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

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?

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]!

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 ?

 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

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?

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?

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 = 2x m 2 /s, =(6Dt) 1/2 = 10  m, so proteins have time to bind. Is depletion zone important?

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.

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[3x x400]  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?

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?

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?

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

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?

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?

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

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?

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?