An Investigation of Clathrin-MediatedEndocytosis through Three-ColorSuper-Resolution Microscopy

Olivia WaringUniversity of Tokyo Research Internship Program

Ozawa Laboratory

Abstract

Since the discovery of GFP, fluorescent proteins have revolutionized the field ofmolecular imaging, allowing researchers to tag specific molecules with glowing reportersand thereby track their progress through living cells. The study of subcellular compo-nents has also benefited greatly from the advent of super-resolution microscopy, whichexploits the blinking and photobleaching of single molecules to circumvent the diffrac-tion limit of visible light. By combining fluorescent reporting with super-resolutionmicroscopy, we have at our disposal a powerful methodology for probing subcellular pro-cesses. The phenomenon of immediate interest to the Ozawa Lab is clathrin-mediatedendocytosis, through which the plasma membrane engulfs extracellular particles andpinches off to form a vesicle. A number of proteins are implicated in this process:most notably clathrin itself, which assembles on the cytosolic surface of the cell duringvesicle formation; but also transferrin receptor, a transmembrane protein that bindsselectively to iron-bearing transferrin; and dynamin, a GTPase thought to mediatevesicle scission by mechanical twisting. In order to more precisely characterize theinteractions between these three proteins, the Ozawa group sought to tag each targetmolecule with a fluorescent reporter and quantify co-localization via super-resolutionmicroscopy. During my six-week stay, I assisted in the preparation of three fluores-cent systems: clathrin-light-chain cloned to PAmCherry; transferrin receptor clonedto EYFP; and dynamin linked to AlexaFluor 647 via antibody conjugation. The twoplasmids were co-expressed in COS-7 cells, followed by immunostaining with the an-tibody construct. We first used confocal microscopy to validate the expression of thetarget proteins and their associated fluorophores. We then observed the samples ona total internal reflection microscope at a sampling rate of about 30 milliseconds perframe. Once data had been acquired, images were processed using ImageJ softwarewith the Octane plugin. PALM analysis was performed, after which clustering and co-localization were qualitatively verified. In order to subject our data to more rigorous,quantitative treatment, I proceeded to implement Ripley’s K function and a standardpair correlation algorithm in MATLAB. These cluster analysis techniques confirmedthat localization had indeed occurred. Throughout the coming months, I plan to im-prove upon this software, rendering the code more robust, versatile, and conducive tothe Ozawa labs specific requirements.

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1 Background

1.1 Fluorescence Microscopy

Fluorescent emission is essentially a three-step process: an electron is promoted to an excitedstate by an incident photon; the electron relaxes to a lower energy state via non-radiativedecay; and finally, the electron returns to the ground state by emitting a photon of higherwavelength than the incident photon (see Figure 1). Beginning in 1913 with the work ofOtto Heimstaedt and Heinrich Lehmann, the native fluorescence of certain organisms (suchas autofluorescing bacteria) has been harnessed as a novel visualization technique. In con-ventional microscopy, the specimens under study simply reflect incident light; in fluorescentmicroscopy, however, the fluorescent samples themselves serve as the light source.

Figure 1: A schematic of the fluorescence mechanism

1.1.1 Green Fluorescent Protein: The Revolution

The discovery of Green Fluorescent Protein in 1961 (for which Osamu Shimomura deservedlysnagged the 2008 Nobel Prize) ushered in a new era in the field of microscopy, allowingresearchers to use GFP and related fluorescent proteins as exogenous labels for biologicalimaging [1]. Martin Chalfie was the first to express GFP in E. coli, thus importing fluorescentfunctionality into a non fluorescent organism. A few years later, Tulle Hazelrigg (who alsohappens to be Chalfie’s wife) generated the first GFP fusion protein, which allowed her toexpress a fluorescently-tagged exu molecule in Drosophilia melanogaster. This constituted asignificant departure from previous labeling techniques [2], all of which required “exogenouslyadded substrates or cofactors.” As Chalfie wrote in his groundbreaking 1994 Science paper,“Because the detection of intracellular GFP requires only irradiation by near UV or blue light,it is not limited by the availability of substrates. Thus, it should provide an excellent meansfor monitoring gene expression and protein localization in living cells.” Chalfie’s predictionshave been borne out in laboratories worldwide ever since. The last decade and a half has seenan explosive proliferation of fluorescent technology, with new colors, labeling techniques, and

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applications being pioneered each year. There is even a species of transgenic glowing zebrafish being sold in pet stores throughout Asia [2].

Figure 2: The barrel-shaped GFP molecule that revolutionized molecular imaging

These developments have given rise to a brand new technique for analyzing subcellularphenomena: multicolor imaging. Provided their emission channels are spectrally distinct,we can (in theory) obtain simultaneous images of an arbitrary number of fluorophores. Thisprovides a powerful tool for analyzing the interactions between molecules in cells [3]. For ex-ample, in a groundbreaking 2005 experiment, Koyama-Honda et. al. successfully confirmedthe co-localization of E-cadherin (a transmembrane protein responsible for cell adhesion)and anti-E-cadherin antibody using two-color fluorescent microscopy [4].

1.1.2 Labeling Strategies

There are two principle methods for applying fluorescent labels to target molecules. Inthe case of fluorescent proteins, genetic recombination is the prevailing technology, whereasimmunostaining is the preferred approach for organic fluorescent dyes.

In genetic recombination, the nucleotide sequence encoding the target protein is clonedto the DNA encoding the fluorescent protein. The resulting recombinant plasmid is thentransfected into the host cells, and upon expression, a chimeric protein with the propertiesof both the target molecule and the fluorescent probe is generated. One drawback of thistechnique is low transfection efficiency, which is compounded in the case of co-transfection:in general, only a small fraction of cells can be expected to express both constructs.

With organic fluorescent dyes - which, as a rule, are brighter and more photostable thanfluorescent proteins [1] - genetic recombination is not an option, so immunolabelling is uti-lized. In this procedure, the molecule to be labelled is tagged with a primary antibody, whilethe fluorescent reporter is tagged with a secondary antibody. The primary and secondaryantibodies associate exclusively, giving rise to selective affinity between the target moleculeand its tag. In theory, all cells containing the target molecule are uniformly labeled, andin this respect, immunostaining is more robust than genetic recombination. However, onesignficant disadvantage of immunostaining is the comparatively large size of the fluorescentconstruct, which limits spatial resolution. Immunostaining also precludes the imaging of livecells, since antibodies are unable to cross the plasma membrane unless it is punctured.

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Figure 3: Labeling strategies: genetic recombination and immuolabeling

1.2 Super-resolution Imaging

1.2.1 The Diffraction Limit

In an ideal world, visualizing subcellular structures would simply be a matter of arbitrarilyincreasing the magnification. Unfortunately, however, there is a certain point beyond which“zooming in” fails to produce a resolvable image [3]. Conventional optical microscopy issubject to a fundamental limitation: the finite wavelength of visible light. When a wavestrikes an object, it diffracts around the incident point and, upon returning to the detector,is registered as an intensity distribution rather than a point. This intensity distribution(or point-spread function, in mathematical terms) can be characterized by its localizationprecision:

∆loc =0.61λ

NA(1)

In Equation 1, λ is the wavelength of incident light and NA is the numerical aperture of theobjective lens. Therefore, the spatial resolution of any image is bounded by the illuminationwavelength. For green light striking a standard oil immersion objective, there is a lateralresolution limit of about 200 nm [3], whereas sub cellular components are on the order ofangstroms.

Equation 1 would imply that decreasing the wavelength of the incident beam is a viablemeans of increasing the spatial resolution. In fact, this principle has been harnessed todevise novel imaging techniques, most notably electron diffraction. A beam of electrons hasa wavelength of approximately 1 to 10 pico meters - about 3 orders of magnitude smallerthan the wavelength of a visible light ray - and can therefore probe matter at much higherresolution. However, due to the invasivity of this methodology, electron diffraction cannotbe used to investigate living specimens [5]. Another approach is required.

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1.2.2 General Strategy

By appealing to the temporal domain, researchers have devised a means of circumventingthe diffraction limit without compromising the integrity of living tissues. This technologyharnesses the optical highlighting properties of certain fluorescent probes to generate a com-posite image from successive frames. The procedure can be summarized as follows:

1. Observe the fluorescence of a few particles at a time, provided they are separated by adistance larger than the diffraction limit.

2. Fit each diffracted spot to a Gaussian distribution to estimate the centroid location1.

3. Repeat this procedure for approximately 10,000 frames and superimpose all the pro-cessed frames to generate the final image [1].

Figure 4 provides a schematic of super-resolution image generation:

Figure 4: A schematic of super-resolution image reconstruction

The localization precision is no longer limited by wavelength, but rather by the numberof measurements of the centroid location, which is equivalent to the number of photons (N)emitted by each fluorophore [3] .

∆loc =σPSF√N

(2)

We have thus circumvented the wavelength-dependence of spatial resolution. Using thisiterative procedure of activation + visualization + bleaching [1], we are able to achieveresolutions up to one order of magnitude higher than before (which translates into a laterallocalization of about 20 nm for a standard optical setup). Thus, the sub-cellular regimeis accessible with visible light. Figure 5 demonstrates the amazing capabilities of super-resolution microscopy as compared to conventional imaging techniques.

1Of course, this step relies on the assumption that the point-spread function is perfectly Gaussian, whichis not generally true.

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Figure 5: Super-resolution microscopy applied to microtubules

1.2.3 Optical Highlighting

As described in the preceding section, super-resolution imaging technology relies on the abil-ity to image single molecules at a time. When two fluorophores are separated by a distanceshorter than the localization precision, their intensity distributions overlap, and centroiddetermination is compromised [3]2. Only when dealing with spatially isolated molecules canwe be confident that each PSF is being generated by a single light source, allowing us toperform Gaussian fitting to localize the centroid [1]. One prerequisite for suitably separatedsingle molecules is the use of imaging techniques such as TIRFM, which is described below.Another is the employment of fluorophores that exhibit optical highlighting: that is, theability to be photoactivated, photoconverted, and/or photobleached [1]. In essence, opticalhighlighting allows us to increase spatial resolution by invoking the temporal domain. Opti-cal highlighting takes many forms, all of which involve fluorophores that can switch betweena bright and a dark state. The switching mechanisms, however, are crucially different de-pending on the type of fluorescent probe, and the methods for generating super-resolutionimages vary accordingly. Two of the most prominent techniques are PALM - used withfluorescent proteins - and STORM - used with fluorescent dyes.

Photo-Activated Localization Microscopy (PALM) is predicated on fluorescentproteins that can undergo a chemical switch from an “OFF” state to an “ON” state upon

2Compare this to the familiar macroscopic phenomenon of watching the headlights of an approaching car:they are only resolvable into two separate light sources at distances below a certain threshold.

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light irradiation. One of the most well-established photoactivatable fluorescent proteinsis PAmCherry, developed by Subach et. al. in 2009. The group performed site-specificmutagenesis on conventional mCherry in the hopes of identifying mutants that might exhibitphotoactvatable character. Further rounds of random mutagensis improved the fluorescentproperties of this probe [6].

In the OFF state, PAmCherry absorbs at 405 nm; in the ON state, it absorbs at 564nm (see Figure 9). The absorbance shift involves the formation of a double bond (via alight-induced Kolbe-type radical pathway) between the beta-carbon atom in the Tyr-67 sidechain and the imidazol-5-ol ring of the chromophore. (This reaction requires the abstractionof a proton from the beta-carbon atom, which can be accomplished by a lysine residue inposition 70; site-selected mutagenesis confirmed the crucial role played by this neighboringlysine.) The double bond gives rise to pi-bond conjugation between the imidazol-5-ol ringand the phenyl ring in tyrosine, which is ultimately responsible for the fluorescence activityof the activated chromophore. Crucially, exciting the PAmCherry chromophore with 405nm light under anaerobic conditions does not lead to fluorescence., implying that oxidationplays a fundamental role in the photo-activation pathway. The mechanism is discussed atlength in [7].

Direct Stochastic Optical Reconstruction Microscopy (dSTORM) relies on thefluorescent intermittence of certain organic probes: that is to say, these fluorophores oscillaterandomly between dark and bright states under continuous excitation. In order to success-fully localize single molecules, we need to minimize the number of actively fluorescing probesat any given time. In theory, a sparse population of activated probes can be achieved bystabilizing the OFF states of the fluorophores; but in practice, how is this accomplished?

So-called “switching buffers” provide one solution. Recall that when fluorophores arestimulated, valence electrons are excited to a singlet state, from which they can either returnradiatively to the ground state or relax nonradiatively to a triplet state. This triplet statecan be quenched by the addition of a reducing agent (such as mercaptoethanol or DTT [8]),thereby trapping the fluorophore in a long-term OFF state. In the presence of oxygen, thereduced triplet state is reoxidized and fluorescent emission is once again enabled. AlexaFluor647, for example, has been shown to blink stochastically in the presence of a switching bufferalkalinized with KOH. Unfortunately, switching buffers have a finite lifetime: as soon as thereducing agent is consumed, the fluorophores remain continuously in their ON states [9].

1.2.4 TIRF

One well-established tool for single molecule spectroscopy is the Total Internal ReflectionFluorescence Microscope. This device illuminates an effectively unicellular slice of sample(100 to 150 nm) at a time, thereby reducing the number of target molecules within thefield of view. The operating principle is as follows: when a ray of light strikes an interfaceat an angle higher than the critical angle (which is determined by the refractive indices ofthe media on either side of the interface), the ray is reflected back into the source medium.At the same time, an evanescent wave is generated at the incident plane, which propagatesaway from the interface on the opposite side. The intensity of this evanescent wave decreasesexponentially with distance from the interface. Therefore, only a thin slice of the specimenis appreciably excited, limiting the region of study to a single plane of cells and increasing

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the signal-to-noise ratio [8]. Figure 6 elucidates this technique.

Figure 6: TIRF Microscopy setup

1.2.5 Spatial vs. temporal resolution

Super-resolution imaging via optical highlighting illustrates a fundamental trade-off betweenspatial and temporal resolution. The generation of a single image requires about 30 ms ofexposure; therefore, in order to acquire the 10,000 frames required for thorough PALM orSTORM processing, approximately 5 minutes of acquisition time is required. This precludesdynamic imaging of most cellular processes - for example, clathrin-mediated endocytosis(which will be discussed at length in the subsequent section) proceeds on the order of 30to 90 seconds. Conceivably, we could increase the temporal resolution by shortening theexposure time of each frame. However, recall that the localization precision is inverselyproportional to the square root of the number of recorded photons (see Equation 2). Themore time spent acquiring each image, the more photons are used to compute the centroid,and the higher the spatial resolution. Engineering brighter fluorescent probes can mitigatethis difficulty somewhat, but ultimately the trade-off is unavoidable.

1.3 Clathrin-Mediated Endocytosis: The Subject of Study

Endocytosis is the process by which the plasma membrane engulfs an extracellular particleand invaginates to form a cargo-containing vesicle. Endocytosis (in conjunction with itsinverse process, exocytosis) is crucial to the maintenance of homeostasis, and is one of theprinciple means by which a cell interacts with its environment. Endocytotic mechanismscan be broadly classed into two main types: facultative and constitutive. Facultative en-docytosis (also called phagocytosis in some contexts) exists primarily for the transport of

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large particles across the plasma membrane, and only occurs when certain membrane recep-tors are specifically triggered. Constitutive endocytosis (or pinocytosis), on the other hand,continuously shuttles small particles across the membrane without a concerted stimulus [10].

Clathrin-mediated endocytosis - a constitutive process - is the most common endocytoticmechanism, and is employed by all known eukaryotes [11]. We use this term to refer specif-ically to endocytosis occurring at the plasma membrane, though an analogous process canoccur in organelles within the cell [12]. The functions of clathrin-mediated endocytosis arecrucial and varied, and include “regulating the surface expression of proteins, sampling thecell’s environment for growth and guidance cues, bringing nutrients into cells, controllingthe activation of signaling pathways, retrieving proteins deposited after vesicle fusion, andturning over membrane components by sending these components for degradation in lyso-somes” [12]. Clathrin-mediated endocytosis is a modular pathway consisting of five discretestages:

1. Nucleation: preliminary membrane deformation

2. Cargo selection: association of membrane receptors with their intended cargo

3. Coat assembly: recruitment of clathrin to the deforming membrane

4. Scission: pinching off of the vesicle

5. Uncoating: dispersal of clathrin [12]

The entire process (depicted in Figure 7) occurs on a minute time-scale [13].

Figure 7: Clathrin-mediated endocytosis

A number of proteins are implicated in clathrin-mediated endocytosis, any of which mightbe suitable target molecules for a fluorescence-based co-localization experiment. The presentinvestigation, however, is limited to three molecules of immediate interest. Our selection ofthese particular targets is motivated by a combination of functional salience, labeling facility,and scientific precedent.

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1.3.1 Clathrin

As its name suggests, clathrin-mediated endocytosis depends first and foremost on the pro-tein clathrin, which induces membrane curvature. Each clathrin molecule is comprised ofthree so-called “heavy chains” (190 kDa, 450 A) and three corresponding “light chains”(23-26 kDa), which adopt a triskelian structure radiating outwards from a central hub [11].Following nucleation and cargo binding, clathrin molecules are recruited to the cytosolicsurface of the budding membrane, where they polymerize to form a stiff lattice of alternat-ing pentagons and hexagons. A geometrical consequence of this three-dimensional patternis that the membrane deforms into a dome, ultimately curving in on itself to form whatMcMahon and Boucrot poetically describe as a “[vesicle] in a basket.” The radius of mem-brane curvature - which can be anywhere from 20-80 nm - depends on the ratio of hexagonsto pentagons in the clathrin coat [12]3.

1.3.2 Transferrin Receptor

Transferrin receptor is a transmembrane glycoprotein which binds selectively to the iron-bearing transferrin molecule [13], and is thus responsible for delivering iron into the cell4.Morphologically speaking, its ectodomain is a homodimeric protein comprised of two 11 nmwing-shaped structures, each of which is composed of three domains: apical, central helical,and protease-like. Cargo binding occurs through the the latter two domains. Betweenrounds of endocytosis, transferrin receptors diffuse freely throughout the membrane; duringendocytosis, they have been shown to localize around budding pits.

1.3.3 Dynamin

Dynamin is a GTPase that readily oligimerizes to form long helical spirals. Its name hintsat its function [5]: dynamin is a mechanochemical enzyme [12] whose dynamic propertiesare crucial to its role in endocytic fission. Mettlen et. al. propose one possible mechanismfor dynamin-induced fission: exogenous dynamin in the cytoplasm binds to GTP and thenassembles around the narrowing neck of a clathrin-coated pit. The subsequent hydrolysis ofGTP into GDP results in dynamin constriction, which in turn induces vesicle scission [5].Other research suggests that constriction alone cannot precipitate the vesicle’s pinching offfrom the plasma membrane, but that longitudinal membrane tension is also required [15] toform a full-fledged vesicle.

1.3.4 Other important molecules

Though not directly involved in our study, a number of auxiliary proteins play a crucial rolein clathrin-mediated endocytosis. Transmembrane receptors such as TfR do not interactwith clathrin directly, but rather through specially tailored adaptor proteins (AP’s). The so-called AP-2 molecule binds to the cytosolic domain of TfR (recall that the ectodomain of TfR

3Some clathrin coated pits fail to bud into full-fledged vesicles; these abortive structures never associatewith cargo, and typically have lifetimes of about 20 seconds.

4In fact, overexpression of TfR has been linked to atherosclerosis, an arterial condition thought to resultfrom excess iron [14].

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Figure 8: a) A single clathrin triskelion highlighted inside a clathrin cage; b) The ectodomainof Transferrin Receptor; c) Dynamin polymer

associates with transferrin), thereby sequestering the appropriate cargo in the region primedfor endocytosis [5]. The AP-2 adaptor complex is also responsible for clathrin recruitmentto the cytosolic surface [13]. Following vesicle scission, adaptor proteins are recycled backinto the cytoplasm, where they await future deployment [12].

Recent research has suggested that the actin cytoskeleton might also participate inclathrin-mediated endocytosis [11]. Though the exact mechanism of this interaction is stillunclear, actin filaments are known to localize around the clathrin-coated pits during endo-cytosis and seem to play nontrivial roles in “invagination, constriction, and scission” [5].

2 Results

2.1 Experimental Design

Using the protocols outlined in Section 5, we generated two chimeric proteins (transferrin re-ceptor + EYFP and clathrin light chain + PAmCherry) and one immunoconjugate (dynamin+ AlexaFluor 647). The fluorophores were chosen to have easily distinguishable excitationand emission properties, as shown in Figure 9.

We co-expressed the two chimeric proteins in simian, fibroblast-like COS-7 cells. Afterfixation and permeabilization, we performed immunostaining to introduce the dynamin im-munoconjugate into the cells. Using confocal microscopy, we confirmed the expression ofthese three constructs and troubleshooted the photo-activation mechanism of PAmCherry;one set of confocal images is shown in Figure 10. We spent a significant amount of time op-timizing the intensity of the activation signal: if too intense, the EYFP and AlexaFluor 647signals would suffer bleaching, but if too diffuse, the PAmCherry would remain in its OFFstate. Ultimately, we exposed our samples to a 405 nm activation signal at 30% intensityfor 10 seconds.

We then proceeded to collect data on an Olympus Total Internal Reflection Miscroscope.

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Figure 9: Spectral details of the chosen fluorescent probes

Figure 10: Confocal images validated our expression protocol

Through extensive trial and error, we observed that the strongest signals were obtainedwhen AlexaFluor 647 was imaged first, followed by EYFP, followed by PAmCherry. Weachieved a great deal of qualitative evidence to support clustering of the individual targetmolecules. Figures 11 through 13 show the heterogeneous localization of our three labeledproteins. Co-localization between TfR and CLC was also observed, as shown in Figure 14.Dynamin, however, does not seem to interact proliferatively with the other target molecules.This is not altogether unexpected, since the rate of dynamin’s recruitment and dispersalduring clathrin-mediated endocytosis is faster than the temporal resolution of our imaging

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techniques.

Figure 11: Clathrin Light Chain clustering

Figure 12: Transferrin Receptor clustering

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Figure 13: Dynamin co-localization

Figure 14: Putative co-localization

2.2 Cluster Analysis

Achieving qualitative co-localization is undeniably encouraging; however, we cannot set muchstore by our results without subjecting them to more quantitative treatment [16]. Tan et. al.warn against purely qualitative analysis, since apparent clustering might be a mere “artifactof the human visual system” [17], and Figure 15 illustrates the ambiguity associated withperforming cluster analysis “by hand”. Lippitz et. al. elaborate on the importance ofperforming statistical analysis on PALM or dSTORM-processed data: “Both the randomness

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of single photon counting, and the irreproducibility of random blinking make statisticalevaluations indispensable to establish firm conclusions and fully exploit single-molecule data”[18]. In this section, we investigate a number of cluster analysis techniques which enable usto rigorously characterize homogeneous clustering and heterogeneous co-localization.

Figure 15: The difficulty of interpreting clustered data by sight alone [17]

There are a number of ways to define and identify a “cluster,” the most common andversatile of which are described below:

1. Well-separated: in this idealized scenario, the clusters are spatially distinct and straight-forward to identify with the naked eye.

2. Centroid-based: an event belongs to a certain cluster if it is more similar to the centroidof that cluster than the centroid of any other cluster.

3. Density-based: a cluster is a region of high event density surrounded by a region oflow event density.

4. Conceptual: cluster memberships are assigned based on abstract characteristics.

5. Objective function: different cluster assignments are experimented with until someobjective function is minimized.

Thus, though individual approaches may vary, all clustering algorithms capitalize on thesimilarities within groups (cohesion) and the differences between them (separation) [17].

We begin our quantitative analysis by representing our PALM-processed data5 as theresult of a spatial point process. According to this model, an “event” is defined as a singlebright pixel or group of tightly clustered bright pixels [19], which we assume emanates

5The data could just as easily have been processed using STORM or another super-resolution analysistechnique; the method by which we generated the final image is irrelevant here.

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from a single fluorescent probe. Our task is to determine whether there is any spatialdependence governing these events6. In most cluster analysis scenarios, data is comparedto a condition known as complete spatial randomness (CSR), which serves as our control.CSR data consists of events resulting from the execution of a homogenous Poisson pointprocess. Under conditions of CSR, there is no spatial dependence among the points [20];in the context of this experiment, we could identify CSR with the signals of fluorescentlylabeled proteins which do not interact.

2.2.1 K-Nearest Neighbor Approach

One of the most intuitive cluster analysis methods is K-Nearest-Neighbor (KNN) Algorithm.Though more robust techniques are available, the KNN approach merits discussion because ofits simplicity and historical importance. The naive implementation is as follows: all N pointsare assigned a unique class label, C1 through CN . An NxN matrix encoding the Euclideandistances between each pair of points is computed. Then, in an iterative “machine-learning”process, each point is considered in turn and assigned the most common class label of itsK nearest neighbors7. Although relatively easy to understand and remarkably effective incertain contexts, the KNN approach can be computationally intensive for large values of N,so it has been supplanted by more efficient algorithms in recent years.

2.2.2 Ripley’s K Function

Ripley’s K function is a density-based cluster analysis technique. In this approach, we definea “cluster” as a region of high density surrounded by a region of lower density, relative toCSR. Generally speaking, Ripley’s K function takes the form:

K(d) =E[number of events occurring within distance d of the given event]

λ(3)

where λ denotes the density of events and E represents the expectation operator [21]. Inpractice, evaluating Ripley’s K Function involves selecting a point, drawing successivelylarger concentric circles around that point, and evaluating the number of events encompassedwithin each circle. Thus, Equation 3 becomes:

K(d) =A

n2

n∑i=1

n∑j=1

δij (4)

where d is the radius of a circle centered around point i, A is the area of the region beingconsidered, n is the total number of points in area A, and δij = 1 if δij < r and 0 otherwise.For a homogeneous Poisson process (which results in a CSR-type distribution), the expected

6In order to represent our data as a series of discrete events, we needed to convert our grayscale image fileinto a binary matrix. We accomplished this by applying a threshold to each pixel. The choice of thresholdvalue is somewhat arbitrary; we followed the lead of Owen et. al. and chose a threshold value of 60% of thepeak pixel intensity [8].

7If there is a tie among the neighbors, the iteration is repeated with the nearest K-1 neighbors, and soon.

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number of events is λ ∗ π ∗ d2, and therefore K(d) = π ∗ d2. In the event of clustering, weexpect to see a higher K value than π ∗ d2 for small values of d and a lower K value thanπ ∗ d2 for large values of d. Higher K(d) values indicate aggregation, whereas lower K(d)values correspond to “spatial inhibition.”

Figure 16: Calculating Ripley’s K Function

After implementing a simple version of Ripley’s K Function in MATLAB, we applied theprogram to our PALM-processed data (as well as an artificially-generated CSR distribution)and achieved the results shown in Figure 17. Note that Ripley’s K Function can also berepresented as K(d) - d, where positive values correspond to regions of high density andnegative values correspond to regions of low density [8].

Figure 17: Our clustering data subjected to Ripley’s K Function analysis

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When coding Ripley’s K function, we ought to bear a few implementation details in mind.In order to account for edge effects, we define a border region around the perimeter of theimage. Events within this border region are not themselves subjected to cluster analysis,though they are factored into the analyses of neighboring points. Also, rather than dividingthe area of study into a grid of quadrates, we define a moving “window” of fixed size [20].This can be implemented by applying a kernel weighting function to the PALM or dSTORM-processed image, which “zeros out” the signals outside the region of immediate interest [20].Ripley’s K function can also be made to accommodate temporal dependence, rendering itsuitable for live-cell applications.

2.2.3 Pair Correlation Analysis

Perhaps the technique most commonly used to evaluate PALM or dSTORM data is PairCorrelation Analysis (PCA), which relies on the use of correlation functions. As its nameimplies, a correlation function describes the spatial or temporal correlation between twosets of data. For a standard correlation function, nonzero values represent some sort ofmutual dependence between the variables, whereas a value near zero indicates that thevariables are independent. Cross-correlation functions quantify the relationship betweentwo different signals (in our case, two different proteins); an autocorrelation function issimply the cross-correlation function of one signal with itself. Therefore, we can use anautocorrelation function to quantify the localization of a single target molecule and a cross-correlation function to quantify the co-localization of multiple target molecules.

Pair Correlation Analysis is an extremely powerful tool for cluster assignment. Unlike themethods previously described, PCA allows us to distinguish between genuine clusters (whichrepresent separate proteins interacting with one another) and spurious clusters (which arisefrom conflicting localizations of a single protein at different time points). The apparentmotion of a solitary protein between frames is a stochastic phenomenon, arising because ofuncertainty in centroid localization [22]. This effect - which causes both the human observerand cluster analysis algorithms to perceive multiple molecules where there is, in fact, onlyone - can severely distort our results if not taken into account.

The total pairwise correlation function is expressed as:

g(r)peaks = (g(r)centroid + g(r)protein) ∗ g(r)PSF (5)

= g(r)stoch + g(r)protein ∗ g(r)PSF (6)

where g(r)peaks represents the probability of finding another protein at a distance r from agiven protein; g(r)centroid represents the protein correlation function at r = 0; g(r)protein rep-resents the protein correlation function at r > 0; g(r)PSF represents localization uncertainty;and g(r)stoch accounts for “multiple appearances of the same molecule” [19]. In essence, thisequation relates observed patterns in the binarized data (g(r)peaks) to the protein interactionsthese patterns represent (g(r)protein). Under CSF conditions, we expect to see:

g(r)peaks = g(r)stock + 1 (7)

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For clustered data, we observe an equation of the form:

g(r)peaks = g(r)stoch + (Ae−r/ξ + 1) ∗ g(r)PSF ) (8)

Fortunately, “the cluster of peaks belonging to a particular protein has a well-defined spa-tial signature” [22]. This allows us to estimate g(r)stoch based on the average protein densityand the width of the Gaussian function being fitted. By subtracting away the stochastic con-tribution to g(r)peaks, solving for g(r)protein, and fitting the protein correlation function to thesecond term of Equation 8, we can extract the parameters A and ξ, which provide estimatesof cluster size and density. Thus, PCA allows for the removal of stochastic misinformationand the precise characterization of the clusters’ physical properties8. Figure 18 shows theresults of our own PCA implementation in MATLAB. The calculated parameters are onlyrough estimates of cluster radius and population; however, the analysis clearly confirms theexistence of large, stable clusters of all three target molecules.

Figure 18: Our data subjected to pair correlation analysis

2.2.4 Cluster Validation

No cluster analysis technique is ironclad. In order to ensure that we have not simply identifiedserendipitous patterns in signal noise, we must subject our results to cluster validation.According to Tan et. al., there are three types of cluster validation:

8Another benefit of PCA is its ability to account for noise-induced over-counting [23].

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1. Relative validation: compare the results of two or more clustering algorithms.

2. Internal validation: analyze the cluster analysis results using only the data at hand (i.e.evaluate the cohesion and separation of the putative clusters using the matrix-basedtechnique described in the following paragraph).

3. External validation: cross-check the cluster analysis results against exogenous infor-mation (i.e. a known number of clusters) [17].

We have already performed relative validation by implementing both Ripley’s K Functionand a simple PCA algorithm and comparing their respective outcomes. One potentiallyinformative internal validation scheme would be the following: first, we would generate anN x N proximity matrix, which encodes the Euclidean distance between each pair of points.Following cluster analysis, we would assemble the N x N incidence matrix, where an entry of1 means points i and j have been classified into the same cluster and an entry of 0 means theyhave been classified into different clusters. We would then calculate the correlation betweenthese two matrices: if it is high, the cluster analysis would be deemed successful [17]. Theimplementation of this validation technique is currently in progress.

3 Discussion and Future Directions

Super-resolution imaging through photoactivated localization microscopy provides a power-ful means for circumventing the diffraction limit. In this study, chimeric protein expressionand antibody conjugation were used to fluorescently label clathrin light chain, transferrinreceptor, and dynamin, three proteins thought to collectively mediate endocytosis. The fluo-rescent probes were imaged with confocal and TIRF microscopes using 3 distinct laser lines.Cursory investigation of the data seemed to corroborate the clustering and co-localizationhypotheses, and more rigorous analysis using Ripley’s K Function and PCA confirmed ourhunch that all three target molecules exhibit heterogeneous clustering during endocytosis.

3.1 Correcting for Chromatic Aberration

One persistent difficulty in optical microscopy is a phenomenon known as chromatic aber-ration. Refractive indices are wavelength dependent; therefore, when polychromatic lightpasses through a lens, the individual wavelengths converge on slightly different focal points,giving rise to a blurry image. In multicolored fluorescent imaging, each excited fluorophoreemits a different wavelength of light. Chromatic aberration renders the resulting imagesnon-superimposable, thus precluding co-localization analysis. We can mitigate this effect byincorporating “fluorescent beads” into our experimental set-up. These minute polystyrenespheres - available from a number of laboratory suppliers - are conjugated with fluorescentdyes that emit at a known wavelength, and can be used to assist in spatial calibration.

3.2 Improved Cluster Analysis

The cluster analysis algorithms used to analyze our results were rather crudely implemented.For example, the parameters extracted from PCA were disconcertingly dependent upon ini-

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Figure 19: Fluorescent beads can be used to correct for chromatic aberration

tial conditions, and computation times were prohibitively long. Refinement of our customizedMATLAB code is currently underway. Future efforts may also involve implementation of DB-SCAN (Density-Based Spatial Clustering of Applications with Noise), one of the most sophis-ticated cluster analysis algorithms currently available. DBSCAN is a density-based approachwhich can accommodate noise and arbitrarily-shaped clusters [17]. We also plan to performcross-correlation analysis in order to rigorously characterize TfR-CLC co-localization.

3.3 Computational Docking with HADDOCK

As Vries et. al. eloquently write, “to fully understand how the various units work togetherto fulfill their tasks, structural knowledge at an atomic level is required” [24]. in silicodocking simulations are a powerful complement to experimental techniques, offering a high-resolution glimpse into protein-protein interactions. Armed with atomic insights into thebinding conformations of our target molecules, we can modify individual residues to enhanceor abrogate native interactions.

Computational docking software iteratively adjusts protein positions to find the bindingconformations that minimize the system’s total energy. There are many docking packagesavailable, but HADDOCK (High Ambiguity Driven protein-protein DOCKing) bimoleculardocking software is among the most powerful, thanks to its data-driven approach: ratherthan assessing binding conformations in an ab initio fashion, it employs existing experimentaldata to preemptively narrow configurational space. For example, the user can input a listof putative “active” and “passive” residues - identified through random mutagenesis - whichgives the algorithm a substantial head-start [24]9. Once primed with experimental data,HADDOCK employs a three-part algorithm to probe configurational space and estimate thebest docking orientation:

1. Rigid body minimization, in which the individual molecules are treated as immobilestructures

9If such data is unavailable, the user can use an interface prediction algorithm such as CPORT (ConsensusPrediction Of interface Residues in Transient complexes) to identify salient residues [25].

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2. Semi-flexible refinement, in which the side chains are allowed to fluctuate

3. Fine-tuning in explicit solvent [24]

Future endeavors may involve performing docking simulations on all-atom models of TfR,CLC, and dynamin, using PDB crystal structures and CPORT Prediction Interface resultsas inputs.

4 Acknowledgements

I am sincerely grateful to Professor Takeaki Ozawa, for being such an accessible and inspiringteacher; to Yusuke Nasu, for his tireless patience and unflagging mentorship; to the entireOzawa lab, for welcoming me so warmly into their midst; to Sachiko Soeda and the othercoordinators of the UTRIP program for ensuring such a smooth and rewarding study-abroadexperience; and to Friends of Todai, Inc. for funding my stay in Japan.

5 Materials and Methods

5.1 Sample Preparation

5.1.1 Subculture

A subculture is performed on stock cells approximately every three days in order to eliminate metabolicwastes, refresh the nutrient supply, and ensure that the population does not grow too dense. For COS-7cells, the optimum confluency for transfection is approximately 90%.

1. Remove old medium by aspiration.2. Wash dead cells away with phosphate-buffered saline (PBS).3. Add Trypsin-EDTA to unstick live cells from dish10.4. Incubate sample at 37 degrees C for 5 minutes.5. Centrifuge sample until a pellet forms (about 2 minutes), and remove supernatant by aspiration.6. Resuspend pellet in 1 mL pre-warmed DMEM glucose medium.7. Add a few hundred microliters of cell solution and 10 mL fresh medium to a clean dish and mix gently.

5.1.2 Co-Transfection

The transfection protocol is designed to introduce custom-made genetic constructs into host cells. Thereadily-available lipofectamine kit promotes engulfment of plasmid DNA into the cell.

1. Combine 200 micro liters Opti-MEM reduced serum medium and 1 µg of each plasmid to be co-transfected in an Eppendorf tube (the plasmid concentrations can be adjusted to maximize expression).

2. Add 2 µL Lipofectamine 1025 reagent 1 (orange cap), microcentrifuge, and incubate at room temper-ature for 5 minutes.

3. Add 6 µL Lipofectamine 1025 reagent 2 (green cap), microcentrifuge, and incubate at room temper-ature for 20 minutes.

4. Add resulting solution to sample cells and incubate overnight.

10COS-7 cells are belong to a class known as “adherent cells.”

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5.1.3 Fixation and Permeabilization

The cell fixation procedure preserves biological tissues so as to prolong observation time. When immunos-taining is involved, the plasma membranes must also be permeabalized to permit entry of the antibodiesinto the cell.

1. Prepare a sample dish for observation.2. Wash twice with 2 mL PBS.3. Add 1 mL of 4% paraformaldehyde (PFA) solution and incubate sample at 37 degrees for 10 minutes.4. Wash sample three times with PBS.5. Add permeablization buffer (1.4 mL PBS + 2.8 µL Triton X-100) and incubate sample at room

temperature for 5 minutes.

5.1.4 Immunostaining

In this procedure, we add the primary antibody (tagged with the target molecule) and the secondary antibody(tagged with the fluorescent reporter) to the host cells. The purpose of the blocking buffer is to eliminatenon-specific binding of the antibodies, which could lead to spurious signal.

1. Add 1mL of blocking buffer (0.2% gel from cold water fish skin + PBS) and 20 µL primary antibody.2. Incubate sample on spinner (40 rpm) at room temperature for 1 hour.3. Remove medium and save for later (the primary antibody can be reused up to 5 times).4. Wash sample three times with 1 mL blocking buffer.5. Add 0.75 µL secondary antibody.6. Incubate sample on spinner (40 rpm) at room temperature for 1 hour.7. Remove and discard medium.8. Wash sample three times with 1 mL blocking buffer.9. Add 1 mL blocking buffer and deposit on labeled slide.

5.2 Image Acquisition

5.2.1 Confocal Microscopy

We used EYFP emission to identify viable imaging candidates: i.e. cells that exhibit strong fluorescence andclear nuclear structure. We defined a photoactivation region and irradiated this area with 405 nm light at30% intensity for 10 seconds to switch PAmCherry into its ON state. We then acquired PAmCherry, EYFP,AlexaFluor 647, and bright field images.

5.2.2 TIRF Microscopy

Images were acquired on an Olympus Total Internal Reflection Microscope. EYFP signal (488 nm excitation)was measured with a 525/45 nm filter. PAmCherry signal (561 nm excitation following 405 nm activation)was measured with a 609/59 filter. EYFP and PAmCherry images were captured at an exposure rate of 30ms per frame; AlexaFluor 647, however, emits at a higher intensity, so an exposure rate of 20 ms per framewas sufficient.

5.3 Image Analysis

Freely available ImageJ software was used to perform PALM and dSTORM analysis on TIRFM images. The

raw data was processed with a Gaussian blur low-pass filter (σ = 0.75). The Octane plugin was used to

analyze the image stack (size = 2, σ = 0.94, threshold = 2000). For the Ozawa laboratory’s optical system,

1 pixel corresponds to approximately 80 nm.

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References

[1] G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolu-tion imaging using single-molecule localization,” Annual Review of Physical Chemistry,vol. 61, pp. 345–367, 2010.

[2] M. Zimmer, Glowing Genes: A Revolution in Biotechnology. Prometheus Books, 2005.

[3] B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” An-nual Review of Biochemistry, vol. 78, pp. 993–1016, 2009.

[4] I. Koyama-Honda, K. Ritchie, T. Fujiwara, R. Iino, H. Murakoshi, R. S. Kasai, andA. Kusumi, “Fluorescence imaging for monitoring the colocalization of two singlemolecules in living cells,” Biophysical Journal, vol. 88, pp. 2126–2136, March 2005.

[5] M. Kaksonen, C. P. Toret, and D. G. Drubin, “Harnassing actin dynamics for clathrin-mediated endocytosis,” Nature Reviews: Molecular Cell Biology, vol. 7, June 2006.

[6] F. V. Subach, G. H. Patterson, S. Manley, J. M. Gillette, J. Lippincott-Schwartz, andV. V. Verkhusha, “Photoactivatable mcherry for high-resolution two-color fluorescencemicroscopy,” Nature Methods, vol. 6, pp. 153–158, February 2009.

[7] F. V. Subach, V. N. Malashkevich, W. D. Zencheck, H. Xiao, G. S. Filonov, S. C.Almo, and V. V. Verkhusha, “Photoactivation mechanism of pamcherry based on crystalstructures of the protein in the dark and fluorescent states,” PNAS, vol. 106, pp. 21097–21102, December 2009.

[8] D. M. Owen, C. Rentero, J. Rossy, A. Magenau, D. Williamson, M. Rodriguez, andK. Gaus, “Palm imaging and cluster analysis of protein heterogeneity at the cell surface,”Journal of Biophotonics, vol. 3, no. 7, pp. 446–454, 2010.

[9] M. Heilemann, S. van de Linde, A. Mukherjee, and M. Sauer, “Super-resolution imagingwith small organic fluorophores,” Angewandte Chemie, vol. 48, pp. 6903–6908, August2009.

[10] B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biologyof the Cell. Garland Science, 5th ed., 2008.

[11] T. Kirchhausen, “Imaging endocytic clathrin structures in living cells,” Trends in CellBiology, vol. 19, no. 11, 2009.

[12] H. T. McMahon and E. Boucrot, “Molecular mechanism and physiological functionsof clathrin-mediated endocytosis,” Nature Reviews: Molecular Cell Biology, vol. 12,pp. 517–533, August 2011.

[13] D. K. Cureton, C. E. Harbison, E. Cocucci, C. R. Parrish, and T. Kirchhausen, “Limitedtransferrin receptor clustering allows rapid diffusion of canine parvovirus into clathrinendocytic structures,” Journal of Virology, vol. 86, pp. 5330–5340, May 2012.

24

[14] W. Li, L.-H. Xu, C. Forssell, J. L. Sullivan, and X.-M. Yuan, “Overexpression of trans-ferrin receptor and feritin related to clinical symptoms and destabilization of humancarotid plaques,” Experimental Biology and Medicine, vol. 233, pp. 818–826, July 2008.

[15] A. Roux, K. Uyhazi, A. Frost, and P. D. Camilli, “Gtp-dependent twisting of dynaminimplicates constriction and tension in membrane fission,” Nature, vol. 441, May 2006.

[16] J. C. Waters and J. R. Swedlow, Evaluating Techniques in Biochemical Research, ch. In-terpreting Fluorescence Microscopy Images and Measurements. Cell Press, 2007.

[17] P.-N. Tan, M. Steinbach, and V. Kumar, Introduction to Data Mining.

[18] M. Lippitz, F. Kulzer, and M. Orrit, “Statistical evaluation of single nano-object fluo-rescence,” Chemical Physical Chemistry, vol. 6, pp. 770–789, 2005.

[19] P. Sengupta, T. Jovanovic-Talisman, D. Skoko, M. Renz, S. L. Veatch, and J. Lippincott-Schwartz, “Probing protein heterogeneity in the plasma membrane using palm and paircorrelation analysis,” Nature Methods, vol. Advance Online Publication, 2011.

[20] A. C. Gatrell, T. C. Bailey, P. J. Diggle, and B. S. Rowlingson, “Spatial point patternanalysis and its application in geographical epidemiology,” Transactions of the Instituteof British Geographers, vol. 21, no. 256-274, 1996.

[21] P. M. Dixon, Encyclopedia of Environmentrics, vol. 3, ch. Ripley’s K Function, pp. 1796–1803. John Wiley and Sons, Ltd, 2002.

[22] P. Sengupta and J. Lippincott-Schwartz, “Quantitative analysis of photoactivated local-ization microscopy (palm) datasets using pair-correlation analysis,” Bioessays, vol. 34,pp. 396–405, 2012.

[23] S. L. Veatch, B. B. Machta, S. A. Shelby, E. N. Chiang, and D. A. Holowka, “Correlationfunctions quantify super-resolution images and estimate apparent clustering due to over-counting,” Public Library of Science ONE, vol. 7, February 2012.

[24] S. J. de Vries, M. van Dijk, and A. M. J. J. Bonvin, “The haddock web server fordata-driven biomolecular docking,” Nature Protocols, vol. 5, no. 5, pp. 883–896, 2010.

[25] S. J. de Vries and A. M. J. J. Bonvin, “Cport: A consensus interface predictor andits performance in prediction-driven docking with haddock,” Public Library of ScienceONE, vol. 6, no. 3, 2011.

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