Cantilever sensor with “sample inside”Burg et al (Manalis lab) Weighing biomolecules…in fluid. Nature 446:1066 (2007)

Basic mechanism ofcantilever as mass sensor:

fr = (1/2 )p (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 end¼ if evenly distributed

What is m for cantilever? (Does it make sensein terms of vol x sp grav?)

What is fr?

What is k? What are units for k?

How accurately can you measure Dfr (and hence Dm)?

Depends on “sharpness” of resonance, measured byQuality 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]!

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 energyof 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 surprisedif Q appeared in formula for dfr?

dfr/fr ~ (kBT/EC)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 kBT compared to EC

100-fold decrease in Q can -> ~ 10-fold loss ofsensitivity to measure small Dm

Q in vacuum ~ 15,000Q in water ~ 150

So putting aqueous sample inside cantilever insteadof cantilever in water sample may permit ~ 10-fold greater sensitivity to detect small masses

How important is it for cantilever to be in vacuum ratherthan air (given that sample is inside)? How doesQ vary with viscosity?

Does water inside the cantilever lead to damping?

Why doesn’t Fig 2bshow a shift in freq.on filling with water?Doesn’t water changethe mass?

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?

Charging up device w/capture antibody – whatis coating method?Est. # capturing mol. boundAnalyte binding: in steady state, b/bm= (c0/KD)/(1+c0/KD)Estimate KD = co at half- max binding. Is this higher than expected?Estimate koff (= 1/2tequil at c0 = KD). Is it longer than expected? ? rebinding Est. lowest detectable conc.

In steady state,b/bm= (c0/KD)/(1+c0/KD)

If they can reliably detect2nM analyte, estimate howhow 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?

Does sample need to bind to inside wall of cantileverto be sensed?

What is this figuresupposed to show? What should be thetime scale of the x axis?Could you check ifthis is what you expect for given P?

mcant ~ 5x10-8gfr ~ 200kHzDfr ~ 0.05HzDm ~ 10fgDfr/fr ~ Dm/2mAre the masses reasonable (vol x sp grav)? Are the Dfr’s expected for these masses?

Why might they be able to detect smaller Dfr‘s here thanin protein binding?

Could they get 5x106-fold sensitivity increase(detect single molecules) if they dida sandwich assay by flowing in 100nm goldparticles coated with 20 antibody?

A tethered gold np could act as a “mass amplifier”

Would the drag force on a tethered gold np belarge enough to break one antigen-antibody bond?Estimate Fdrag = 6phrv ~ 5pN at 1/3 atm pressure, probably close to limit where bond destabilized

Why mightbacteriahave a broaderdistribution offrequency shiftsthan the goldbeads?

How big are bacteria compared to channel dimensions?What might you worry about?

Remarkable reproducibility after regenerating surfacewith acetic acid/H2O2! So (presumably mod. expensive)chips could be reused.

Without subtracting change dueto 1mg/ml BSA in sample

Can devices be re-used for multiple assays?

Area

(100mm)2

1mm2

1cm2

Exercise – convert total mass to # mol. if MW = 105

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 ~5x106 protein molecules ~2nM at standard KD 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 amplifiernp” to detect single protein molecules?

Next week – ELISA with magnetic read-out using giantmagneto-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?