Today’s Topic: AFM Experimental Approach via Atomic Force Microscopy Imaging Mode, Force Mode. Example: Measuring strength of Heart Muscle (Titin) Strength of a single Covalent Bond Imaging: Correlation Functions

AFM — Force y= &nid= &id= Force – one place

Reversible Unfolding of Individual Titin Immunoglobulin Domains by AFM, Science, M. Reif, H. Gaub, 1997 Reversible Unfolding by AFM Pulling on Titin Gold Simple model: Upon reaching a certain force (peaks, e.g. 1), the abrupt unfolding of a (Titin) domain lengthens the polypeptide by 28 to 29 nm and reduces the force (troughs) to that of the value predicted by the force extension curve of the enlarged polypeptide (2). Start on next domain. As it’s pulling, polymer behaves like WLC. Why does curve look like it does? Why non-linear? Why repeat? Does repeat tell you anything about polymer?

Example of AFM-Force: Muscle & Titin

The Sarcomere: unit of muscle Myosin head binds to actin; rotates upon ATP binding, pulls actin together.

Myosin II moves Actin (Vale & Milligan, Science) Notice: ATP induces a conformational change: rotation of lever arm Myosin II acting as a fulcrum, rotating with ATP while driving actin 2 heads of Myosin II; only one head per dimer active. Myosin II spends about 5% of it’s time bound to actin. Myosin II is a non-processive motor, i.e. by itself, it takes 1 step on actin. is processive only because it works in groups which are held together via the thick filament.

Titin: Human’s Biggest protein Titin: 4.2MDa; Gene (on # 2) = 38,138 aa: Goes from Z-disk to Center; stretchy =I Band Cardiac (N2B &N2BA), Skeletal (N2A), Smooth all have different regions. Silicon Nitride lever: 10’s pN – several nN’s measureable Each domain IgG

Picking up a single protein “needle in a haystack”: usually pick up > 1 protein “Fingerprint” of e.g. (I91) 8 : by using identical repeats, unfolding forces are nearly identical with peaks equally spaced. (see Fig d) Protein stretched at constant velocity Titin: ≈ 1 um/sec Physiological range Worm-like Chain (WLC) is very good approximation to F vs. x of individual unit (protein, DNA) expansion.

ΔX ~ (In 1 -In 2 ) / (In 1 + In 2 ) ΔY ~ (Out 1 -Out 2 ) /(Out 1 +Out 2 ) N P N P In 1 In 2 Out 1 Out 2 POSITION SIGNAL Position sensitive detector (PSD) Useful in AFM, Optical Traps… Over a fairly wide range, it’s linear

How Strong is a Covalent Bond? Recall: what did we say it was? How Strong is a Covalent Bond? Gaub, Science, 1999 Note: It’s actually the C-Si which breaks! About k B T Force Spectroscopy Covalent bond to the tip, substrate-- gold or glass-- and within Amylose. We stretched the molecules until one of the covalent bonds in series ruptured. By analyzing the bond rupture, we were able to identify the bond that failed. Within amylose (covalent bonds) was found not to rupture.

Figure 2 (A) Force versus extension curve of amylose covalently bound between an AFM tip and a silicon oxide surface. M Grandbois et al. Science 1999;283: Published by AAAS Thus, this transition can be used as a molecular strain gauge that can be built into an experiment to report the force that is acting on any point of the molecular bridge. Control: no covalent attachment with amylose. Reversible stretching of amylose (polysaccharides). Not dependent on rate of stretching. Sugar rings switch into a more extended arrangement. With amylose, this results in a characteristic plateau at 275 pN with an extension of 0.5 Å per ring unit (Fig. 2A). 2B: Covalent attachment: sudden ruptures about 2 pN. With amylose: 275 pN (low-force) with an extension of 0.5 Å per ring unit = (275pN)(0.05nm) = pN-nm = 3k B T At the given force-loading rates of 10 nN/s, the histogram peaks at a value of 2.0 ± 0.3 nN.

Figure 3 (A) Histogram of the length gain after the events were measured in the force versus extension curves showing multiple ruptures for amylose, which was covalently attached to the silicon oxide surface and the tip. M Grandbois et al. Science 1999;283: Published by AAAS No EDC or NHS used. Attachment non-specific: lower force. Pop, pop, pop

F = 2.0 nN = 2000pN C-Si: nm (estimate) (2000pN)(0.185 nm) = 370 pN-nm 1k B T = 4pN-nm E = 92.5 k B T Example Rupture Force Breaking of a covalent bond C-C ≡ 1600 pN Breaking of a non-covalent bond. Biotin/streptavidin ≡ 160 pN (strongest known) Breaking of a weak bond. Hydrogen bond ≡ 1- 4 pN A Single Covalent bond Sulfur-gold anchor ruptured at 1.4 +/- 0.3 nanonewtons at force-loading rates of 10 nanonewtons/second.

Which is Covalent Bond that breaks? How Strong is a Covalent Bond? Gaub, Science, 1999 Four bonds are unique to the attachment: Si–O, Si–C, C–C, and C–N bonds. The C–O bond is found in the attachment and in the amylose backbone. At first, it was difficult to decide which of these four different bonds was breaking in our experiment. We ruled out the rupture of the Si–O bond because three of these bonds hold in parallel at the surface. As a first approximation, we correlated the strength of a covalent bond with the ratio of the dissociation energy and the bond length. Considering the enthalpy for dissociation and the bond length (20), we decided that the Si–C bond was the most likely candidate for rupture in our experiment. Largely theoretical argument.

AFM Images Bacteria Mosquito eye DNA molecules t&view=article&id=51&Itemid=57

Convolution of tip and sample size Tobacco Mosaic Virus (TMV) In truth, diameter of 180 Å. Due to finite tip size, w~ 350 A

Typically, probe radius varies from 5 to 20 nm If tip size is large, have to worry about distortions. Convolution What will image look like?

Cross-correlation Cross- correlation Correlation functions Can also do auto-correlation:(as in WLC) What if red curve is like a delta function (really narrow)?Reproduce blue box What does cross- correlation look like?

Class evaluation 1. What was the most interesting thing you learned in class today? 2. What are you confused about? 3. Related to today’s subject, what would you like to know more about? 4. Any helpful comments. Answer, and turn in at the end of class.