CHEM 5181 – Fall 2010
Homework Assignment #2: assigned Thu 16-Sep-10; due Tue 28-Sep-09.


Please make an effort to produce a clean solution. Please briefly explain your
answers, and solution procedures. We grade as much on the thinking process as
on the final result.
This homework will be posted in Word format on the course web page, so that
you can download it and type your answers after each question.
Problem 2.1. Analysis of a time-of-flight mass spectrum.
(a) Download the time-of-flight mass spectrum file from the course web page. Knowing
that this is a spectrum of aerosol particles in air, and that the points in the spectrum are
separated by 1 ns, determine the calibration equation and parameters to convert point
number (ns) into m/z.
(b) Estimate and plot the mass spectrometer resolution (FWHM definition) vs. m/z
(choose 10 ions across the range of m/z). Is the resolution constant with m/z? Why?
(c) Focus on the largest two ions in the spectrum. Are their shapes approximately
Gaussian? Is there any major deviation from that assumption?
(d) Could you separate N2+ and CO+ with the resolution in this spectrum?
Problem 2.2. Simulation and optimization of the Lab MALDI-TOFMS. In this
problem you will simulate the time-of-flight mass spectrometer used in Lab #1 using
Igor. You need to turn in your Igor experiment via email to Jose. Include a notebook on
the top of your Igor experiment that details the functions that need to be executed to
generate the answers to each of the parts of the problem below.
V1
V2
Vg
Detection
Region
Flight Tube
Sample Plate
Oscilloscope
PC
In this problem, you will predict the distribution of recorded flight times for the singly
charged protonated ions of the following 3 peptides:
- Angiotensin II
- Angiotensin I
- Glu1 fibrinopeptide B
mH+ = 1046.62 Da
mH+ = 1296.69 Da
mH+ = 1570.68 Da
The basic schematic above is identical to the sketch of the linear TOFMS that you will
use in lab #1.






The distance (d1) between the back plate (V1) and the first grid (V2) is 0.39 cm
The distance (d2) between the first grid and the grid at the beginning of the drift
region (Vg) is 1.48 cm
The total length of the drift region (D) between Vg and the detector is 128.9 cm
The voltage applied V1 is 20 kV
The voltage applied to V2 for extraction is 90% of the voltage applied to V1, or
18 kV.
Vg and the detector are held at ground.
Questions:
(a) What resolving power do we need to resolve the flight times of the 3 ions (FWHM
definition)?
(b) Draw the mass spectrometer and grids in an Igor graph. (Igor trick: define the vertices
of the instrument as points on two waves, x_inst and y_inst, and just display y_inst vs
x_inst).
(c) Calculate and plot the X position vs. time-of-flight (with TOF = 0 for the laser shot)
for each of the 3 types ions, assuming that they originate at the sample plate with zero
initial velocity.
(d) Simulate the trajectories of the three ions simultaneously on top of the instrument
drawing of part (b) as an animation in Igor. Offset the ions slightly in the y-direction for
clarity.
(Igor trick: to do an animation, just create for each ion two 1-point waves that contain the
X and Y positions at a given point in time. Then step thru the calculated positions at
regular intervals with the following instructions:
DoUpdate
Sleep /T 4
(You can change the “4” to other numbers >= 1, to change the speed of the
animation)
(e) Effect of the initial distribution of ion velocities. A key problem that limits the MS
resolution in MALDI experiments is that there is a wide distribution of initial ion
velocities in the X-direction. We will assume that this distribution of velocities for
Angiotensin I is a lognormal distribution with a mean of 500 m/s and a standard deviation
of 500 m/s. Simulate the peak shape of the mass spectrum of Angiotensin I, by means of
a Monte Carlo simulation of 1000 ions in Igor. What is the resolution of the mass
spectrometer (in mass space, not time space) under these conditions? How does it
compare with what you saw in the lab when using linear mode and no delayed
extraction? What do you conclude from this comparison?
(f) As an alternative solution for (e), simulate the trajectories of 10 ions that represent the
probability-weighed center of the 10 deciles of this lognormal distribution (i.e. the ions
that delimit probabilities of 5%, 15%...). Estimate the spectrometer resolution from these
simulations. How does it compare with what you obtained under (e)?
(h) Effect of delayed extraction. As discussed in class, this is a strategy used to increase
the resolution of the TOFMS when the distribution of initial ion velocities is wide as in
this case. Using the technique on (e), determine the optimum resolution of the mass
spectrometer and the optimum extraction delay. How do these compare with what you
saw in the lab using linear mode, and with the manufacturer specifications?
(g) Reflectron. Now assume that the instrument is operated in reflectron mode. Assume
that the reflectron is located 110 cm away from the Vg grid, that the physical depth of the
reflectron is 10 cm, and that the detector for reflectron mode is located 4 cm before the
start of the reflectron. Ignore the motion on the Y direction. Draw this version of the
instrument in Igor.
(h) The entrance of the reflectron is at ground, and the back of the reflectron is set at 21
kV, while the mid-point of the reflectron is set at 10.5 kV. We will assume that the
voltage varies linearly between these points. What is the resolution obtained for the
angiontensin ions in this case? Assume that no delayed extraction is used. (using the
Monte Carlo simulation method).
(i) Now optimize the reflectron by changing the voltages of the mid-point and the back of
the reflectron independently. What are the optimum voltage settings and the optimum
resolution for angiotensin I, and what resolution is obtained? How does this compare with
what you obtained in the lab, and with the manufacturer specifications?
(j) Bonus points: now optimize delayed extraction and reflectron settings together (3
parameters to optimize, i.e. extraction delay, reflectron mid-point voltage, and reflectron
backplane voltage). Is there much of a difference when optimizing the delayed extraction
and reflectron together, vs. separately?