Collision Cross Section:Ideal elastic hard sphere collision:

221 )( rr

Where is the collision cross-section

21

21 )(

rr

Where is the collision distance

These equations negate potential interactions between the two molecules (atoms), attractive and repulsive, and assume spherical geometry.

r2r1

Motion in an Applied Field(Maxwellian ions)KEv d

meK

vd=drift velocity(cm/sec)

K=mobility(cm2/Vsec)

E=applied field (V/cm)Langevin Equation:

Assumptions: ignoring coulombic interaction,Low field limit, close to thermal equilibrium.

e=ionic charge(Volts)=mean free path(m)

We then arrive at the Nernst-Townsend-Einstein Equation, sometimes referred to as the Einstein relation:

TkqDK

b

The main assumption of the Einstein relation is that mobility theory (motion acting on one species, but not the other) and diffusion theory are at equilibrium. Wannier no longer assumed that the applied field was weak and the ion mass was small.

qKE

MmMmm

qTkKD b

32

908.13

qKE

MmMmm

qTkKD b

32

|| 908.172.3

3

At this point we can solve the resolution using either the Einstein relation or Wannier’s relation. We will see from some of the future results that the maximum resolution is attained from systems that fit the Einstein relation. So, if we solve the resolution equation in terms of the Nernst-Townsend-Einstein equation:

o

b

KEL

qTKk

LR32.3

Simplifies to for single charges ions:

TLER o33.32

(2.8)

(2.9)

qKE

MmMmm

qTkKD b

z

32

908.172.3

3

MmMmm

w 908.12.3

3

2232.3 KETkqKtER

wb

d

Taking Wannier’s relation in the z direction:

Simplify the mass term in the relation:

Resolution for a broader range of fields:

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 2 4 6 8 10KO

(cm2/Vs)

Diff

usio

n (m

2 /s)

Wannier Relation, 15cm Drift Cell1 Torr

E=50V/cm

E=20V/cm

E=10V/cm

Nernst-Einstein Relation

0

10

20

30

40

50

60

0 5 10 15 20 25 30

KO(m2/Vs)

Res

olut

ion

E=50V/cm

E=20V/cm

E=10V/cm

Comparison of Reduced Mobility vs. Resolution1 Torr, 15cm Drift Cell

EI Source

Drift Cell

Liq. Flow Collar

4 ElementElectrostatic Lens

ChanneltronDetector

TOF Detector

200 400 600 800 1000 1200 1400 1600

950

900

850

800

750

700

650

600

550

500

450

peptide line

carbon clusterline

Arrival Time (Ion Mobility) us

m/z

SID

Source Region

Drift Region

d = drift length

(Acceleration Region)E = V/d

E = 0

Time-of-Flight (TOF)

Es

Detector

2

21 mveV Kinetic Energy given to the Ion in the Source Region

21

2

meVv Solving for Velocity

tdv Solve for Flight Time d

eVmt

21

2

So, with a constant acceleration voltage and a known drift length, the drift time is proportional to the square root of the mass to charge ratio (m/e).

Time-of-Flight (TOF)

Time-of-Flight (TOF)

Mass spectrometrists define resolution as:

mm

In TOF we start from the drift time equation:

22

2 tdeVm

And the derivative is: tdt

deVdm 22

2

So,

dtt

dmm

2

So time-of-flight resolution is defined by:

tt

mmR

2

t is usually defined a peak width at half height.

zELR

Why is resolution so important?

2428.0 2435.2 2442.4 2449.6 2456.8 2464.0Mass (m/z)

5046.1

0

10

20

30

40

50

60

70

80

90

100

% In

tens

ity

Voyager Spec #1[BP = 1395.8, 5907]2452.2063

2453.1960

2454.1958

2435.1855

2434.1841

2451.20612436.18022455.1926

Time-Lag Focusing

Es Ea

Detector

E=0Field Free Drift Region

Low draw out voltageTo correct for randomDistribution of ion energy.Ex. ~300V

Acceleration region

r

ro

orr 148.1

22

8

o

yx mreUaa

22

4

o

yx mreVqq

Linear Quads

21

oz rL

ER

Quad Ion Traps

0

21

)2( 2222 zyx

ro

o

Transform into cylindrical coordinates:

)2sincos( 222222 zrr

ro

o )1sin(cos 22

)2( 222 zr

ro

o Geometrical constraints:

22 2 oo zr

Quad Ion Traps

22

162

orz mr

eUaa

22

82

orz mr

eVqq

RFcyclestR trap #

Ion Motion in a Static Magnetic Field:

)(

BvqFLorentzian Force:

)(

Bvqam

Lets take a constant magnetic field in the direction z:

•The cross product states that the particles acceleration is always orthonormal to the direction of the magnetic field.

•This will be true even if B varies with position (r), but will change if B varies with time (t).

oBkB

Unit vector in the z-direction (k).

100)( zyxo vvv

kjiqBBkvqam

(1.1)

(1.2)

(1.3)

(1.4)

Cyclotron Motion:

rvxy Angular velocity

Substitute angular velocity:

rqBrm o 2

Simplify into the celebrated “ion cyclotron equation”:

mqBo

•This equation is the heart of ICR. It tells us that the cyclotron frequency is independent of the ions initial velocity, and all ions with the same mass/charge (m/q) will have the same frequency.

(2.5)

(2.6)

(2.7)

Cyclotron Motion:

BO

Z

X

Y

+•We can see from our equations that cations will cyclotron counter-clockwise to the in-the-plane magnetic field direction, while anions will cyclotron clockwise

100

1000

10000

100000

1000000

10000000

100000000

1000000000

1 10 100 1000 10000 100000m/z

v(Hz

)

3.0

7.0

9.4

20.0

Upper Mass Limit in FT-ICR MS:

Note: Magnetron motion and cell shapes:

TVBa

qm

4

22

So in a 7T field in a cylindrical trap of 2cm radius the mass limit will be about 250 kD.

Hitachi M8000 LC/MSn

QStar

ESI

38

Multidimensional Analyses

time

response

chromatogram

m/zm/z

m/z

39

Collision induced dissociation

• Collision conditions (FRAGMENTATION) is controlled by altering:

– The collision energy (speed of the ions as they enter the cell)– Number of collisions undertaken (collision gas pressure)

Argon gas

O

O

CH3

CH3CH3

Precursor ion Product ions

OCH

2

CH2

CH3

O

CH3

CH3

• In the collision cell, the TRANSLATIONAL ENERGY of the ions is converted to INTERNAL ENERGY.

4020 40 60 80 100 120 140 160 180 200 220

m/z0

100

%

0

100

%

0

100

%

0

100

%

0

100

% 5eV

10 eV

30 eV

40 eV

20 eV

collision energy >  fragmentationProd

uct ion

 scanning

41

Product Ion Spectrum: Progesterone

300 305 310 315 320 325 330m/z0

100

%

315.1

316.1

Mass Spectrum from MS1

100 125 150 175 200 225 250 275 300 325m/z0

100

%

109.097.0

Product ion spectrum from MS2Prod

uct ion

 scanning

Product ions

OCH

2

CH2

CH3

O

CH3

CH3

O

O

CH3

CH3CH3

Precursor ion

42

Sirolimus: MS Spectrum

790 795 800 805 810 815 820 825 830 835 840 845 850m/z0

100

%

821.5

810.5

822.5

826.5

827.5[M+H]+

[M+NH4]+

[M+Li]+

[M+Na]+

[M+K]+

Full Scan

 Acquisition Mod

e

43

Sirolimus:LC-MS (SIM) vs LC-UV

0

100

%SIR m/z 821

30µg / L

1.5 min

HPLC‐UV

HPLC‐MS

Single ion mon

itorin

g (M

S)

44

Sirolimus: MS Spectrum

790 795 800 805 810 815 820 825 830 835 840 845 850m/z0

100

%

821.5

810.5

822.5

826.5

827.5[M+H]+

[M+NH4]+

[M+Li]+

[M+Na]+

[M+K]+

Full Scan

 Acquisition Mod

e

45

MS1 MS2CollisionCell

Static (m/z 821.5) Scanning

The first quadrupole mass analyzer is fixed, or Static, at the mass-to-charge ratio (m/z) of the precursor ion to be interrogated while the second quadrupole is Scanning over a user-defined mass range.

The first quadrupole mass analyzer is fixed, or Static, at the mass-to-charge ratio (m/z) of the precursor ion to be interrogated while the second quadrupole is Scanning over a user-defined mass range.

Ar (2.5 – 3.0e-3mBar)Ar (2.5 – 3.0e-3mBar)

PrecursorPrecursorProductsProducts

Prod

uct ion

 scanning

46

790 795 800 805 810 815 820 825 830 835 840 845 850m/z0

100

%

821.5

810.5

822.5

826.5827.5

Mass spectrum from MS1Mass spectrum from MS1

200 250 300 350 400 450 500 550 600 650 700 750 800 850 900m/z0

100

%

768

576

558548718 750

786821

Product ion spectrum from MS2Product ion spectrum from MS2

Prod

uct ion

 scanning

NH4+

47

MS1 MS2CollisionCell

Static  (m/z 821.5)     Static (m/z 768.5)

Ar (2.5 – 3.0e-3mBar)Ar (2.5 – 3.0e-3mBar)

Precursor(s)Precursor(s)Product(s)Product(s)

MS/MS : Compound‐Specific Monitoring

Multip

le Reaction Mon

itorin

g

48

SirolimusLC-MS(SIM) vs LC-MS/MS (MRM)

SIR m/z 821

0.50 1.00 1.50Time0

100

%

0

100

%

0.50 1.00 1.50Time0

100

%

0

100

%

MRM m/z 821>768

3µg / L 30µg / L

Multip

le Reaction Mon

itorin

g

Amino Acid 3 Letter Code Single Letter Code Residue Mass

Monoisotopic Average

Glycine Gly G 57.02147 57.052

Alanine Ala A 71.03712 71.079

Serine Ser S 87.03203 87.078

Proline Pro P 97.05277 97.117

Valine Val V 99.06842 99.133

Threonine Thr T 101.04768 101.105

Cysteine Cys C 103.00919 103.144

Isoleucine Ile I 113.08407 113.160

Leucine Leu L 113.08407 113.160

Asparagine Asn N 114.04293 114.104

Aspartic Acid Asp D 115.02695 115.089

Glutamine Gln Q 128.05858 128.131

Lysine Lys K 128.09497 128.174

Glutamic Acid Glu E 129.04260 129.116

Methionine Met M 131.04049 131.198

Histidine His H 137.05891 137.142

Phenylalanine Phe F 147.06842 147.177

Arginine Arg R 156.10112 156.188

Tyrosine Tyr Y 163.06333 163.170

Tryptophan Try W 186.07932 186.213

Homoserine Lactone 83.03712 83.090

Homoserine 101.04768 101.105

Pyroglutamic acid 111.03203 111.100

Carboxyamidomethyl Cysteine 160.03065 160.197

Carboxymethylcysteine 161.01466 161.181

Pyridylethylcysteine 208.06703 208.284

Peptide Fragmentation

Peptide Fragmentation