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 and stick, creating depletion region Diffusion 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  ) initially grows As  increases, the diffusive flux j diff  D(c 0 - 0)/  decreases until it is matched by convective flux into the depletion region  Qc 0. At this point  is at steady state

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  eq  Da  rxn when Da>>1, where Da = k on b m L/D(Pe S ) 1/3

Time to reach “quasi” steady state  time to diffuse  which is usually (but doesn’t have to be) << time for receptors to fill up with ligand Example: if  m, D > m 2 /s (molecule r < 200nm) t  2 /D < (10 -6 m) 2 / m 2 /s = 1s whereas  eq  k off -1  1/10 -3 s -1 = 1000s As receptors fill up with ligand, rate of removal from depletion zone drops, and  decreases until flow cell reaches real equilibrium

Details of geometry and flow rate determine shape of depletion zone and relationship between  and Pe H, Pe S, in quasi steady state When depletion zone extends “upstream”,  >H and  /H = 1/Pe H, Pe H < 1, Pe H = HWD/Q When depletion zone = “sliver” over sensing surface,  /L = (1/Pe S ) 1/3, L = length of sensing surface Pe S = 6(L/H) 2 Pe H

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 (m+  m) = (1/2  ) [k/(m e +  m)] 1/2  f r /f r  -  m/2m e  = 1 if at end ¼ if evenly distributed

How do they measure resonance frequency?

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 measurement of f r ? Let  f r = st. dev. of repeated measurements of f r  f r /f r  (k B T/E C ) 1/2 (1/Q) 1/2 E c = 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 in sensitivity to measure small  m (if measurement limited only by Brownian noise)

Q in vacuum  15,000 Q in water  150 How important is it for cantilever to be in vacuum rather than air (given that sample is inside)? How does Q vary with viscosity?

What should depletion zone look for this device in transient steady-state before equilibrium? How long to reach equilibrium if k off = /s, K D = 1nM? Q said to be 1.6nl/s W = 3  m, L = 400  m, H = 8  m What pressure should this require? P = 12  LQ/H 3 W = Assume D for ligand  3* m 2 /s (what size does this =>?) Does depletion zone extend full H?  H /H = 1/Pe H = W C D/Q How far up does it extend?Pe S = 6(L/H) 2 Pe H =  S = L/(Pe S ) 1/3 = How fast to reach equil?  eq = Da  rxn when Da>>1 Da = k on bL/D(Pe S ) 1/3 =assume b = /cm 2, k on = k off /K D  rxn = k off -1 /(1+ [L]/K D ) = approx what is [L]? 3.6*10 4 N/m 2 =.4atm 7*10^8.4  m.2 500s nM =1.5*10 -4, so No 7nm

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?

Relationship between  f x and  m x for unknown x f r (m e +  m) = (1/2  ) [k/(m e +  m)] 1/2 =(1/2  ) [k/m e ](1+  m/m e ) -1/2  f r (m e )(1-  m/2m e ) =>  f r /f r  -  m/2m e Knowing  f r /f r when you fill channel with water (with known  m) you can calculate m e, then det.  m x from  f x more simply,  m x /  m w =  f r,x /  f r,w

Reality check: What  f r /f r do you expect if you fill with water? What is mass of silicon in cantilever (2.5  m thick walls) compared to mass of water channel? V s  2x(2.5/3)v w +2x(9/8)(2.5/3)v w = 3.5v w  s =2.3  w => m s  5.8m w  f r /f r should  -  m w /2m s  1/46 whereas observe  1/10

Charging up device w/ capture antibody – What is coating method? PLL= poly-lys sticks to SiO 2 with --- surface PEG is water-like polymer to “passivate” surface, biotin = small ring, binds NA NA = tetramer so can bind biotinylated capture Ab after sticking to bio-PEG Es Estimate mass/Hz  f r  m x =  m w df r,x /df r,w = 3x5x400* l*10 3 g/l* (1Hz/20,000Hz) = 3* g/Hz = 300fg/Hz How many molecules of PLL-PEG (if MW=20kDa)? ~2Hz->6* g*6*10 23 /20000g -> 2*10 7 => 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  f => same # molecules If IgG 2.5x heavier than NA but only 5/7 th  f, (5/7) *(1/2.5) .3x # of molecules (  10 7 IgG/Hz or 5x10 7 total)

In steady state, AbL/Ab T = (c 0 /K D )/(1+c 0 /K D ) What K D would you estimate from this? If AbL/Ab T  1 at 0.7  M ligand, then relative  f =>  1/10 of 5*10 7 total receptors bind ligand at 2nM Is  f r consistent with  m predicted from this # molecules? c 0 that give half max binding  70nM

What do you estimate for  eq from this? Is this c/w your prediction from mass transport analysis? Does human IgG bind at 70nM? Why?

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?

Is 10fg the expected mass of a 100nm gold particle? (4/3)  r 3  g/ml Would 30mHz shift be reliable  f r in protein binding (fig 3)? Why might they do better here? This suggests they can detect 10fg, but they claim 1 fg (resolution) in supplementary table (  and drift time)

Area 10 4  m 2 1mm 2 1cm 2 Exercise – convert total mass to # molecules. MW = 10 5 g/6* > 1/6ag (= g)/molecule More realistic measure of cantilever sensitivity for protein is.1Hz  30fg

They also claim they can detect pM ligand with nM K D Ab based on 1/1000 Ab’s binding ligand ->  10 5 ligand molecules,  20fg But fig 3 suggests not much better than nM LOD

Could they get  fold sensitivity increase (detect single molecules) if they did a sandwich assay by flowing in 100nm gold nanoparticles (np) 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 an antigen-antibody bond? Empirically, such bonds are stable for several minutes at  5pN force. Estimate F drag = 6  rv for bead  100nm from surface at 1/3 atm pressure driving flow

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?

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; 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 amplifier np” 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, 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.

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