1 \section{Review of current research}
3 \citet{rief02} provide a general review of force spectroscopy with a short section on protein unfolding.
4 There's not all that much information here, but it's a good place to go to get
5 a big-picture overview before diving into the more technical papers.
7 There are two main approaches to modeling protein domain unfolding under tension: Bell's and Kramers'\citep{schlierf06,dudko06,hummer03}.
8 Bell introduced his model in the context of cell adhesion\citep{bell78}, but it has been widely used to model mechanical unfolding in proteins\citep{rief97b,carrion-vazquez99a,schlierf06} due to it's simplicity and ease of use\citep{hummer03}.
9 Kramers introduced his theory in the context of thermally activated barrier crossings, which is how we use it here.
11 There is an excellent review of Kramers' theory in \citet{hanggi90}.
12 The bell model is generally considered too elementary to be worth a detailed review in this context, and yet I had trouble finding explicit probability densities that matched my own in Eqn.~\ref{eq:unfold:bell_pdf}.
13 Properties of the Bell model recieve more coverage under the name of the older and equivalent Gompertz distribution\citep{gompertz25,olshansky97,wu04}.
14 A warning about the ``Gompertz'' model is in order, because there seem to be at least two unfolding/dying rate formulas that go by that name.
15 Compare, for example, \citet{braverman08} Eqn.~5 and \citet{juckett93} Fig.~2.
17 \subsection{Who's who}
19 The field of mechanical protein unfolding is developing along three main branches.
20 Some groups are predominantly theoretical,
22 \item Evans, University of British Columbia (Emeritus) \\
23 \url{http://www.physics.ubc.ca/php/directory/research/fac-1p.phtml?entnum=55}
24 \item Thirumalai, University of Maryland \\
25 \url{http://www.marylandbiophysics.umd.edu/}
26 \item Onuchic, University of California, San Diego \\
27 \url{http://guara.ucsd.edu/}
28 \item Hyeon, Chung-Ang University (Onuchic postdoc, Thirumalai postdoc?) \\
29 \url{http://physics.chem.cau.ac.kr/} \\
30 \item Dietz (Rief grad) \\
31 \url{http://www.hd-web.de/}
32 \item Hummer and Szabo, National Institute of Diabetes and Digestive and Kidney Diseases \\
33 \url{http://intramural.niddk.nih.gov/research/faculty.asp?People_ID=1615}
34 \url{http://intramural.niddk.nih.gov/research/faculty.asp?People_ID=1559}
36 and the experimentalists are usually either AFM based
38 \item Rief, Technischen Universität München \\
39 \url{http://cell.e22.physik.tu-muenchen.de/gruppematthias/index.html}
40 \item Fernandez, Columbia University \\
41 \url{http://www.columbia.edu/cu/biology/faculty/fernandez/FernandezLabWebsite/}
42 \item Oberhauser, University of Texas Medical Branch (Fernandez postdoc) \\
43 \url{http://www.utmb.edu/ncb/Faculty/OberhauserAndres.html}
44 \item Marszalek, Duke University (Fernandez postdoc) \\
45 \url{http://smfs.pratt.duke.edu/homepage/lab.htm}
46 \item Guoliang Yang, Drexel University \\
47 \url{http://www.physics.drexel.edu/~gyang/}
48 \item Wojcikiewicz, University of Miami \\
49 \url{http://chroma.med.miami.edu/physiol/faculty-wojcikiewicz_e.htm}
51 or laser-tweezers based
53 \item Bustamante, University of California, Berkley \\
54 \url{http://alice.berkeley.edu/}
55 \item Forde, Simon Fraser University \\
56 \url{http://www.sfu.ca/fordelab/index.html}
59 \subsection{Evolution of unfolding modeling}
61 Evans introduced the saddle-point Kramers' approximation in a protein unfolding context 1997 (\citet{evans97} Eqn.~3).
62 However, early work on mechanical unfolding focused on the simper Bell model\citep{rief97b}.%TODO
63 In the early `00's, the saddle-point/steepest-descent approximation to Kramer's model (\citet{hanggi90} Eqn.~4.56c) was introduced into our field\citep{dudko03,hyeon03}.%TODO
64 By the mid `00's, the full-blown double-integral form of Kramer's model (\citet{hanggi90} Eqn.~4.56b) was in use\citep{schlierf06}.%TODO
66 There have been some tangential attempts towards even fancier models.
67 \citet{dudko03} attempted to reduce the restrictions of the single-unfolding-path model.
68 \citet{hyeon03} attempted to measure the local roughness using temperature dependent unfolding.
70 \subsection{History of simulations}
72 Early molecular dynamics (MD) work on receptor-ligand breakage by Grubmuller 1996 and Izrailev 1997 (according to Evans 1997).
73 \citet{evans97} introduce a smart Monte Carlo (SMC) Kramers' simulation.
75 \subsection{History of experimental AFM unfolding experiments}
78 \item \citet{rief97b}:
81 \subsection{History of experimental laser tweezer unfolding experiments}
84 \item \citet{izrailev97}: