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!

diff --git a/src/calibcant/theory.tex b/src/calibcant/theory.tex
index abc801413dbfbcbaaea251182f1e5eebc2ef0678..6baa1a6939e85d7f61d0e438f241170d921463ee 100644 (file)
--- 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 1c7b88bf5b8b1d99b6756b31398cd1c6c90e0b33..0c2d785f522bfa95b0fd8f531be6fb8d77d2ab7a 100644 (file)
--- 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