From 16edc81ea5efdec7f3cc521cdf5603cc2668bc6c Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Wed, 8 May 2013 17:41:24 -0400 Subject: [PATCH] calibcant/theory.tex: Cite benedetti12 for eq:DHO-psd He has a similar treatment to my theory section in his section 8.2.1 (Spectrum of a cantilever) starting on page 99. Congratulations on graduating, Fabrizio! --- src/calibcant/theory.tex | 4 +- src/root.bib | 99 ++++++++++++++++++++++++++++++++++++++++ 2 files changed, 102 insertions(+), 1 deletion(-) diff --git a/src/calibcant/theory.tex b/src/calibcant/theory.tex index abc8014..6baa1a6 100644 --- a/src/calibcant/theory.tex +++ b/src/calibcant/theory.tex @@ -269,7 +269,9 @@ Plugging \cref{eq:DHO-var} into the equipartition theorem \end{align} Combining \cref{eq:model-psd,eq:GO}, we expect $x(t)$ to have a power -spectral density per unit time given by +spectral density per unit time given by\footnote{% + \cref{eq:DHO-psd} is Eq.~(8.11) from \citet{benedetti12}. +} \begin{equation} \PSD(x, \omega) = \frac{2 k_BT \beta} { \pi m \p[{(\omega_0^2-\omega^2)^2 + \beta^2\omega^2}] }\;. diff --git a/src/root.bib b/src/root.bib index 1c7b88b..0c2d785 100644 --- a/src/root.bib +++ b/src/root.bib @@ -8742,6 +8742,105 @@ be aptly circumvented by the proposed approach.}, } +@phdthesis{ benedetti12, + author = FBenedetti, + title = {Statistical Study of the Unfolding of Multimodular Proteins + and their Energy Landscape by Atomic Force Microscopy}, + year = 2012, + address = {Lausanne}, + affiliation = {EPFL}, + doctoral = {EDPY}, + pagecount = {153}, + doi = {10.5075/epfl-thesis-5440}, + url = {http://infoscience.epfl.ch/record/181215}, + eprint = {http://infoscience.epfl.ch/record/181215/files/EPFL_TH5440.pdf}, + keywords = {atomic force microscope (AFM); single molecule force + spectrosopy; velocity clamp AFM; Monte carlo simulations; force + modulation spectroscopy; energy barrier model; non kinetic methods + for force spectroscopy}, + abstract = {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.}, +} + @article{ kempe85, author = TKempe #" and "# SBHKent #" and "# FChow #" and "# SMPeterson #" and "# WSundquist #" and "# JLItalien #" and "# DHarbrecht -- 2.26.2