Cantilever sensor with “sample inside”
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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
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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?
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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]!
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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?
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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
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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?
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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?
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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?
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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.
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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?
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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?
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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?
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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
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Why mightbacteriahave a broaderdistribution offrequency shiftsthan the goldbeads?
How big are bacteria compared to channel dimensions?What might you worry about?
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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?
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Area
(100mm)2
1mm2
1cm2
Exercise – convert total mass to # mol. if MW = 105
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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?
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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?