Class 5 Micro-cantilever sensor

Review of mass transport

Cantilever paper

Brief preview of single-molecule fluorescence

Review of last week

Imagine flow cell is suddenly filled

Molecules diffuse to sensor surface andstick, creating depletion region

Diffusion always faster than flow over small distances because time to diffuse x is ~ x2 (1/2 the distancetakes 1/4 the time), while time to flow x is ~ x, so depletion region (length d) initially grows

As d increases, the diffusive flux jdiff ~ D(c0 - 0)/d decreases until it is matched by convective flux into the depletion region ~Qc0. At this point d is at steady state

Time to reach equilibrium is increased (compared solution binding kinetics with complete mixing) because concentration of ligand in region oversensor surface is lower than if there wereno depletion zone

teq @ Da trxn when Da>>1, where Da = konbmL/D(PeS)1/3

Time to reach “quasi” steady state @ time to diffuse d,which is usually (but doesn’t have to be) << time for receptors to fill up with ligand

Example: if d ~ mm, D > 10-12m2/s (molecule r < 200nm)t ~ d2/D < (10-6 m)2/10-12m2/s = 1swhereas teq~ koff

-1 @ 1/10-3s-1 = 1000s

As receptors fill up with ligand, rate of removalfrom depletion zone drops, and d decreasesuntil flow cell reaches real equilibrium

Details of geometry and flow rate determineshape of depletion zone and relationship between d and PeH, PeS, in quasi steady state

When depletion zone extends “upstream”, d>H and d/H = 1/PeH, PeH < 1, PeH = HWD/Q

When depletion zone = “sliver” over sensing surface,d/L = (1/PeS)1/3, L = length of sensing surfacePeS = 6(L/H)2 PeH

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 = (1/2p)(k/me)1/2

Correcting for position of Dm along length of cantilever: fr (m+Dm) = (1/2p) [k/(me + aDm)]1/2 Dfr/fr ~ -aDm/2me

a = 1 if at end¼ if evenly distributed

How do they measureresonance frequency?

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 measurement of fr?Let dfr = st. dev. of repeated measurements of fr

dfr/fr ~ (kBT/EC)1/2 (1/Q)1/2

Ec= potential energy of driven cantilever

Ekinci et al, J Appl Phys 95:2682 (2004)

So Brownian motion (which limits Q) provides fundamental limit to mass detection

100-fold increase in Q -> ~ 10-fold increase insensitivity to measure small Dm (if measurementlimited only by Brownian noise)

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

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

What should depletion zone look for this device in transient steady-state before equilibrium?

How long to reach equilibrium if koff = 10-3/s, KD = 1nM?Q said to be 1.6nl/s W = 3mm, L = 400mm, H = 8mmWhat pressure should this require?

P = 12hLQ/H3W = Assume D for ligand ~3*10-11m2/s (what size does this =>?)Does depletion zone extend full H? dH/H = 1/PeH = WCD/Q

How far up does it extend? PeS = 6(L/H)2PeH = dS= L/(PeS)1/3 =

How fast to reach equil? teq = Da trxn when Da>>1 Da = konbL/D(PeS)1/3 = assume b = 1012/cm2, kon = koff/KD

trxn = koff-1/(1+ [L]/KD) = approx what is [L]?

3.6*104N/m2 = .4atm

7*10^8.4mm

.2500s nM

=1.5*10-4, so No

7nm

Does water inside the cantilever lead to damping?

How do you estimateQ from fig 2b?What dB <-> ½ max A?

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

Relationship between dfx and dmx for unknown x

fr(me+Dm) = (1/2p) [k/(me + aDm)]1/2

=(1/2p) [k/me](1+aDm/me)-1/2

@ fr(me)(1-aDm/2me)

=> dfr/fr @ -aDm/2me

Knowing dfr/fr when you fill channel with water (with known Dm) you can calculate me, then det. dmx from dfx

more simply, dmx/Dmw = dfr,x/Dfr,w

Reality check:

What dfr/fr do you expect if you fill with water?

What is mass of silicon in cantilever (2.5mm thick walls)compared to mass of water channel?

2.53 9

8 2.5

Vs ~ 2x(2.5/3)vw+2x(9/8)(2.5/3)vw

= 3.5vw rs=2.3rw

=> ms @ 5.8mw

dfr/fr should @ -amw/2ms @ 1/46whereas observe ~1/10

Charging up device w/capture antibody –

What is coating method?PLL= poly-lys +++.. sticks toSiO2 with --- surfacePEG is water-like polymer to“passivate” surface,biotin = small ring, binds NANA = tetramer so canbind biotinylated capture Abafter sticking to bio-PEG

Es

Estimate mass/Hz dfr

dmx = dmw dfr,x/dfr,w

= 3x5x400*10-15l*103g/l*(1Hz/20,000Hz)

= 3*10-13 g/Hz = 300fg/HzHow many molecules of PLL-PEG (if MW=20kDa)?~2Hz->6*10-13g*6*1023/20000g -> 2*107 => areal density ~.2/(10nm)2

Similarly can estimate # molecules of NA (MW 60kDa)and capture Ab (MW 150kDa)that stick to surface

Es

Or, more simply:

If NA 3x heavier than PLL and 3x df => same # molecules

If IgG 2.5x heavier than NA but only 5/7th df,(5/7) *(1/2.5) ~ .3x # of molecules (~107 IgG/Hz

or 5x107 total)

In steady state,AbL/AbT= (c0/KD)/(1+c0/KD)

What KD would youestimate from this?

If AbL/AbT @ 1 at 0.7mM ligand, then relative df => @ 1/10 of 5*107 total receptors bind ligand at 2nM

Is Dfr consistent with Dm predicted from this # molecules?

c0 that give half max binding ~70nM

What do you estimatefor teq from this?

Is this c/w yourprediction from masstransport analysis?

Does human IgG bind at 70nM? Why?

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

What is this figuresupposed to illustrate? What should be thetime scale of the x axisif flow is 10pl/s and cantilever vol is ~10pl?

Is 10fg the expected mass of a 100nm goldparticle? (4/3)pr3r, r=19g/ml

Would 30mHz shift be reliable dfr in proteinbinding (fig 3)?Why might they do better here?

This suggests they can detect 10fg, but they claim1 fg (resolution) in supplementary table

(a and drift time)

Area

104mm2

1mm2

1cm2

Exercise – convert total mass to #molecules. MW = 105g/6*1023

-> 1/6ag (=10-18g)/molecule

More realistic measure of cantilever sensitivity for protein is .1Hz ~30fg

They also claim they can detect pM ligandwith nM KD Ab based on 1/1000 Ab’s bindingligand -> ~105 ligand molecules, ~20fg

But fig 3 suggests not much better than nM LOD

Could they get ~106-fold sensitivity increase(detect single molecules) if they dida sandwich assay by flowing in 100nm goldnanoparticles (np) 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 an antigen-antibody bond?Empirically, such bonds are stable for severalminutes at ~5pN force. Estimate Fdrag = 6phrvfor bead ~100nm from surface at 1/3 atm pressuredriving flow

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?

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; similar to 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: immuno-assay with single-molecule sensitivity based on fluorescence labels and Total Internal Reflection Fluorescence Microscopy (TIRFM)

Read Jain et al Nature 473:484 (2011)

Basic idea – capture analyte on transparent surface introduce fluorescent label (e.g. on second ab) record fluorescent image using TIRFM

sample negative control

TIRF microscopy reduces background, allowingdetection of single fluorescent molecules

Jargon - sorry protein names: YFP, PKA, ADAP, mTor, etc. epitopes (= small chemical features, can be peptides,

that antibodies bind to): FLAG, HA fluorescent proteins (e.g. from jellyfish, corals): often

named for emission color yellow (YFP), red (mCherry) IP = immunoprecipitation, here usually means

capture of analyte on surface by antibody FRET – Fluorescence Resonance Energy Transfer:

when different fluors are within nm of eachother, excited state can transfer -> altered em. color

photobleaching – light-induced chem. change killing fluor.

Authors describe technique mainly for researchpurposes: e.g. to detect what other proteinsa test protein binds to, or how many moleculesin a complex

Our focus: how does this method compare to othersas a sensor

Issues to think about as you read:background, dynamic range, field of view size,potential for automation, cost