Cantilever sensor with “sample inside”

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: fr = (1/2p)(k/me)1/2 Correcting for position of Dm along length of cantilever: f’r = (1/2p) [k/(me + aDm)]1/2 Dfr/fr~-aDm/2me a = 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 fr? What is k? What are units for k?

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

4. What limits precision in measurements of fr? Let dfr = st. dev. of repeated measurements of fr What happens if you don’t drive the cantilever? Do these motions add to motion of driven cantilever? Would you be surprised if kBT/average driving energy of cantilever EC appeared in formula for dfr? 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 dfr?

5. dfr/fr~(kBT/EC)1/2 (1/Q)1/2 Ekinciet 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 kBT compared to EC 100-fold decrease in Q can -> ~ 10-fold loss of sensitivity to measure small Dm

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 fr; expected sensitivity from Dm for given # of molecules bound; flow channel vol.; flow rate as function of P; PeH, PeS, ds, Da; receptor density, sensor area, equil. fraction of receptors with tgt. at different co, KD; teq and compare all to observed values! Example: ds = av. distance diffused in time it takes to flow L At flow rate 10pl/s, flow chamber 3x8x400mm (HxWxL) vol = 10pl, so time to flow L = 1s. For 10nm molecule, D=kBT/6phr = 2x10-11m2/s, <x>=(6Dt)1/2 = 10mm, 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/bm= (c0/KD)/(1+c0/KD) Estimate KD = coathalf- max binding. Is this higher than expected? Estimate koff(= 1/2tequil at c0 = KD). Is it longer than expected? ? rebinding Est. lowest detectable conc.

10. In steady state, b/bm= (c0/KD)/(1+c0/KD) If they can reliably detect 2nM analyte, estimate how how many molecules are bound at this conc. If closely packed, # receptors= (1/100nm2) x area = 2x[3x400 + 8x400]mm2/100nm2 = 108 b/bm = 1/10 => # bound molecules = 107 Is Dfr consistent with Dm 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. mcant~ 5x10-8g fr~ 200kHz Dfr~ 0.05Hz Dm ~ 10fg Dfr/fr~Dm/2m Are the masses reasonable (vol x sp grav)? Are the Dfr’sexpected for these masses? Why might they be able to detect smaller Dfr‘s here than in protein binding?

13. Could they get 5x106-fold sensitivity increase (detect single molecules) if they did a sandwich assay by flowing in 100nm gold particles coated with 20 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 Fdrag = 6phrv ~ 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. Can devices be re-used for multiple assays? Without subtracting change due to 1mg/ml BSA in sample Remarkable reproducibility after regenerating surface with acetic acid/H2O2! So (presumably mod. expensive) chips could be reused.

16. Area (100mm)2 1cm2 1mm2 Exercise – convert total mass to # mol. if MW = 105

17. Summary Very nice idea of putting flow cell inside cantilever! Do they need fancy vacuum? How does Q vary with h? Sensitivity for mass detection ~5x106protein molecules ~2nM at standard KDin “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?