STAGE 2007-2008 Isaac Theurkauff M1 Option Physique

Formation Sciences de la Mati`ere ´ Ecole Normale Sup´erieure de Lyon Universit´e Claude Bernard Lyon 1

Single-protein AFM-based force spectroscopy

The recently developed single molecule force spectroscopy enables the detailed study of the mechanisms of protein unfolding and refolding under a stretching force. It has revealed many signatures of complexity of the underlying energy landscape that were previously overlooked in bulk experiments. For example, the broad distribution of unfolding times of the protein ubiquitin has been suggestive of glassy protein dynamics. During this twelve-week internship, I set out to test whether this complexity is related to structural features. Using a mutant protein, one can restrict the portion of the molecule exposed to force, thus diminishing its structural complexity. In this study, we found that indeed, reducing the structure to a single β-sheet gives rise to single exponential kinetics, characteristic of a two-state process. This has important consequences on how the architecture of the protein affects its mechanical properties. Keywords : AFM, cantilever calibration, protein unfolding, single-molecule force spectroscopy Les performance des microscopes ` a force atomique permettent d’´etudier exp´erimentalement la r´eponse m´ecanique de l’ubiquitine et d’un mutant de I-27. Sont mesur´es, la force qu’il faut exercer pour allonger la prot´eine ` a vitesse constante et le temps au bout duquel une prot´eine soumise `a une force constante se d´eplie. Apr`es avoir calibr´e et caract´eris´e l’instrument, les premi`eres mesures permettent une exploration du paysage ´energ´etique des prot´eines. Des travaux r´ecents r´ev`elent une cin´etique complexe dans la distribution des temps de d´epliement pour l’ubiquitine et I-27 , l’´etude d’un mutant a structure simplifi´ee par un pont disulfure de I-27 permet de montrer que la complexit´e de la structure affecte celle du paysage ´energ´etique, le mutant ayant un paysage ´energ´etique a deux ´etats, tandis que I-27 a un paysage ´energ´etique tr`es rugueux. Mots-clefs : AFM, calibration de pointe, d´epliement de prot´eines, spectroscopie de force sur molecule unique.

NYU-Center for Soft Matter Research

Supervised by Jasna Brujic [email protected] May 19 – August 8

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NYU-CSMR NYU’s Center For Soft Matter Research is dedicated to research at the interface between chemistry, biology, and physics. Researchers study very different topics in the field of soft condensed matter, from photonics to the self-assembly of colloidal particles. Our team, formed in the fall of 2007, has two main research subjects: the random packing of emulsions explored by confocal microscopy, and force spectroscopy of proteins using a custom-made atomic force microscope (AFM). During this 12-week internship at the CSMR, I used an AFM to study the mechanical response of a single protein. More precisely, the study involved the measurement of the distribution of unfolding times of a mutant of I-27, a protein found in cardiac muscles, which would then be compared to the wildtype. We show that the mutant has a simpler unfolding time distribution, owing to its reduced structural complexity.

Introduction Proteins are a most interesting family of molecules, not simply for their exceptional abilities in chemical engineering, but also for being accountable formost biological functions. They are polymers of amino-acids, whose structure is determined by molecular interactions. How the sequence of amino acids determines the proteins’ 3-D structure and how this structure impacts their chemical and mechanical properties is a question of great importance inasmuch as many neuro-degenerative diseases were recently linked to variations in the protein 3-D structure. Our research project aims at making the link between the structure of the protein and its mechanical properties, through the monitoring of its unfolding. Pulling on proteins with a constant 130pN force results in staircases whose length is a fingerprint of the protein, and the unfolding time of each stable domain, known as the dwell time. The statistics of these dwell-times is a signature of the protein’s energy landscape. The simplest two-state model gives an exponential distribution for the cumulative probability of unfolding. If this distribution strays from the exponential, it can be seen as a signature of the roughness and complexity of an energy landscape where multiple barriers determine the unfolding process as shown in [1] for ubiquitin. I-27 is structurally simpler than ubiquitin, yet, the same deviations have been observed for I-27 in [2], but not yet thoroughly analyzed. To investigate the impact of structure on unfolding kinetics, we have engineered a mutant form of I-27 where a disulfide bond introduced by two substituted cysteines in the sequence restricts the part of the molecule exposed to force. Does this simplification in the structure also lead to a simplification in the unfolding kinetics? This internship aims at gathering enough unfolding statistics to answer this question. I also studied force extension curves to validate our calibration procedure, and verify both the quality of the protein and the proper behavior of the instrument. After a brief overview of the literature of protein unfolding, the experimental setup will be scrutinized, and the main results obtained analyzed. A short extension will present other results and new research ideas.

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Contents NYU-CSMR

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Introduction

2 2

1 A brief overview of protein unfolding 1.1 Protein structure . . . . . . . . . . . . . . . . 1.2 Protein characterization techniques . . . . . . 1.3 Single-molecule manipulation using an AFM . 1.3.1 Force Extension Experiments . . . . . 1.3.2 Force-clamp experiments . . . . . . . .

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2 Experimental setup and instrumentation 2.1 AFM setup . . . . . . . . . . . . . . . . . 2.2 Protein adhesion . . . . . . . . . . . . . . 2.3 Acquisition system and calibration . . . . 2.4 Piezo controller and PID . . . . . . . . . .

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13 13 13 13 14 15 15

4 Further work 4.1 I-27 unfolding statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Bio-polymer Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18 18 18

Conclusion Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19 19 20

3 Results 3.1 Instrument Characterization . . . 3.1.1 Noise Level . . . . . . . . 3.1.2 Drift . . . . . . . . . . . . 3.1.3 Other . . . . . . . . . . . 3.2 Force extension measurements on 3.3 Force clamp data on I-27 mutant

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1 A brief overview of protein unfolding This first chapter is dedicated to the basics of protein unfolding. Once the role of entropic elasticity and hydrogen-bond linking are over viewed, the response of the protein under mechanical constraint is studied.

1.1

Protein structure

A protein is a linear polymer of amino-acids linked by peptide bonds. Unlike many polymeric structure, proteins have a polarity, i.e. each amino-acid has a ”beginning” that is different from its ”end”, thus the structure also has a beginning and a end called either C-terminal if the organic function present at this extremity is a carboxyl, and N-terminal if it is an amino. Unlike a usual polymer whose monomers can be considered independent, the structure of polymers is ruled by the interactions between monomers, and especially weak hydrogen bonds of approximately 0.5kB T at room temperature. The sequence of amino acids is called the primary structure, and determines the secondary structure, that is the repeating structure formed by local arrangement of amino acids, and stabilized by hydrogen bonds. This structure is characterized by the map of amino-acids engaged in a α-helix or a β-sheet. These structures locally change the behavior of the polymer, introducing high correlations between close neighbors. The relative spatial arrangement of these structures is called the tertiary structure, stabilized by nonspecific Van der Waals forces[3] . The secondary structure affects the polymer response to force since α-helices and β-sheets are relatively stable; even if the tertiary structure is unfolded, β-sheets can remain in place at high forces although α-helices may be unfolded. Our goal is to better know how the structure impact mechanical response. There is a true interplay between the secondary and tertiary structure. The first does not determine the other, since there exist many cases where a protein can change its tertiary structure, and thus its function, without changing the secondary structure. And the stability of β-sheets can be increased by interactions with other anti-parallel β-sheets. All the highly mechanically resistant proteins we’re studying, whose breaking force are over 100pN, have anti-parallel β-sheets, and these seem to be necessary for high mechanical stability. Ubiquitin, 1.1 a degradation regulatory protein, is 76 amino-acids long, and has two antiparallel βsheets, and an α-helix. Its mechanical stability comes from the β-sheets. To study the influence of the α-helix on the complexity of protein mechanical response, we have to study a simpler protein. The immunoglobulin 27 domain of the titin protein1 , 98 amino-acids long, only has antiparallel β-sheets. Our I-27 mutant is even simpler, with only one active antiparallel β-sheets, the others being unable to unfold because of a disulfide bond that holds the structure together. To increase the probability of picking a protein, and to also have nicer curves, we use polymers of mechanically stable proteins. Between each protein monomer are short sections of two cysteine each, whose sulfur atom easily adsorbs on gold surfaces. They also allow size fingerprinting, so that we can check that all the unraveling structures in our experiments have the same size, which is a way to check that the individual proteins are behaving properly. Previous work[2] studying monomers has shown that in polyproteins, the individual stable domains are independent from one another. We can thus make experiments on polyproteins and get meaningful results on the monomers. 1 This protein plays a key role in muscular contractions, during which the I-27 domains undergo several cycles of folding and unfolding

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Figure 1.1: Ubiquitin (left) and I-27 mutant[4]. Both proteins have anti-parallel β-sheets that give rise to a high mechanical stability. The I-27 mutant has a cysteine-induced disulfur bond (yellow spheres) such that only the red part unfolds, while the green part is being held by the disulfide bond.

1.2

Protein characterization techniques

Structure determination Determining the sequence of amino acids (primary structure) is the first step towards characterizing a protein. The next step is to figure out the secondary and tertiary structure[5][4]. X-ray diffraction analyses the diffraction pattern to get the crystal structure and the electron density of the protein, then calculates its structure. It is the most widely used technique but requires proteins that form well-defined crystals, that are radiation resistant to some extent, and whose tertiary structure does not change when crystallized. Electron microscopy is often used when x-ray diffraction cannot, for proteins whose structure would change if crystallized, for example membrane proteins, or for radiation sensitive samples. It yields images of a much lower resolution, which limits its use to rather simple proteins. MNR measures the interaction between a strong magnetic field and spin 1/2 nuclei and its modifications by the electron cloud. The key advantage of this method is its using proteins in aqueous solution and at ambient temperature, thus having the protein in their native state. Large proteins are harder to image, since overlapping peaks make peak attribution very difficult. Our proteins being around 80 amino-acids long, their structures were determined by MNR.

Investigating protein dynamics Once the structure is determined, protein dynamic behavior can be investigated. multiple protein experiments either average the behavior of many independent proteins, or measure their collective nonindependent response. MNR is also used to see fluctuations of a protein. Only the parts of the protein that are not involved in a secondary or tertiary structure move, inducing peak widening and coupling modification. The fluctuation of the tertiary structure is dampened by the hydrogen bonds that hold it together, and the secondary structure is almost unaffected, α-helices and β-sheets holding together with respect to thermal fluctuation. Bulk experiments probe the collective behavior of proteins, by measuring the mechanical response of biological tissues or protein crystals. The quaternary structure, that is the relative arrangement of several proteins together has to be taken into account, and its properties understood before the individual behavior is characterized.

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Single protein experiments free themselves from collaborative effects between proteins at the cost of experimental difficulties created by a change in the scale of the experiment by several order of magnitude. Single molecule fluorescence . Using light amplification systems and specially designed proteins, one can observe the unfolding of proteins when a denaturant is introduced in the system, through microfluidic mixing. Donor and acceptor dyes are grafted onto each end of the protein, and the probability of transition gives the end-to-end distance. This method is extremely useful to observe the chemical influence of denaturant on a protein[6]. Optical tweezers are used to study the mechanical response of a bio-polymer such as DNA[7], but has also been used to study protein mechanical response[8][9]. Typically, one end of the molecule is bond to a cover slip as in AFM experiments, and the other to a bead that is trapped in an optical trap. The cover slip can be moved with a piezo, while the force exerted on the bead can be tuned by modifying the trap’s intensity. This technique is extremely accurate, and has a wide force range; from 0.1 to 50pN. This is perfect for most proteins, whose breaking force is generally much lower than 50pN, and for DNA, which almost behaves as an entropic spring. However, if one wants to probe the properties of mechanically stable proteins, whose breaking force are of order 100pN, one has to use an AFM.

1.3

Single-molecule manipulation using an AFM

When it is not used for imaging, the Atomic Force Microscope can be used in single molecule experiments. One end of the protein is bound to the tip and the other to a cover slip whose position is controlled by a piezo. The experimental setup, especially the way force and protein length are controlled, being described in chapter 2, we’ll simply describe here what we are trying to measure and analyze.

1.3.1

Force Extension Experiments

In force-extension experiments, the operator stretches the protein by attaching one end on the tip and one end on a gold cover slip, then pulls away the cover slip at constant speed with a piezoelectric actuator.

Figure 1.2: Several experiments in force-extension mode on ubiquitin, performed during my training on the instrument, at 400nm·s−1 . The red curve is the force measured during the approach to the surface, while the blue curve is recorded while the tip has picked a protein and moves away from the surface. The sawtooth pattern is the unfolding of Ubiquitin mechanically stable domains. These are 24nm long, and the characteristic breaking force is approximately 200pN.

The sawtooth pattern observed is due to the sequential unraveling of the polyprotein, that is the unfolding of its mechanically stable parts. The peak force before unraveling characterizes the resistance of its mechanically stable domains, while the distance between two unravellings reveals the length of these

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domains. To obtain the number of amino acids in the stable parts, one has to link the measured polymer length with its contour length. The worm-like chain model seems to be the best simple model for protein unfolding [10][11][12][13] The force-extension relation is given by :   z −2 z F 1 1 1 1− = − − , kB T lp 4 L L 4 where z is the protein size, L its contour length, F the exerted force, and lp the persistence length, which represents the rigidity of the protein2 . This formula is an approximation of the model, valid up to several hundreds of piconewtons, and that never strays more than 10% from the actual solution. By fitting the parts of force-extension curves that exhibit polymer elasticity, we can have a good fingerprint of the stable domains size. This model is meant for non-interacting polymers, but since proteins, having strong neighbor interactions, do not really fit into that category, we have to be cautious while using it.

1.3.2

Force-clamp experiments

In this experiment, the I-27 mutant is held at constant force, and we wait until its mechanically stable parts unravel. The parts that break are always the same size[2]: 10.5±.4nm. This means that the protein has a single mechanically stable region comprising ≈30 amino-acids. We then record the unraveling times.

Figure 1.3: A good force clamp experiment, performed during the data gathering of results presented in section 3.3. 8 out of 9 modules are unfolded. The red lines gives the protein length and the black, the force exerted on the protein. The unfolding times are measured from the moment the force becomes constant, and the unfolding causes a quick jump in the force that is taken as the unfolding time.

The detachment of the protein from the tip hides long unfolding times. To correct for this, we have to measure the unfolding times statistics, in long experiments3 and use the measured detachment time statistics to debias the unfolding time distribution. 2 l can be seen as the length below p 3 experiments have to be long when

which the protein is almost linear. compared to the characteristic detachment time.

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The parameter that interests biologists being the overall unfolding rate, it is a good first approximation to fit the cumulative probability of unfolding by single exponentials. This assumes independence of each stable domain, and a two-state energy landscape for a single monomer4 . Measuring unfolding rate at several forces can yield other parameters, such as the distance to the transition state, and the height of the energy barrier. Mechanical failure (unfolding) of stable system has been studied during the past century. From work done by Arrhenius, Eyring , and Kramer, the breaking dwell-time depends exponentially on the applied stress. Bell has been the first to apply these results to the breaking of bonds, such as those who occur between proteins[14], he predicted a rate of unfolding depending exponentially on the stretching force : α = α0 exp(

F ∆x ), kB T

where F is the force, α0 the unfolding rate without force5 , and ∆x the distance to the transition state. Further work confirmed this exponential dependence, and [15] confirmed that this approach could also be used to model the behavior of intra-protein links. This simple two-state model gave interesting insight in the protein structure, allowing measurements of the distance to the transition state, thus allowing to map the energy landscape. Recent experiments [1][2] have shown a clear deviation from the single exponential behavior. The stable domains being independent, as shown in [2], The deviation from the single exponential must come from the stable domains themselves. The cause of this deviation has yet to be determined, but hypotheses include cooperative effects between the hydrogen bonds in the secondary structure, a rough energy landscape created by the high dimensionality of the protein’s phase space, or glassy dynamics[1] (see fig. 1.4).

Figure 1.4: Cumulative probability of unfolding for ubiquitin at 110pN, from [1], the “theory” line represents the glassy dynamics model developed in the article. The exponential fit clearly shows that ubiquitin does not have a two-state energy landscape.

These experiments were conducted on complex proteins, where interaction between multiple β-sheets were possible. To discover the relation between structure complexity and energy landscape, we study the simpler I-27 mutant, whose unfolding domain only has a single β-sheet.

4 The same model also occurs in α-emission in nuclear physics, and the results are very similar. the unfolding rate becoming the disintegration rate. 5 This rate is linked to the frequency at which the protein vibrates around its equilibrium state. and to the height of the energy barrier. The height is experimentally measured, and α0 can be estimated by molecular dynamics simulations, and is approximately 10−2 s for ubiquitin.

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2 Experimental setup and instrumentation The experimental setup has two different goals: first, to be able to pick a single protein, and second, once it is attached to the AFM tip on one hand and the piezoelectric actuator on the other hand, to be able to measure the force and the distance between the tip and the piezo. As in most experiments, the measured quantities and the control parameters are electric voltages, which allows the use of electronic controls, but also implies the need to convert the measured values in meaningful physical values such as distance between the tip and the force exerted on the picked protein.

2.1

AFM setup

Figure 2.1: Scematic of the experiment, showing the concept, and the setups for force clamps and force extensions (length clamps)

We use a Veeco instruments AFM head, stripped from imaging controls, to control cantilever position, Laser position and alignment with a fast photodiode (approx 100kHz), and a physik instrumente 3-D actuator and position controller with a range of 5µm[15] and a resonant frequency of ≈10kHz. The protein is bound to the surface of the cover slip, and to the cantilever, and then pulled on. The measured cantilever deviation (bending), and the piezo position gives the force exerted on the protein and its length .

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Figure 2.2: The AFM head, the syringes control the amount of fluid in the cell, whose top part is made of plexiglass, the various screws control the laser position and alignment.

2.2

Protein adhesion

Picking a single protein is tough, for they are only a few nanometer in gyration radius, and a strong binding on the tip and the cover slip surface is needed so that the protein domains are weaker than the surface-protein or the protein-tip links. More precisely, the breaking force of those bonds has to be significantly higher than the protein unfolding force for force-extension measurements (approximately 400nN versus 200nN), and the characteristic detachment time must be significantly greater than the characteristic unfolding time for kinetics measurements (approximately 6s versus 1s). The first thing is to have properly engineered proteins with 12 extra residues in the C-terminus and 4 in the N-terminus, to serve as handles in our experiments. The experiment is performed in a way very similar to fishing. The first part of the experiment is an approach of the tip to the surface until a significant contact force is reached1 then a short waiting time, from 0 to 1.5 s to allow protein adsorption on the surface, These values are set to optimize protein fishing probability, and strong link formation, but one must set them to also ensure single-protein picking, for if several proteins are adsorbed at the same time, no meaningful information can be retrieved from the force-extension nor from force-clamp curves, since the force applied is shared between proteins. Obviously, the materials used must be chosen carefully to ensure good protein adsorption. The cover slips are gold-covered23 , which favors protein adsorption, and the tip material, silicon nitrile, is thought to favor adsorption because of dangling bonds in its non-stoichiometric matrix, which come from the vapor deposition process[16]. The pulling away from the surface then occurs, the manner of which depends on the kind of experiment performed. For Force-extensions, the piezo will pull away the cover slip at constant speed (≈400nm.s−1 ) while in Force-Clamps, the piezo is set by a feedback loop to pull so that the protein exerts a constant force on the tip. We also tune the protein concentration (to approximately 10-100µg/mL for ubiquitin and I-27), keeping in mind that a low concentration means less multiple protein picking, but also less fishing. All these parameters are set empirically, and change from one protein to the other, and even during the lifetime of one protein, since, as the protein ages, more aggregation effects manifest, thus the overall concentration has to increase to compensate. 1 typically

1100pN for force-extension experiments, and 800pN for force Clamps with a 1nm Cr cover to ensure good gold adhesion on the glass surface, then 3-4 nm of gold to have a smooth surface and enough resistance to abrasion. The cover slips used were made in NYU’s Molecular Design Institute using a vacuum deposition chamber by Brian K. Olmsted, who is preparing a thesis on Crystal epitaxy and polymorphism. 3 glass cover slips were found to be less efficient, and a cheaper alternative to gold, etched glass, is quite difficult to prepare properly, because unless the etching is well-controlled, the surface becomes very rough during the process. 2 glass

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2.3

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Acquisition system and calibration

Reading voltages from the four quadrants of our photodiode, we want to measure the force exerted by the protein on the cantilever, and the cantilever deflection. Since we only take into account movement along the vertical axis, we only need to measure the voltages in the top and bottom parts of the photodiode. To this effect, I built a small analog controller from existing design[1] that sums together the two top quadrants (A) and the two bottom quadrants (B), and feeds these voltages to the ”black box” that outputs the sum (A+B) of the top and bottom part, and their difference (A-B). We use cantilevers with an approximately 30pN/nm spring constant, in their linear regime where the cantilever deflection is proportional to the force exerted (this is true if forces don’t go over 3000pN, at which point the nonlinearity of the system begins to appear.). To get the relation between displacement and voltage reading, we drive the cantilever tip in contact with the piezo. We then measure the V = A−B A+B versus z, where z is the piezo position (see subsection on piezo controller) let’s call this value (constant over the range of forces used) S. Thus z = V /S. To measure the spring constant two main methods exist[16]. The very accurate but tip-damaging added mass method, where small masses are added on the cantilever to measure its deflection. The added mass versus deflection curve is drawn, and from there, the spring constant is calculated. Then one has to assume that the standard deviation of spring constant is small so that the mean spring constant of the measured set of cantilever has significance for any given cantilever. This method also cannot be used in our solvent (PBS). Our tips spring constant varying widely from one another ∆k k ≈ 0.3, we use a second method, based on the equipartition theorem, a variant of the method presented in [17]: This conveniently offers a way to calibrate each tip separately, in our experimental setup, thus the calibration procedure takes into account interaction affects with the solvent. The thermal noise, around room temperature, creates small movements of the tip of the order of 0.1nm for our cantilevers. The Hamiltonian of the system is Gaussian and can be written : H(k1 , ..., kN ) =

N X

H(ki ) where H(ki ) =

i=1

p2i 1 + ki qi2 , 2mi 2

where pi is the momentum of the oscillator, mi its mass, ki the spring constant of the oscillator, and qi its displacement. From the equipartition theorem, follows that, for each i, < 1/2ki qi >= 1/2kB T, where T is the temperature and kB the Boltzmann constant. thus k=

kb T < (δz)2 >

for the fundamental mode of vibration of the cantilever. By measuring the fluctuations of V , one can extract < (δz)2 > since in the reciprocal (frequency ) space, the integral of the power spectrum P under the peak of the fundamental frequency is simply < (δV )2 > . Thus k=

kB T . P

We then fit all peaks by Lorentzians, and the background low frequency noise by a Lorentzian also it is in fact a power in law ω −2 . and extract P from the Lorentzian fit of the fundamental resonant peak (fig. 2.3).

2.4

Piezo controller and PID

The piezo has the key role of controlling the cover slip position, thus the length of the protein. the piezo is made of ceramic material whose size changes when a voltage is applied. It has 3 active axes so the tip can be used to fish on different spots on the gold surface. It can move 3µm in each direction, and measures its

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Figure 2.3: Power spectrum of V , and fits of the observed peaks, the fit yields P=1,2·10−5 V2rms , the resonant frequency is ≈ 1kHz and the amplitude of the movements ≈ 2nm.

own size with capacitors with an accuracy of 0.1 nm. Its resonant frequency is of order 10kHz, so for any phenomenon happening slower than 1ms we can assume the response of the piezo to be instantaneous. To control the force exerted on the cantilever, we use a three-element feedback loop, composed of a proportional, an integral, and a derivative feedback systems in parallel. It compares the force exerted on the cantilever to the desired force and pulls the surface away if the force is too low (and closer if the force is too high). Its response time is approximately 20ms in the worst cases. The values of the PID coefficients are neither known nor easily measurable. And the PID cannot be plugged off, making manual tuning is very difficult, and excluding the use of the Ziegler-Nichols method. This component is being replaced for the next AFM currently under construction, by a digital feedback.

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13

Results

This chapter shows the experimental work done during this internship. The first part is instrument characterization, and the second presents the results themselves: the breaking force, and the cumulative probability of unfolding for I-27 mutant.

3.1

Instrument Characterization

We now want to know how our instrument is performing, by characterizing noise levels and being able to set error bars and uncertainty values meaningfully.

3.1.1

Noise Level

For Force-extension curves, we get the error on the force : ∆F ≈8pN, by drawing the histogram of forces at 0 force(see fig.3.1), while the tip is moving away from the surface and once the protein is detached (see fig. 1.2).

Figure 3.1: Histogram of the force at 0 force for force-extention experiments yields the error on the force for these experiments. Gaussian fit yields σFC ≈ 8pN.

From the distribution of forces and length (fig. 3.2), we get the values of the fluctuations of F and l, in force clamp mode : ∆F ≈ 20pN and ∆l ≈ 3nm. Alas the software and the ”Black box” also do their own, uncharacterized filtering1 , so these fluctuations are not the actual fluctuations, but rather the measured fluctuations. We trust that the software-induced corrections are small enough.

3.1.2

Drift

A drift is present in the experimental setup, inducing a change in the intensities measured of up to 10−2 V/s, thus inducing a shift in the forces measured of ≈4pN/s. It is generally very high at the beginning of the experiment and can last from a few minutes to a full hour. It sometimes reappears later on; a very 1 Time constraints prevented proper characterization of the unspecified low pass filtering with a cutoff at 2.5kHz induced by the software. Design constraints prevented characterization of the black-box-induced filtering.

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Figure 3.2: Probability density of forces (left) and lengths (right) in force clamp experiments, the force is set at 130pN, and the length repartition measured at a length plateau. Gaussian fits yields σF =20pN and σl =2nm

unpredictable phenomenon, not explained yet. It should not induce any error, in Force-Extension mode, where we do not take into account the trace where it appears (as in fig 3.4). In force-clamp mode, each experiment lasts 7 seconds, and the drift is characterized on fig 3.3. If there is more than 20pN of drift during a given force-clamp, the trace is automatically rejected.

Figure 3.3: We plot The difference between the target force and the actual force at the beginning and at the end of the experiment; The Gaussian fits give x ¯=0.3pN and σ=2.2pN for the force before, and x ¯=1.5pN and σ=10pN for the force after the experiment. There are 434 experiments in this histogram.

Figure 3.4: drift effect in force-extension mode, the red curve represent the measured force during the approach towards the surface, and the blue that measured while going away. The force difference is ≈ 20pN

If there is more than 20pN of drift during a given force-clamp, the trace is automatically rejected.

3.1.3

Other

Vibrations (see fig3.5) are dampened using a minus-k dampening table whose dampening is -10dB at 1kHz and 20dB at 100Hz. However, very strong vibrations such as the subway can still be felt. Interferences (see fig3.6 )due to multiple laser reflexion in the AFM head can be seen, and can sometimes cause force reading deviations of as much as 20pN. They often appear and disappear spontaneously. Protein freshness is also extremely important in this experiment, since old protein, (more than one

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Figure 3.5: Power spectrums of the tip position fluctuation whithout dampening (left) and on the minus-k table (right) the noise level is reduced by approximately 20dB at 100Hz

month after purification) has a strong tendency to form aggregates thus not behaving a all as a single protein.

3.2

Force extension measurements on I27 mutant

These force-extension experiments are not my primary research, but are here used to verify the proper behavior of the AFM. Few force-extension experiments are run before each force-clamp, typically 300 runs, 30 protein picking, and 20 good single-protein traces yielding 100 unfolding times. They are very useful since they also allow protein concentration tuning, and verification of protein freshness. The measure of breaking forces yields for I-27 mutant Fc = 192 ±8pN (see fig. 3.7) these values can be compared to [12] who measured Fc =160±40pN for myomesin. The high number of traces analyzed, and our keeping only traces where no drift or interferences were present (yielding approximately 300 unfolding forces), account for the high precision of our measurement. Unlike many researchers, I didn’t find the Worm-like chain model to be helpful. Its accuracy is more than dubious simply from eye fit. Moreover, the optimal persistence length has been determined as 0.4nm, which is the same order of magnitude as the monomer length, but for the model to work properly, the persistence length has to be long compared to the monomer size2 [13]. We also try to use this model out of its range, because we use it at high forces, and non-linear effects manifest as soon as 100pN from covalent bonds[13]. To confirm the usefulness of the WLC model it is necessary to compare the length of the unfolding proteins predicted by the WLC model and to compare them to the apparent length of the unfolding polymers given by another model such as the FJC, or simply by the distance between peaks. Comparing the standard deviation and mean values of each model would yield hints of each model’s quality.

3.3

Force clamp data on I-27 mutant

From traces such as the one seen fig. 1.3, dwell-times are measured. From this, I programed a basic IDL routine to extract the cumulative probability of unfolding3 . To ensure our having single-protein experiments, we count the dwell time not from the moment the force becomes constant, for we could be pulling on several proteins, but from the first force plateau before all unfolding are ≈10nm. (see fig.3.8). To be able to have a sufficient number of unfolding times, we used short experiments (≈7s), while the characteristic detachment time of the protein from the cantilever is around 5s. We thus could not 2 for example, D.Wang[7] uses the WLC to model DNA which has no secondary structure, at forces below 50pN, and finds a persistence length of ≈40pN, which is larger than the monomer size: 0.33nm 3 That is to say, the probability P(t) that a proteins unfolds before time t

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Figure 3.6: Effect of the interferences in force extension mode the peak to peak amplitude of the oscillation is ≈40pN

Figure 3.7: Unfolding force for I-27 at a 400nm.s−1 pulling speed. Gaussian fit yields Fu = 190±8pN (see 3.1.1)

measure the detachment statistics. In this case, the decorrelation is not so critical, since our characteristic unfolding times are of order ≈1s. The induced error is much smaller that the total error. To validate our single-exponential fits (P (t) = 1 − e−αt ),of the cumulative probability (see fig. 3.8), β we compare them to stretched exponentials (P (t) = 1 − e−(αt) . The stretched exponential is a natural extension of the exponential, and the additional degree of freedom allows better fit of the data. If the extra parameter remains close to its fixed value in the single-exponential model (β = 1) then we can assess that the single-exponential is a valid model. At 130pN, we conclude with great accuracy that I-27 mutant has an exponential unfolding time distribution. Thus I-27 mutant has a two-state energy landscape. This is really new, for no mechanically stable protein has been found with such unfolding kinetics. This kind of time repartition is generally linked with much simpler molecules such as DNA or simple polymers. At 110pN, a slight deviation to the single exponential appears, but the number of unfolding times is too low to conclude. Moreover, our protein was also older, creating more aggregation, and strange behavior in most experiments. The few clean traces left ≈ 30 could have hidden defects.

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Figure 3.8: Cumulative probability for unfolding times, at 130pN (Blue line, 200 unfolding events) and 110pN (Red, 102 unfolding events), the dotted green line represents exponential fits (1 − e−αt ) and yields α=1.2±.2s−1 at 130 pN (χ2 = 4 · 10−2 ) and β = 0.7 ± .2s−1 at 110pN (χ2 = 1 · 10−1 ) . The black dashed β lines are stretched exponential fits (1 − e−(αt) ) and yield α = 1.2 ± .2s−1 and β = 1.0 ± .1 at 130pN (χ2 = 3 · 10−2 ) and α=0.7±.2s−1 and β = 0.8 ± .1 at 110pN (χ2 = 5 · 10−2 ). This proves that at 130 pN, I-27 mutant has a two-state behavior, and hints that it also is the case at 110pN although more data is needed to conclude.

To estimate the error on the values measured, we used error propagation simulation. The error on the measurement of an unfolding time has two causes: error in measuring the time at which the experiment begins4 . The unfolding time measurement accuracy is very good approx.2ms because of the fast acquisition rate ≈50kHz. Taking into account the response time of the PID we can estimate that error around 30ms. By assuming this error is Gaussian, we simulate its propagation by adding a Gaussian correction to each unfolding time. The resulting error on the fit parameters is very small ≈ 1h. The main cause of error is much subtler5 . It is a sampling error due to the small number (statistically speaking) of unfolding time gathered. It is estimated by generating a large number ≈ 3 · 105 of times following a stretched exponential law and then by randomly choosing a small number N of these events and fitting them to a stretched exponential. The standard deviation on α is approximately 20% for N = 200 and 30% for N = 100; the standard deviaton on β is approximately 10% for N = 200 and 15% for N = 100.

4 this is critically important at low force, since the unfolding times are longer, thus more experiment can feature several attached proteins without our knowing. 5 this part of the work has been done by M. Clussel, postdoctoral fellow on our team

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Further work

This section briefly presents the future of the work done during this internship. We will overview the work needed before a publication is possible, and the preliminary work done on protein characterization, in collaboration with the Polytechnic Institute.

4.1

I-27 unfolding statistics

Once the fact that unfolding statistics of the mutant differ from those of the wild-type, we must characterize how they differ. We have to gather unfolding statistics on the wild-type with our experimental setup. To have an accuracy better than 10% on α and 5% on β, we must gather approximately 500 dwell-times for each force. This comparison in unfolding kinetics of a protein and its mutant is unprecedented for mechanically resistant proteins, and could lead in this form to a publication. The Force dependence of the time distribution also has to be investigated. This is quite difficult, for dwell-time measurements at high forces is limited by the time resolution of the AFM, and single protein unfolding, fingerprinted by clear 10nm steps, becomes a big jump of several unfolding happening at the same time, that cannot be easily distinguished from agglomerated protein, that also unfolds with big jumps. To solve this, the new AFM that is being built is a lot faster, thus should be able to resolve the mess created by several almost-simultaneous1 unfoldings. At low forces, the experiments become longer, thus increasing the chance for protein detachment, the unfolding statistics is a lot harder to gather, and the force noise is the same at lower force, inducing a higher overall error.

4.2

Bio-polymer Characterization

Jennifer Haghpanah is a grad student at the Polytechnic Institute, she came to our team to characterize the mechanical resistance of her synthetic protein polymers. Our very preliminary work showed that a her very large protein made of α-helices, a tri-bloc copolymer of cartilage oligomeric matrix protein and elastin, had a mechanical resistance. I presentend the preliminary results at the City College Protein Mega-meeting on June 25, and the collaboration continues with the synthesis of new bio-polymers, longer and more repetitive, for a better AFM characterization. Our goal is to be able to measure the average breaking force and the stable domains size of these new proteins. It is also important for our main research topic, for very few proteins have a mechanical stability at high forces (≈ 100pN, the AFM probing domain), and being able to characterize with force-extension experiments new ones is the first step to gather the dwell-times in new proteins, thus enlarging our pool of proteins. However, it must be noted that of mechanically stable proteins only those that unfold in only one way, that is don’t have stable sub-structures, can be investigated with force-clamp force spectroscopy. We also need proteins that have a high “fishing” rate.

1 our

current resolution for unfoldings is ≈20ms

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Conclusion This internship was a great opportunity to be immersed in a very large multidisciplinary lab. The sheer amount of different topics studied, implies that you will learn everyday. The AFM is a difficult tool to master. The many sources of noise and drift, the sometimes strange behavior of the protein, the fact that a single dust particle or bubble can ruin a day of work, and the very small amount of clean traces gathered per “fishing” attempt, made he experimental part of the internship very challenging. It is also a unique tool, being able to pull on single proteins at very high forces. The results gathered reveal an interesting behavior of I-27 mutant that hints that simple structures in proteins give rise to simple unfolding kinetics. If generalized, this result would directly link the structure of the protein with its structural complexity.

Acknowledgments I’d like to thanks Jasna Brujic, who gave me the very enriching opportunity to work on this project, and supervised my work and this report with attention. Maxime Clussel, who introduced me to the statistics of protein unfolding, and whose insight on the many physical problem I encountered has been extremely helpful. Eric Corwin, who taught me how to use the AFM, the strange ways of Igor pro, and how to program in IDL. The experimental part of this internship would not have been possible without him. Jennifer Haghpanah, from the Polytechnic Institute, who presented us a challenging new protein characterization project. Sergi Garcia-Manyes, from Columbia, master of the AFM, who kindly gave us the proteins that made these experiments possible. Alexander Siemens, my office mate, whose presence I greatly enjoyed. He also revealed me the secret hiding place of the m&ms The labs leprechauns made our experiments possible by their goodwill. All the CMSR who made this stay really enjoyable.

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