Editing Force spectroscopy (section)

===Atomic force microscope cantilevers===
Molecules [[adsorption|adsorbed]] on a [[Interface (matter)|surface]] are picked up by a 
microscopic tip (nanometres wide) that is located on the end of an elastic cantilever.  In a more sophisticated version of this experiment (Chemical Force Microscopy) the tips are covalently functionalized with the molecules of interest.<ref>{{cite journal | vauthors = Ott W, Jobst MA, Schoeler C, Gaub HE, Nash MA | title = Single-molecule force spectroscopy on polyproteins and receptor-ligand complexes: The current toolbox | journal = Journal of Structural Biology | volume = 197 | issue = 1 | pages = 3–12 | date = January 2017 | pmid = 26873782 | doi = 10.1016/j.jsb.2016.02.011 }}</ref> A [[piezoelectric]] controller then pulls up the cantilever.  If some force is acting on the elastic cantilever (for example because some molecule is being stretched between the surface and the tip), this will deflect upward (repulsive force) or downward (attractive force).  According to [[Hooke's law]], this deflection will be proportional to the force acting on the cantilever.  Deflection is measured by the position of a [[laser]] beam reflected by the cantilever. This kind of set-up can measure forces as low as 10 pN (10<sup>−11</sup> [[newton (unit)|N]]), the fundamental resolution limit is given by the cantilever's thermal [[noise]].

The so-called force curve is the graph of force (or more precisely, of cantilever deflection) versus the piezoelectric position on the Z axis. An ideal Hookean [[spring (device)|spring]], for example, would display a straight diagonal force curve.
Typically, the force curves observed in the force spectroscopy experiments consist of a contact (diagonal) region where the probe contacts the sample surface, and a non-contact region where the probe is off the sample surface. When the restoring force of the cantilever exceeds tip-sample adhesion force the probe jumps out of contact, and the magnitude of this jump is often used as a measure of adhesion force or rupture force.  In general the rupture of a tip-surface bond is a stochastic process; therefore reliable quantification of the adhesion force requires taking multiple individual force curves. The histogram of the adhesion forces obtained in these multiple measurements provides the main data output for force spectroscopy measurement.

In biophysics, single-molecule force spectroscopy can be used to study the energy landscape underlying the interaction between two bio-molecules, like proteins. Here, one binding partner can be attached to a cantilever tip via a flexible linker molecule (PEG chain), while the other one is immobilized on a substrate surface. In a typical approach, the cantilever is repeatedly approached and retracted from the sample at a constant speed. In some cases, binding between the two partners will occur, which will become visible in the force curve, as the use of a flexible linker gives rise to a characteristic curve shape (see [[Worm-like chain]] model) distinct from adhesion. The collected rupture forces can then be analysed as a function of the bond loading rate. The resulting graph of the average rupture force as a function of the loading rate is called the ''force spectrum'' and forms the basic dataset for ''dynamic force spectroscopy''.<ref>{{cite book | vauthors = Bhushan B  |title=Springer handbook of nanotechnology |date=2017 |isbn=9783662543573 |oclc=1012104482 }}{{page needed|date=October 2019}}</ref><ref name=":1">{{cite book | vauthors = Hinterdorfer P, Van Oijen A |title=Handbook of single-molecule biophysics |date=2009 |publisher=Springer |isbn=9780387764979 |oclc=534951120 }}{{page needed|date=October 2019}}</ref>

In the ideal case of a single sharp energy barrier for the tip-sample interactions the dynamic force spectrum will show a linear increase of the rupture force as function of a logarithm of the loading rate, as described by a model proposed by Bell et al.<ref>{{cite journal | vauthors = Bell GI | title = Models for the specific adhesion of cells to cells | journal = Science | volume = 200 | issue = 4342 | pages = 618–627 | date = May 1978 | pmid = 347575 | doi = 10.1126/science.347575 | bibcode = 1978Sci...200..618B }}</ref>  Here, the slope of the rupture force spectrum is equal to the <math>\frac{k_BT}{x_\beta}</math>, where <math>x_\beta</math> is the distance from the energy minimum to the [[transition state]]. So far, a number of theoretical models exist describing the relationship between loading rate and rupture force, based upon different assumptions and predicting distinct curve shapes.<ref name=":1" /><ref>{{cite journal | vauthors = Petrosyan R | year = 2020 | title = Unfolding force definition and the unified model for the mean unfolding force dependence on the loading rate | journal = J. Stat. Mech. | volume = 2020 | number = 33201 | page = 033201 | doi = 10.1088/1742-5468/ab6a05|arxiv=1904.03925 | bibcode = 2020JSMTE..03.3201P | doi-access = free }}</ref>

For example, Ma X.,Gosai A. et al., utilized dynamic force spectroscopy along with molecular dynamics simulations to find out the binding force between thrombin, a blood coagulation protein, and its DNA aptamer.<ref>{{cite journal | vauthors = Ma X, Gosai A, Balasubramanian G, Shrotriya P |title=Force spectroscopy of the thrombin-aptamer interaction: Comparison between AFM experiments and molecular dynamics simulations |journal=Applied Surface Science |date=May 2019 |volume=475 |pages=462–472 |doi=10.1016/j.apsusc.2019.01.004 |bibcode=2019ApSS..475..462M |s2cid=104310868 }}</ref>