Class 5 Micro-cantilever sensor - PowerPoint Presentation

Slide1

Class 5 Micro-cantilever sensor

Review of mass transport

Cantilever paper

Brief preview of single-molecule fluorescenceSlide2

Review of last week

Imagine flow cell is suddenly filled

Molecules diffuse to sensor surface and

stick, creating depletion region

D

iffusion always faster than flow over small distances

because time to diffuse x is

~

x

2

(1/2 the distance

takes 1/4 the time), while time to flow x is

~

x,

so depletion region (length

d

)

initially

grows

As

d

increases, the diffusive flux

j

diff

~

D(c

0

- 0)/

d

decreases

until it is matched by convective flux into the

depletion region

~

Qc

0.

At this point

d

is at steady stateSlide3

Time to reach equilibrium is increased

(compared

solution binding kinetics with complete mixing)

because

concentration

of ligand in region over

sensor surface is lower than if there were

no depletion zone

t

eq

@

Da

t

rxn

when Da>>1, where Da =

k

on

b

m

L

/D(

Pe

S

)

1/3Slide4

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 ~ m

m, D

>

10

-12

m

2

/s (molecule r < 200nm)

t

~ d

2

/D

<

(10

-6

m)

2

/10

-12

m

2

/s = 1s

whereas

t

eq

~

k

off

-1

@

1/10

-3

s

-1

= 1000s

As receptors fill up with ligand, rate of removal

from depletion zone drops, and

d

decreases

until flow cell reaches real equilibriumSlide5

Details of geometry and flow rate determine

shape of depletion zone and relationship

between

d

and

Pe

H

,

Pe

S

, in quasi steady state

When depletion zone extends “upstream”,

d

>H and

d

/H = 1/

Pe

H

,

Pe

H

< 1,

Pe

H

= HWD/Q

When depletion zone = “sliver” over sensing surface,

d

/L

= (1/

Pe

S

)

1/3

, L = length of sensing surface

Pe

S

= 6(L/H)

2

Pe

HSlide6

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 end ¼ if evenly distributedSlide7

How do they measure

resonance frequency?Slide8

How accurately can you measure

d

f

r

(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 cycleCaveat – this Q is not the same as Qflow [vol/s]!Slide9

What limits precision in measurement of f

r

?

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 detection100-fold increase in Q -> ~ 10-fold increase in sensitivity to measure small Dm (if measurement limited only by Brownian noise)Slide10

Q in vacuum

~

15,000

Q in water

~

150How important is it for cantilever to be in vacuum rather than air (given that sample is inside)? How does Q vary with viscosity?Slide11

What should depletion zone look for this device in

transient steady-state before equilibrium?

How long to reach equilibrium if

k

off

= 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

t

rxn

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

.2

500s

nM

=1.5*10-4, so No

7nmSlide12

Does water

inside

the cantilever lead to damping?

How do you estimate

Q from fig 2b?

What dB <-> ½ max A? Why doesn’t Fig 2b show a shift in freq. on filling with water? Doesn’t water change the mass?Slide13

Relationship between

d

f

x

and

dmx for unknown xfr(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 d

f

r

/

f

r

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,wSlide14

Reality check:

What

d

f

r

/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?2.5398

2.5

V

s

~

2x(2.5/3)v

w

+2x(9/8)(2.5/3)vw = 3.5vw rs=2.3rw => ms @ 5.8mwdf

r/fr should @ -

amw/2ms

@ 1/46whereas observe ~1/10Slide15

Charging up device w/

c

apture 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-PEGEsEstimate mass/Hz dfrdmx = dmw dfr,x/dfr,w = 3x5x400*10-15l*103g/l* (1Hz/20,000Hz) = 3*10

-13

g/Hz = 300fg/Hz

How many molecules of PLL-PEG (if MW=20kDa)?

~2Hz->6*10

-13

g*6*10

23

/20000g -> 2*107 => areal density ~.2/(10nm)2Slide16

Similarly can estimate #

molecules of NA (MW 60kDa)

and capture

Ab

(MW 150kDa)

that stick to surfaceEsOr, more simply:If NA 3x heavier than PLL and 3x df => same # moleculesIf 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)Slide17

In steady state,

AbL

/

Ab

T

= (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 2nMIs Dfr consistent with Dm predicted from this # molecules?c0 that give half max binding ~70nM Slide18

What do you estimate

for

t

eq

from this?

Is this c/w yourprediction from masstransport analysis?Does human IgG bind at 70nM? Why?Slide19

Does sample need to bind to inside wall of cantilever

to be sensed?

What is this figure

supposed to illustrate? What should be the time scale of the x axis if flow is 10pl/s and cantilever vol is ~10pl? Slide20

Is 10fg the expected

mass of a 100nm gold

particle?

(4/3)

p

r3r, r=19g/mlWould 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)Slide21

Area

10

4

m

m

21mm21cm2Exercise – convert total mass to #molecules. MW = 105g/6*1023-> 1/6ag (=10-18g)/moleculeMore realistic measure of cantilever sensitivity for protein is .1Hz ~30fgSlide22

They also claim they can detect

pM

ligand

w

ith

nM KD Ab based on 1/1000 Ab’s bindingligand -> ~105 ligand molecules, ~20fgBut fig 3 suggests not much better than nM LODSlide23

Could they get

~

10

6

-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 flowSlide24

Why might

b

acteria

have a broader

d

istribution offrequency shiftsthan the goldbeads?How big are bacteria compared to channel dimensions? What might you worry about?Slide25

Remarkable reproducibility after regenerating surface

w

ith acetic acid/H

2

O

2! So (presumably mod. expensive)chips could be reused.Without subtracting change dueto 1mg/ml BSA in sampleCan devices be re-used for multiple assays?Slide26

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 throughCould it be used in sandwich format with “mass amplifier np” to detect single protein molecules?Slide27

Next week:

immuno

-assay with single-molecule

sensitivity based on fluorescence labels and

T

otal 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 TIRFMsamplenegative controlSlide28

TIRF microscopy reduces background, allowing

detection 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 each other, excited state can transfer -> altered em. color photobleaching – light-induced chem. change killing fluor.Slide29

Authors describe technique mainly for research

purposes: e.g. to detect what other proteins

a test protein binds to, or how many molecules

in a complex

Our focus: how does this method compare to others

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