1. Cantilever sensor with “sample inside” Burg et al (Manalis lab) Weighing biomolecules…in fluid. Nature 446:1066 (2007) Basic mechanism of cantilever as mass sensor: f r = (1/2  (k/m e ) 1/2  Correcting for position of  m along length of cantilever: f’ r = (1/2  ) [k/(m e +  m)] 1/2  f r /f r  -  m/2m e  = 1 if at end ¼ if evenly distributed

2. What is m for cantilever? (Does it make sense in terms of vol x sp grav?) What is f r ? What is k? What are units for k?

3. How accurately can you measure  f r (and hence  m)? Depends on “sharpness” of resonance, measured by Quality factor Q = f r /width at half-max Q is also measure of damping of resonance = 2  x energy stored/energy dissipated per cycle Caveat – this Q is not the same as Q flow [vol/s]!

4. What limits precision in measurements of f r ? Let  f r = st. dev. of repeated measurements of f r What happens if you don’t drive the cantilever? Do these motions add to motion of driven cantilever? Would you be surprised if k B T/average driving energy of cantilever E C appeared in formula for  f r ? Is Brownian motion related to viscous damping? (both due to random hits …) Since Q is related to dissipation, would you be surprised if Q appeared in formula for  f r ?

5.  f r /f r  (k B T/E C ) 1/2 (1/Q) 1/2 Ekinci et al, J Appl Phys 95:2682 (2004) So Brownian motion (which limits Q) provides fundamental limit to mass detection and is more important the bigger k B T compared to E C 100-fold decrease in Q can ->  10-fold loss of sensitivity to measure small  m

6. Q in vacuum ~ 15,000 Q in water ~ 150 So putting aqueous sample inside cantilever instead of cantilever in water sample may permit  10-fold greater sensitivity to detect small masses How important is it for cantilever to be in vacuum rather than air (given that sample is inside)? How does Q vary with viscosity?

7. Does water inside the cantilever lead to damping? Why doesn’t Fig 2b show a shift in freq. on filling with water? Doesn’t water change the mass?

8. Perfect paper to calculate m (from cantilever dim.); expected f r ; expected sensitivity from  m for given # of molecules bound; flow channel vol.; flow rate as function of P; Pe H, Pe S, d s, Da; receptor density, sensor area, equil. fraction of receptors with tgt. at different c o, K D ;  eq and compare all to observed values! Example: d s = av. distance diffused in time it takes to flow L At flow rate 10pl/s, flow chamber 3x8x400  m (HxWxL) vol = 10pl, so time to flow L = 1s. For 10nm molecule, D=k B T/6  r = 2x10 -11 m 2 /s, =(6Dt) 1/2 = 10  m, so proteins have time to bind. Is depletion zone important?

9. Charging up device w/ capture antibody – what is coating method? Est. # capturing mol. bound Analyte binding: in steady state, b/b m = (c 0 /K D )/(1+c 0 /K D ) Estimate K D = c o at half- max binding. Is this higher than expected? Estimate k off (= 1/2  equil at  c 0 = K D ). Is it longer than expected? ? rebinding Est. lowest detectable conc.

10. In steady state, b/b m = (c 0 /K D )/(1+c 0 /K D ) If they can reliably detect 2nM analyte, estimate how how many molecules are bound at this conc. If closely packed, # receptors = (1/100nm 2 ) x area = 2x[3x400 + 8x400]  m 2 /100nm 2 = 10 8 b/b m = 1/10 => # bound molecules = 10 7 Is  f r consistent with  m predicted from this # molecules?

11. Does sample need to bind to inside wall of cantilever to be sensed? What is this figure supposed to show? What should be the time scale of the x axis? Could you check if this is what you expect for given P?

12. m cant  5x10 -8 g f r  200kHz  f r  0.05Hz  m  10fg  f r /f r   m/2m Are the masses reasonable (vol x sp grav)? Are the  f r ’s expected for these masses? Why might they be able to detect smaller  f r ‘s here than in protein binding?

13. Could they get 5x10 6 -fold sensitivity increase (detect single molecules) if they did a sandwich assay by flowing in 100nm gold particles coated with 2 0 antibody? A tethered gold np could act as a “mass amplifier” Would the drag force on a tethered gold np be large enough to break one antigen-antibody bond? Estimate F drag = 6  rv  5pN at 1/3 atm pressure, probably close to limit where bond destabilized

14. Why might bacteria have a broader distribution of frequency shifts than the gold beads? How big are bacteria compared to channel dimensions? What might you worry about?

15. Remarkable reproducibility after regenerating surface with acetic acid/H 2 O 2 ! So (presumably mod. expensive) chips could be reused. Without subtracting change due to 1mg/ml BSA in sample Can devices be re-used for multiple assays?

16. Area (100  m) 2 1mm 2 1cm 2 Exercise – convert total mass to # mol. if MW = 10 5

17. Summary Very nice idea of putting flow cell inside cantilever! Do they need fancy vacuum? How does Q vary with  ? Sensitivity for mass detection  5x10 6 protein molecules ~2nM at standard K D in “label-free” mode; not so diff. from ELISA! Nice idea of counting particles (that change mass  10 fg) as they flow through Could it be used in sandwich format with “mass amplifier np” to detect single protein molecules?

18. Next week – ELISA with magnetic read-out using giant magneto-resistance (GMR) sensors Nat. Med. 15:1327 (09) Issues to pay attention to: How small a fraction of capture antibodies binding analyte can they detect? What is dynamic range? Why does it work in real-time mode (without washing)? How much better is it with washing? How complex is the sensor?