Nanomechanical properties of biopolymers

This thesis presents, develops and applies new methodologies that can quantitatively probe the mechanical and viscoelastic properties of biomaterials at the nanoscale. Elastic and viscous properties are important characteristics of materials, such as many kinds of polymers and polymer solutions, colloidal solutions, but also many biological materials like cells or tissues. Very often, especially biological samples are difficult to obtain in large quantities, and measuring their mechanical properties requires the use of novel techniques that are based on local probing down to the nanoscale, like Atomic Force Microscopy (AFM) or Optical Trapping Interferometry (OTI). First we present a study on the mechanical properties of a single vimentin intermediate filament by elastically deforming it with the tip of an AFM. The resulting deflection gives a direct information on the elastic deformation of the filament itself. The bending modulus of native, non-stabilized IFs was found to be between 300 and 400 MPa. Our results together with the ones of previous works, suggest that IFs present axial sliding between their constitutive dimers, and therefore have a bending stiffness that depends on the filament length. To reduce the axial sliding between subunits, we stabilized vimentin by crosslinking with glutaraldehyde, which allowed us to conclude on a lower limit estimate of the filaments' Young's modulus. After, we present the development of a new tool for one-particle microrheology to measure locally viscoelastic properties of complex fluids with unprecedented bandwidth and resolution. Microrheology allows the characterization of very small quantities of a soft sample in a minimally invasive way, by tracking the Brownian motion of an embedded micron-sized spherical probe only driven by thermal energy. The storage modulus quantifies the elastic energy stored in the system, whereas the loss modulus is a measure for the damping due to viscosity. The method of choice to record the trajectory of the Brownian probe embedded in a complex fluid is Optical Trapping Interferometry (OTI). The optical trap has a twofold function: it ensures that the particle remains within the detector range, and it provides a light source for the position detection. By correctly calibrating the position signal of our detector, we validated a recently developed method, which is independent of any a priori assumption on the medium's viscosity and we could show that OTI can be used as a true in situ viscometer. By achieving considerable improvement in the spatio-temporal resolution of OTI, down to the nanometer and microsecond range, we could access timescales at which the inertia of the probed fluid becomes detectable. The high sensitivity of our set-up allowed us to calculate the velocity autocorrelation function (VAF) of the Brownian particle's motion at short times, where the VAF is very sensitive to the dynamics of thermal fluctuations, and hence to the nature of the structures interacting in the immediate vicinity of the probe. With such advance, we were able to track the dynamics of our Brownian microsphere, confined by a viscoelastic model polymer. Additionally to the viscoelastic modulus G*(ω), characteristic to each solution that we studied, we found that the velocity correlation function exhibits a positive or negative power-law behavior, which is strongly dependant on the solution's morphology, like polymer concentration, length, and mesh size of the network.

Motion of a colloidal particle in an optical trap

László Forró, Sylvia Jeney, Andrzej Kulik, Branimir Lukic

Thermal position fluctuations of a colloidal particle in an optical trap are measured with microsecond resolution using back-focal-plane interferometry. The mean-square displacement MSD(t) and power spectral density are in excellent agreement with the theory for a Brownian particle in a harmonic potential that accounts for hydrodynamic memory effects. The motion of a particle is dominated at short times by memory effects and at longer times by the potential. We identify the time below which the particle's motion is not influenced by the potential, and find it to be approximately tau_k/20, where tau_k is the relaxation time of the restoring force of the potential. This allows us to exclude the existence of free diffusive motion (MSD(t) proprtional t) even for a sphere with a radius as small as 0.27 µm in a potential as weak as 1.5 µN/m. As the physics of Brownian motion can be used to calibrate an optical trap, we show that neglecting memory effects leads to an underestimation of more than 10% in the detector sensitivity and the trap stiffness for an experiment with a micrometer-sized particle and a sampling frequency above 200 kHz. Furthermore, these calibration errors increase in a nontrivial fashion with particle size, trap stiffness, and sampling frequency. Finally, we present a method to evaluate calibration errors caused by memory effects for typical optical trapping experiments.

2007

Statistical Study of the Unfolding of Multimodular Proteins and their Energy Landscape by Atomic Force Microscopy

Fabrizio Benedetti

The aim of the present thesis is to investigate several aspects of: the proteins mechanics, interprotein interactions and to study also new techniques, theoretical and technical, to obtain and analyze the force spectroscopy experiments. The first section is dedicated to the statistical properties of the unfolding forces in a chain of homomeric multimodular proteins. The basic idea of this kind of statistic is to divide the peaks observed in a force extension curve in separate groups and then analyze these groups considering their position in the force curves. In fact in a multimodular homomeric protein the unfolding force is related to the number of not yet unfolded modules (we call it "N"). Such effect yields to a linear dependence of the most probable unfolding force of a peak on ln(N). We demonstrate how such dependence can be used to extract the kinetic parameters and how, ignoring it, could lead to significant errors. Following this topic we continue with non kinetic methods that, using the resampling from the rupture forces of any peak, could reconstruct the rupture forces for all the other peaks in a chain. Then a discussion about the Monte Carlo simulation for protein pulling is present. In fact a theoretical framework for such methodology has to be introduced to understand the various simulations done. In this chapter we also introduce a methodology to study the ligand receptor interactions when we directly functionalize the AFM tip and the substrate. In fact, in many of our experiments, we see a "cloud of points" in the force vs loading rate graph. We have modeled a system composed by "N" parallel springs, and studying the distribution of forces obtained in the force vs loading rate graph we have establish a procedure to restore the kinetic parameters used. Such procedure has then been used to discuss real experiments similar to biotin-avidin interaction. In the following chapter we discuss a first order approximation of the Bell-Evans model where a more explicit form of the potential is considered. In particular the dependence of the curvature of the potential on the applied force at the minimum and at the metastable state is considered. In the well known Bell-Evans model the prefactors of the transition rate are fixed at any force, however this is not what happen in nature, where the prefactors (that are the second local derivative of the interacting energy with respect to the reaction coordinate in its minimum and maximum) depend on the force applied. The results obtained with the force spectroscopy of the Laminin-binding-protein are discussed, in particular this protein showed a phase transition when the pH was changed. The behavior of this protein changes, from a normal WLC behavior to a plateau behavior. The analysis of the force spectroscopy curves shows a distribution of length where the maximum of the first prominent peak correspond to the full length of the protein. However, length that could be associated with dimers and trymers are also present in this distribution. Later a new approach to study the lock and key mechanism, using "handles" with a specific force extension pattern, is introduced. In particular handles of (I27)3 and (I27–SNase)3 were biochemically attached to: strept-actin molecules, biotin molecules, RNase and Angiogenin. The main idea is to have a system composed by "handle-(molecule A)-(molecule B)-handle" where the handles are covalently attached to the respective molecules and the two molecules "A and B" are attached by secondary bonds. This approach allows a better recognition of the protein-protein interaction enabling us to filter out spurious events. Doing a statistic on the rupture forces and comparing this with the statistic of the detachments of the system of the bare handles, we are able to extract the information of the interaction between the molecule A and B. The two last chapters are of more preliminary character that the previous part of the thesis. A section is dedicated to the estimation of effective mass and viscous drag of the cantilevers studied by autocorrelation and noise power spectrum. Usually the noise power spectrum method is the most used, however the autocorrelation should give approximately the same information. The parameters obtained are important in high frequency modulation techniques. In fact, they are needed to interpret the results. The results of these two methods show a good agreement in the estimation of the mass and the viscous drag of the various cantilever used. Afterwards a chapter is dedicated to the discussion of the force spectroscopy experiments using a low frequency modulation of the cantilever base. Such experiments allow us to record the phase and the amplitude shift of the modulation signal used. Using the amplitude channel we managed to restore the static force signal with a lower level of noise. Moreover these signals give us direct information about the dynamic stiffness and the lose of energy in the system, information that, using the standard technique would be difficult (or even impossible) to obtain.

EPFL2012

Shear Thickening Fluid Impregnated Foam Composites for Vibration Control and Impact Protection

Mathieu Soutrenon

Highly concentrated suspensions of silica particles present shear thickening properties, shifting from a low to a high viscosity state, instantly and reversibly at a critical shear rate. Their viscosity increases by up to 3 orders of magnitude, changing from a honey-like liquid to a brittle solid material. This sharp rise in viscosity is associated with a large absorption of energy that can be used in damping applications. These shear thickening fluids (STF) are among the few passive materials that can simultaneously bring both an increase in damping and in stiffness properties. In mechanical design, this leads potentially to a weight reduction of the overall system. This thesis work is aimed to develop and test a composite material solution for vibration control and impact protection, using STF as the damping element. A main challenge was to overcome the fact that STF are liquid at rest, and very sensitive to their environment. The proposed damping material was therefore constituted of foam impregnated with STF and encapsulated with silicone (STF/foam). A comparison of properties with other damping materials such as Smactane®was emphasized along the thesis. Storage and processing conditions of STF constituted of highly concentrated suspensions were shown to affect their rheological properties similarly to other sensitive parameters such as particle concentration. Rigorous processing methods were thus required to produce STF with defined and stable rheological properties. The use of sonication was preferred to disperse the aggregates of particles in concentrated colloidal suspensions due to the packing of the dry powder. Contact with air or humidity deteriorates the shear thickening properties of STF. Storage of STF in a freezer at −24 ◦C or under nitrogen prevents this. The use of a physical barrier to air and humidity such as silicone to protect STF is also shown to greatly reduce the ageing problem. The energy dissipated during a cyclic strain cycle was used as a measure of the damping property of the STF, and compared to that of other materials. It was measured with dynamic rheological measurements performed on suspensions with variations of particle concentration, size and test frequency. STF were shown to dissipate a large amount of energy during their transition, which increases with the increase of frequency and particle concentration and decrease with the increase of particle size. In specific cases of large strain amplitude, they potentially dissipate more energy than viscoelastic materials such as rubber. An open cell melamine resin foam was used as a lightweight scaffold to provide a three dimensional structure to the STF. The foam distributes the load and locally shears the STF. The shape of the foam is easily adjustable. To impregnate the foam with the STF, a system similar to vacuum infusion was used. The foam was placed under vacuum in a mold and the STF heated at 70 ◦C to reduce its viscosity and shear thickening properties was sucked in the foam with the depressurization. The STF/foam systems were then encapsulated in silicone to protect the STF/foam damping pads from contamination and avoid outgassing. During compression tests at low frequencies and large deformations, we demonstrated that STF could be activated in this type of structure, with mechanical properties comparable to those of a viscous honey-like fluid at rest and silicone when the STF is in the solid state. The same behavior was observed during impact solicitations. STF/foam presents a very low coefficient of restitution and absorbs the shock wave associated with impacts. Shock tests done separately confirm the shock absorption properties of STF/foam even if the STF is not activated. The combination of mechanical and damping properties of the foam/STF systems remain lower than for very high performance damping materials like Smactane®. The reasons are their low mechanical compression and shear properties at rest and the need to overcome a threshold strain or stress to activate the STF. However, the large dissimilarity between the states before and after the transition makes these materials interesting for impact or large strain amplitude applications such as sole for running shoes or several space structures.