Difference between revisions of "Lab Manual: Limits of Detection"

Overview

Atomic force microscopy and optical trapping are key techniques for investigating forces in biological systems at cellular and molecular levels. In this lab, you will investigate the limits of force detection using AFM and optical traps. The lab will involve a one hour lab session in which you will take data with an instructor. You will analyze the data to determine the instrument spring constant α, the detector responsivity R, and the limit of force detection δ.

Background reading

• [Neuman & Nagy. Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy Nature Methods - 5, 491 - 505 (2008)|http://www.nature.com/nmeth/journal/v5/n6/full/nmeth.1218.html].

Resolution limit

Second order system

Second order circuit with alternating current source and parallel resistor, capacitor, and inductor.

$ \dfrac{1}{Z_{eq}}=\dfrac{1}{Z_R}+\dfrac{1}{Z_L}+\dfrac{1}{Z_C} $

$ Z_{eq}=\frac{Z_R Z_L Z_C}{Z_R Z_L + Z_R Z_C + Z_L Z_C} $

$ Z_{eq}=\frac{\hat{V}_o(s)}{\hat{I}_{in}(s)}=\frac{RL/C}{RLs+\dfrac{R}{Cs}+\dfrac{L}{C}}=\frac{Ls}{LCs^2+\dfrac{L}{R}s+1} $

Mechanical circuit analogy

Ideal mechanical and electronic lumped elements.

$ \frac{\hat{V}_o(s)}{\hat{F}_{in}(s)}=\frac{\dfrac{1}{m}s}{s^2+ \dfrac{b}{m} s+\dfrac{k}{m} } $

Underdamped system: atomic force microscope

Overdamped system: laser tweezers

Optical trap procedure

AFM procedure