described

the bending energy and tension energy of the membrane respectively, while Ead

describes the adhesion energy of a particle [41].

In the same article, Bahrami et al. elaborate each energetic contribution individually. The bending energy is described as:

Ebe= Z ₁ 2κ 2M − C0 2 + ¯κK dA (11)

in which κ describes the bending rigidity, M the local mean curvature, C0

the spontaneous curvature, ¯κ the modulus of the Gaussian curvature, K the Gaussian curvature and A the area of the membrane. Consecutively, the tension energy is given as:

Ete= σA (12)

where σ represents the membrane tension. Finally, the adhesion energy of a particle is given by:

Ead=

Z

V (d)dA (13)

where V (d) is the interaction potential between the particle and the membrane, d the local distance between the particle and the surface and A the area of the membrane. When the interaction range between the particle and membrane surface was set to be nonzero, Bahrami et al. were also able to model how the membrane will shape around a particle based on the adhesion energy. To do so, they set the interaction potential to be:

V (d) = U (e−2d/ρ− 2e−d/ρ) (14) in which U describes the adhesion energy per area, and ρ indicates the char-acteristic length of the particle-membrane interaction. Furthermore, a rescaled adhesion energy term was introduced:

u = U R2/κ (15)

with R being the radius of the spherical particle. For values of ρ = 0.01R, a minimum-energy profile could be obtained for various rescaled adhesion energy values (see Figure 7, adapted from [41]).

1.6.2 Collective particle adhesion on membranes

Behrami et al. also discussed the cooperative binding of two particles on the membrane, as can be seen in Figure 8 (adapted from [41]). When the rescaled adhesion energy u was set to 2.0, and the area-to-volume ratio v of the vesicle was set to 0.96 (v = 1 represents a sphere), a minimum bound-energy state of two adhering particles could be obtained. This minimum bound-energy state shows that two adhering particles favour cooperative wrapping over individual membrane wrapping. Interestingly, computer simulations show that, at biolog-ically relevant membrane κb values, multiple partially wrapped particles on a

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Figure 7: Minimum-energy profiles for membrane wrapping around a spherical particle for different rescaled adhesion energy values and a set interaction range of ρ = 0.01R. Image adapted from [41].

Figure 8: Minimum-energy state after the cooperative binding of two particles on a membrane, when the rescaled adhesion energy u is set to 2.0 and the area-to-volume ratio v is set to 0.96. This minimum-energy state shows that the combined membrane wrapping of two particles is favoured over wrapping the particles separately. Image adapted from [41].

fluid vesicle membrane will form linear aggregates (see Figure 9, adapted from [53]). Particle adhesion can be driven by oppositely charged surfaces [54] or complex formation of receptor-ligand constructs that decorate both surfaces. When the latter drives the adhesive interactions, it is important to include this interaction to study how the particle will adhere on the membrane. Lipowsky’s model above has been elaborated to describe membrane engulfment by par-ticles driven by receptor-mediated adhesion, although active endocytosis was modelled [55]. Van der Wel et al. have already elucidated how microparticles with fixed linkers can have multiple mechanisms to aggregate on a membrane [56]. However, it is expected that the (im)mobility of the linkers on the parti-cle surface influences how deep the partiparti-cle will penetrate the membrane, and that mobile linkers on the particle will only induce a partial wrapping on the membrane [57].

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1.7 DNA in biology and nanotechnology

Figure 9: Images of computer simulations that predict linear aggregates of partially wrapped nanoparticles on fluid vesicle membranes at biologically rel-evant membrane kb values. On the left and middle image, Rpar is 3.25 times

smaller than Rves, on the right image Rparis 15 times smaller than Rves. Image

adapted from [53].

1.7 DNA in biology and nanotechnology

1.7.1 Discovery of DNA and its building blocks

In biological systems, deoxyribionucleic acid (or DNA) is used to store genetic information. The intriguing properties of this biopolymer that ultimately defines biological life has fascinated scientists for decades. In 1953, Watson and Crick published a groundbreaking article on the discovery of the molecular structure of DNA and the crucial role of base-pairing [58]. At the same time, Franklin and Gosling supported the findings of Watson and Crick by studying DNA crystals, delivering evidence of the proposed helical structure of DNA and revealing that DNA helices could take up multiple conformations, referred as form A and form B [59]. Although Watson and Crick received global recognition at that time and were even awarded a Nobel Prize in 1962 for their findings, it has to be emphasised that Franklin’s work and multiple publications on DNA were crucial contributions to find the solution to the DNA structure [60].

DNA is made up from two strands of nucleotides. These nucleotides are com-prised of a sugar-phosphate group and a nitrogen-containing basic side group, which is either a pyrimidine or purine derivative. Each of the four nucleotides has its own specific basic side group, and it either contains the bases adenine, thymine, cytosine or guanine (see Figure 10, as adapted from [61]). Selective binding (or hybridisation) is driven by specific hydrogen bonding between two distinct base pairs. Adenine binds to thymine to create a base bair consisting of two hydrogen bonds, while guanine binds to cytosine which creates a base pair comprising three hydrogen bonds. As every base has a preferential binding to only one other base, the base sequence in every single polymer chain (referred to as a DNA strand) is vital. Every DNA strand is therefore described by the order of the bases it contains, by using the letter A for adenine, T for thymine, C for cytosine and G for guanine.

In every DNA strand, the sugar-phosphate groups of the nucleotides are covalently bonded and function as a backbone of the DNA strands. In a pro-cess also known as hybridisation, hydrogen bond formation between bases of two single strands create a single double-stranded DNA complex (see Figure 11, adapted from [1]). Due to chemical and sterical effects, the double-stranded

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Figure 10: Selective formation of two distinct base pairs driven by hydrogen bond formation. Adenine binds to thymine (a) to create a base pair consisting of two hydrogen bonds, and guanine binds to cytosine to create a base pair con-sisting of three hydrogen bonds (b). Each base is either a pyrimidine (cytosine and thymine) or a purine (adenine and guanine). Image adapted from [61].

Figure 11: Schematic drawings of the building blocks of DNA. (A) shows the components of a nucleotide. (B) is an example of a single DNA strand, which is a polymer chain consisting out of 4 different nucleotides, covalently bonded via the sugar-phosphate groups in the nucleotides. (C) shows how two single DNA strands bond to form double-stranded DNA through hydrogen bond formation between complementary base groups, a process also referred to as hybridisation. Image adapted from [1].

DNA complex adopts a secondary structure - with the most common config-uration a double helix. For more information about the structure of DNA in biology, please see additional information in Appendix A.

1.7.2 Introduction to DNA in nanotechnology

After the discovery of the structure of DNA, research in DNA was mainly focused on its biological role. In the early sixties, Holliday came up with a model to explain effective pairing and recombination of homologous chromatids in fungi [62, 63]. In this model different stages were introduced in which two sets of double stranded DNA pair up, break and rejoin to exchange parts of their DNA strands. During one of these stages, a cross-shaped junction involving four DNA

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Figure 12: Original schematic drawing of Holliday’s mechanism to illustrate gene conversion. Two pairs of DNA strands are shown (one pair in solid lines and one pair in broken lines) that in four steps pair up, break and rejoin to exchange parts of their DNA strands. Step 3 represents the Holliday junction. Image adapted from [63].

strands is introduced which became known as the Holliday junction (see Figure 12, adapted from [63]). These Holliday junctions generated an interest to design DNA constructs with crystalline symmetry, for example by crystallographer and nanotechnologist Seeman. In 1982, Seeman recognised that the structural and dynamic properties of these Holliday junctions in model systems were not possible to be studied due to sequence symmetry [64].

He argued that it is unlikely that a set of DNA strands will form a junction, as the formation of a double helix is more favourable. Therefore, he introduced a model in which the strands had an asymmetrical sequence. The introduction of these strands meant that it became energetically favourable to form stable immobile junctions. A year later Seeman managed to synthesise and charac-terise these immobile nucleic acid junctions [65]. This discovery motivated more research into synthetic DNA systems. More than a decade later, Seeman was involved in a study with Li et al. to investigate new biomaterials by using DNA as building blocks [66]. This study was done after various constructs were reported to be synthesised, either in solution or on a solid support, such as a DNA truncated octahedron [67]. Eventually, the step from microscopic to macroscopic DNA constructs was established. In 2009, Seeman was involved in a study with Zheng et al. that managed to synthesise a well-defined 3D DNA crystal at macroscopic size (see Figure 13, adapted from [68]). More research has been done to establish unique DNA nanostructures. Brady et al. looked into the synthesis of well-defined three-dimensional DNA nanostructures named DNA C-Stars [69]. In this work, Brady et al. came with a solution that cir-cumvents the dependency of long-range DNA crystals on the structural rigidity of the individual strands. By connecting DNA strands to cholesterol moieties, nanostructures were constructed that contained the selectivity of DNA strands with an increased robustness due to the cholesterol’s hydrophobic interactions. Brady et al. showed that by including hydrophobic interactions the flexibility of DNA junctions becomes crucial for DNA crystallisation [70]. The DNA crystals formed by DNA C-Stars can be observed in Figure 14 (adapted from [70]).

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Figure 13: Schematic drawing and microscopic image of well-defined 3D DNA crystals. a Representation of the unit cell which forms a tensegrity triangle. Three unique DNA strands (in green, magenta and blue) were used. b Micro-scopic image of crystals formed from the tensegrity triangle unit cell. Image adapted from [68].

Figure 14: a Representation of the amphililic assembly used in the study of Brady et al. Four core strands and four anchor strands (with cholesterol moieties attached) bind to form a C-star, as shown in b. In c the hypothesised unit cell of the crystal made from these c-stars is shown, with the red zones showing the connections between the c-stars, driven by hydrophobic interactions. d shows a brightfield micrograph of these crystals. The scale bar equals 20 μm. Image adapted from [70].

1.7.3 DNA nanotechnology applied to soft and hard interfaces The surface of the plasma membrane interacts with soft and hard interfaces dur-ing various biological processes, such as endocytosis or intercelullar membrane adhesion. A closer study on the membrane proteins that drive these interactions helps to improve the fundamental understanding of these important phenomena in biology. Moreover, multivalent interactions induced by membrane proteins between biological interfaces serve as a source of inspiration for applications in novel drug delivery systems or applications in biomimetic systems. DNA nanotechnology has shown to be a useful tool to mimic these multivalent inter-actions. DNA linkers can induce an attractive interaction analogue to biological receptor-ligand complexes, causing the interfaces to which the linkers are teth-ered to bind [71]. DNA linkers are typically constructed out of three components

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Figure 15: Schematic representation of DNA linkers. a. The three main com-ponents of DNA linkers are shown. The sticky end is a domain of ss-DNA, capable to hybridise with sticky ends that contain a complementary base se-quence. The spacer is a construct designed to create a distance between the sticky end and the substrate to which it is attached. A spacer can comprise of ds-DNA (top) or ss-DNA (bottom). The third component of a DNA linker is its anchor, that attaches the DNA linker to a substrate. b. Shows the common hydrophobic anchors selected for DNA linkers to incorporate into soft interfaces, such as lipid bilayers. Image adapted from [71].

(see Figure 15 a., adapted from [71]). The first component comprises the so-called sticky ends. These sticky ends are domains at the end of each DNA linker that consist of ss-DNA. Each pair of DNA linkers is designed such that each individual strand has a sticky end that contains a base sequence that is exactly complementary to the other strand’s sticky end. This enables the favourable Watson-Crick base pair hybridisation between both sticky ends, creating a syn-thetic receptor-ligand complex. The binding between both sticky ends is highly specific due to the nature of base pair hybridisation. The second component of the DNA linker is the spacer. The spacer is a DNA domain which can consist of ss-DNA or ds-DNA. The construct creates a distance between the sticky end and the lipid bilayer, minimising static interactions from the surface. The third com-ponent is the anchor, enabling to tether the DNA linker to the substrate surface. In order to attach DNA linkers to the interface of lipid bilayers, hydrophobic anchors are used that insert into the core of the bilayer due to hydrophobic forces. A variety of anchors can be used that enable reversible or irreversible binding to the lipid bilayer (see Figure 15 b., adapted from [71]). Cholesterol is

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1.8 Statistical thermodynamics and kinetics of DNA linker hybridisation

a popular choice due to its commercial availability. A single cholesterol moiety as anchor enables reversible binding to a lipid bilayer, while a double anchor ensures irreversible binding [71]. To understand the complex behaviour of DNA linkers on soft and hard interfaces, a variety of artificial models have been stud-ied to understand the underlying statistical mechanics. Experimental studies on DNA mediated adhesion between interfaces have been done on a variety of systems, for example: colloidal systems [72], vesicles on supported lipid bilay-ers [73], nanoparticles on vesicles [74], and adhesion between vesicles [75]. The latter study gave an insight into the interesting material properties of adhering vesicles can obtain. These vesicles, clustering together to form soft networks, were reported to have a negative thermal expansion and tuneable, temperature dependent porosity.

1.8 Statistical thermodynamics and kinetics of DNA linker

hybridisation

When DNA linkers are used to bind the interfaces of two membranes, adhesion is accomplished when hybridisation of two complementary sticky ends has taken place. The DNA complex that is formed is then called a bridge formation. To gain a good understanding of the free energy and kinetics of multivalent interactions driven by DNA linkers, it is important to know the basic properties of the DNA linkers that are used. The double helix DNA configuration has the rigidity of a stiff polymer, with a persistence length of approximately 50 nm (or 150 basepairs) [76]. For the construction of DNA linkers, strands are used with a basepair sequence well below the persistence length. This ensures that the rigidity of the ds-DNA domain within the linker may be assumed to be similar to a rigid rod. This is beneficial for studies into the statistical thermodynamics of DNA linkers, as this minimises the spatial configurations the linkers can acquire. Assuming the linkers to be rigid rods simplifies free energy calculations, as will be shown later in this paragraph. The sticky ends that are used often comprise of a short base sequence. The melting transition of short hybridised sticky ends, indicating the breaking of the hydrogen bonds between the base pairs by thermal energy, is relatively low. To give an indication, it is reported that the melting transition of hybridised sticky ends containing 7 base pairs initiate at around 45o_{C, with a temperature interval spanning more than 30}o_{C [73]. The}

low melting temperatures of sticky ends can be exploited in the design of soft networks. For example, the temperature dependence can be used to control the assembly of DNA-coated colloid mixtures into complex networks [77].

1.8.1 Gibbs free energy of base pair hybridisation

The first step of getting to understand the thermodynamics of DNA linkers is to gain knowledge of the free energy that is released upon base pair hybridisation. Santalucia reported an approach to obtain an estimation of the change in Gibbs free energy [78]. In his empirical model, experimental data of seven studies was implemented using the Nearest Neighbour (NN) model. The model is based on

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Figure 16: Molecular structure of a CGTTGA•TCAACG oligonucleotide se-quence. The arrows indicate each NN dimer. This sequence is initiated by a GC terminal on one end and a AT terminal on the other end. Image adapted from [78].

the assumptions that the stability of any given base pair in an oligonucleotide is dependent on the identity and orientation of neighbouring base pairs. In this model, the total ∆Go_{of base pair hybridisation is given by:}

∆Go=X

i

ni∆Go(i) + ∆Goi(XY ) + ∆G

o_(sym) ₍₁₆₎

in which ∆Go_{(i) are the standard-free energy changes for all the possible}

Watson-Crick NNs, ni is the number of occurrences of each nearest neighbour, the

initiation parameter ∆Go

i(XY ) is used to specify which base pair terminal is

used to initiate the oligonucleotide and which either equals to 0.98 kcal/mol if a GC base pair is used or 1.03 kcal/mol if an AT base pair is used, and fi-nally ∆Go(sym) is a term that covers the entropic penalty for C2 symmetry in self-complementary duplexes that equals +0.43 kcal/mol if the strands in the duplex are self-complementary and 0 kcal/mol if not. The maintenance of C2 symmetry requires an entropic penalty as it reduces the amount of microstates available for the configurations of the duplex. To create an insight into the order of magnitude of the hybridisation free energy of short sticky ends, Santalucia included an example duplex (see Figure 16, adapted from [78]). Santalucia’s NN model was implemented on a duplex sequence of CGTTGA•TCAACG, which is not self-complementary and therefore does not need the entropic penalty for C2 symmetry. To estimate the change of Gibbs free energy upon base pairing within the sequence shown in Figure 16, equation (15) can be used. So in this case, ∆Go= ∆Go(CG/GC) + ∆Go(GT /CA) + ∆Go(T T /AA) + ∆Go(T G/AC) + ∆Go(GA/CT ) + ∆Go_i(CG) + ∆Go_i(AT ) + ∆Go(sym) = −2.17 − 1.44 − 1.00 − 1.45 − 1.30 + 0.98 + 1.03 + 0 = −5.35 kcal/mol (17)

compared to the experimentally observed −5.20 kcal/mol hybridisation free en-ergy [78].

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1.8.2 Gibbs free energy of DNA linker hybridisation

The change of Gibbs free energy of base pair hybridisation is not the only factor that contributes to the total change of Gibbs free energy when linkers bind. When DNA linkers are tethered to a membrane, they are tethered to a fluid interface. This means that each indidivual linker is mobile, it posesses translational degrees of freedom across the surface of the membrane. In this project, adhesion will be studied between a vesicle membrane and a colloidal stabilised lipid bilayer (CSLB). This means that both DNA linkers are tethered to a fluid interface, thus both linkers enjoy mobility. When the surface of the colloid binds to the vesicle, the surface of the vesicle adjusts its shape to the curvature of the colloid. Consecutively, when a bridge is formed between two DNA linkers, this bridge is confined to a region where the distance between the membranes is equal or less than the length of the bridge. This narrow area is known as the contact region (CR) between the microparticle and the vesicle surface. This spatial confinement of the bridge has an entropic effect on the hybridisation free energy of mobile linkers and needs to be taken into account. The shape of the contact region is similar for a flat and curved surface, and the CR will either form a circle or a truncated circle [79]. To address the contribution of the confinement of the linkers to the change of Gibbs free energy, the hybridisation free energy of two complementary linkers A and B can be written as follows:

∆GAB(h) = ∆GoAB+ ∆G conf

AB (h) (18)

in which h is the distance between the two surfaces to which A and B are tethered, ∆Go

AB is the standard free energy term already discussed in equation

(5), and ∆Gconf_AB is the term that accounts for the confinement when linkers A and B have hybridised to form a bridge [71]. To derive GAB(h) in the case

of mobile linkers, certain simplifications have to be made. The linkers have to be seen as rigid entities of length L, and h is assumed to be to equal L, which is the case in equilibrium conditions. As discussed before, it is reasonable to assume the linkers are rigid as the length of the linkers are less than its persistence length. If these assumptions are made, Mognetti et al. were able to express the Gibbs free energy of hybridisation with quantifiable parameters. This expression needed multiple derivations, and the final form of ∆GAB, at

h = L, can be observed in equation (17):

∆GAB= ∆GoAB− kBT log ρ0LSCR (19)

in which kBT is the product of the Boltzmann constant and the absolute

tem-perature, ρ0is the number density used for the definition of ∆GoAB(for example,

ρ0 = 1 M [80]), L is the length of the linkers and SCR the area of the contact

region [71]. Equation (19) shows the perhaps counterintuitive result that con-finement of two linkers upon bridge formation lowers the Gibbs free energy. What might be helpful to note is that, while linkers in a bridge might be lim-ited in their translational degrees of freedom, hybridisation of any linker A to any linker B creates a whole new subset of microstates in the form of AB com-plexes. The creation of this new subset of microstates rises the entropy of the

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system, favouring the change of free energy upon hybridisation. Mognetti et al. also expressed the stability of AB hybridisation between soft interfaces in a 2D-equilibrium constant, by using the areal concentration ratio between the free and hybridised linkers and relating ∆GAB(h) as follows:

K_ABeq,2D= nABSCR (nA− nAB)(nB− nAB)

= SCR× exp − β∆GAB(h) (20)

in which β is the inverse of kBT [71]. The combination of equation (19) and

(20) then gives the equilibrium constant K_ABeq,2D = exp[−β∆GAB(h)] for rigid

linkers of length L and h = L. The 3D-equilibrium constant is subsequently given by: K_ABeq,3D= ρAB ρAρB = nABSCRL nA− nAB nB− nAB = K eq,2d AB L (21)

in which ρA, ρB and ρABare local bulk concentrations of freely diffusing linkers

A and B and complex AB [71]. Analysing both equilibrium constants gives a useful insight into the important parameters that are involved. Besides a negative change of Gibbs free energy, a sufficiently large contact region or linker length favour the reaction in the direction of the AB complex.

1.8.3 DNA linkers hybridisation in out-of-equilibrium systems The hybridisation of complementary linkers into a complex is not necessarily a reversible reaction. An out-of-equilibrium situation can occur when the interac-tions between the linkers are strong enough to cause irreversible binding. Such interactions are expected between the DNA linkers used in this project due to the length of the sticky ends. The kinetics of adhesion of particles on biological or biomimetic membranes driven by multivalent interactions is still poorly stud-ied, especially in the case of mobile linkers. Lanfranco et al. have established an understanding of the binding kinetics by studying the adhesion of nanopar-ticles on the membrane of LUVs [74]. In Lanfranco’s study, gold nanoparnanopar-ticles were coated by one set of DNA linkers while the complementary DNA linkers were incorporated into the LUV membrane, with the latter set being able to move freely along the membrane surface. The region of irreversible binding was explored, including parameters that could affect the kinetics of particle adhe-sion. The length of the sticky ends of the DNA linkers is expected to affect the dissociation rate, as the Gibbs free energy of linker hybridisation is dependent on the length of the sticky end. The sticky ends of the DNA linkers used in Lanfranco’s study comprised of 11 base pairs. The rate at which a bond between the LUV membrane and a nanoparticle i would break, the bond breakup rate, was found to be ki

of f = 1.4 ∗ 10−9s−1. Additionally, it was reported that, when

a particle was in the range to interact with the membrane, the time (τbond) to

form a DNA bridge was approximately 200 ms. Parameters that could affect τbondwere the surface density of receptors on the LUV membrane and bulk

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1.9 Objectives

Figure 17: Schematic drawing of the DNA linkers used in this project. DNA linkers are used to bind two membrane surfaces. After the sticky ends of both linkers have hybridised (the domain with both the red and blue strand), a bridge construction is formed. The DNA linkers used in this project have a ds-DNA spacer and a double cholesterol anchor (one yellow ellipse represents one individual anchor) that binds the linker irreversibly to the membrane surface.

nanoparticle was low, receptor depletion could occur which increased τbond. A

high concentration of particles could in turn hinder particle adsorption due to sterical hindrance. When the concentration of nanoparticle compared to LUVs was high, steric interactions could also increase. The kinetics of particle adhe-sion studied by Lanfranco et al. is expected to be important for this project, as the DNA linkers will have a similar design in terms of the sticky ends.

1.9 Objectives

The aim of this project is to elucidate the adhesion and collective behaviour of microparticles on fluid lipid bilayer membranes. The desire is to investigate if the findings of theoretical studies, predicting minimum energy states where particles aggregate on vesicle membranes, can be replicated with experimental studies. If aggregates are observed, it will be of great interest to find out whether the minimisation of deformation energy by the vesicle membrane will drive large aggregates into anisotropic formations. Adhesion between microparticles and the membrane surface are mediated by multivalent interactions, analogue to ligand-receptor mechanisms that are ubiquitous on plasma membranes. The multivalent interactions will be achieved by artificial DNA constructs, able to perform highly specific binding via base pair hybridisation between complemen-tary linkers. The design of the DNA linkers is as follows: the sticky ends are connected to a ds-DNA spacer and a double cholesterol anchor that tethers the linker irreversibly to the membrane surface (see Figure 17).

The mechanical reaction of the membrane on particle adhesion is thought to depend on various properties, such as particle size, linker mobility and mem-brane tension. Investigating these variables and the effects on the adhesion and collective behaviour of microparticles will have a key priority in this project. As the control of the membrane tension during colloidal adhesion is thought to be a

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1.9 Objectives

valuable asset, one of the objectives is to build a novel experimental set-up that will allow us to regulate this parameter. The targeted approach is to include a microcapillary aspiration technique into the set-up. The microcapillary is ca-pable to aspirate a fraction of the membrane with a known pressure difference, allowing us to calculate the induced membrane tension. When the set-up is completed, it will allow the study of adhering colloids on a vesicle membrane in a fashion similar to Figure 18. The aim of this study is to create a bet-ter understanding of the effects of elastic membrane deformation on collective microparticle adhesion. This could potentially help to increase the knowledge on fundamental biological processes reliant on the mechanical properties of the membrane, such as membrane proteins that aggregate as a result of membrane deformations. The collective behaviour of microparticles on the membrane could also be of value for new modern drug delivery techniques, as it could help to understand how colloidal drug carriers interact with the membrane surface.

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1.9 Objectives

Figure 18: Schematic drawing of the designed experimental set-up that will be used during this project. The giant unilamellar vesicle (turquoise) will be aspired with a microcapillary (grey) to be able to modulate the membrane ten-sion of the vesicle. Microparticles (dark-blue) are introduced to the membrane with optical tweezers. The sizes of the vesicles will be approximately 20-100 μm, while the microparticles will have a diameter of 2 or 3 μm. Inset: enlargement of the interacting surfaces that induce adhesion. A. Domain belonging to the CSLB. The grey substrate represents the silica surface that supports the mem-brane. The membrane belonging to the CSLB is dark-blue coloured. The black brushes represent DOPE-PEG(2000) moieties, which are incorporated into the membrane. B. Membrane belonging to the vesicle. C Domain of the interacting DNA linkers. The red DNA linker is attached to the interface of the CSLB, the blue DNA linker is attached to the membrane of the vesicle. The pair of DNA linkers contain complementary ss-DNA sticky ends that are able to undergo highly specific binding due to Watson-Crick base pairing.

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2 Materials and Methods

2.1 Giant Unilamellar Vesicle (GUVs) preparation

In this study GUVs have been used to study the mechanical properties of lipid bilayer membranes. The GUVs are constructed from 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), an unsaturated phospholipid. DOPC was purchased from Avanti Polar Lipids, in chloroform solution, and stored at -20 o_{C. To}

study the lipid systems with fluorescence microscopy assays, a lipid mixture with DOPC doped with fluorescent dye was prepared. Batches contained DOPC and 0.8% Texas RedTM1,2-Dihexadecanoyl-sn-Glycero-3-Phosphoethanolamine (Texas RedTMDHPE). Texas RedTMDHPE was purchased from Thermo Fisher Scientific and stored at -20oC at a concentration of 3 mg/mL. The lipid mixture was also stored at -20o_C.

To create GUVs, the common technique of electroformation was used [81]. This technique uses an electric field to form vesicles from a lipid film in the presence of a buffer solution. First, indium tin oxide (ITO) slides were acquired from Visiontek Systems Ltd. Before use, the ITO slides were sonicated for 15 minutes in isopropanol, for 15 minutes in milliQ and dried under N2 for

cleaning purposes. One slide was taken to spread 45 μL lipid mixture on its conducting surface with a glass coverslide. This slide was then put in a dry silica desiccator under vacuum for at least an hour, to remove the chloroform solvent resulting in a dry lipid film. Afterwards, the ITO slide could be removed from the desiccator to assemble the electroformation chamber. The chamber consisted of the following parts: one clean ITO slide, one ITO slide covered by the lipid film, a U-shaped spacer, a sugar solution and parafilm. The ITO slides were stacked, separated by the spacer and held together by binder clips. It is essential that both conducting surfaces are facing inwards, to allow an electric current to run through the chamber during electroformation. The spacer provided distance between the ITO slides necessary for the GUVs to grow from the lipid film. It contained a U-shape to create an opening on the top to add the sugar solution and retrieve the vesicles in the end. The spacer was prepared from polydimethylsiloxane (PDMS), with a thickness of approximately 1 mm. The sugar solution that was used to hydrate the lipid films consisted of filtered 300 mM sucrose in milliQ water. The buffer was degassed with a syringe and approximately 300 μL was added to the chamber. Parafilm was used to seal the top and bottom of the chamber to prevent leakage from either sides. The ends of the ITO slides were then put in an upright position and attached to electrodes with clips. These electrodes connected the chamber to a Black Star Jupiter 2000 0.2 - 2 MHz function generator. This function generator induced a sinusoidal alternating current into the chamber. First, a potential difference of 2V at a frequency of 10 Hz was applied for two hours. This allowed the lipid film to swell and to grow vesicles on the ITO surface. Consecutively, the frequency was reduced to 2 Hz, for one hour, to enable the vesicles to detach from the surface. The GUVs could then be obtained from the chamber by retrieving them with a gel loading pipette tip (Corning). Finally, the GUVs were stored

Collective microparticle adhesion on fluid lipid bilayer membranes driven by multivalent interactions leads to particle aggregation

Master Thesis