\chapter[Basics in Mass Spectrometry]{Basics in\\ Mass Spectrometry}

\label{chap:basics-mass-spectrometry}

Mass spectrometry has become a ``buzz word'' in the field of
structural biology. While it has been used for long to measure the
molecular mass of little molecules, its recent developments have
brought it to the center of the analytical arsenal in the field of
structural biology (also of ``general'' polymer science). It is now
current procedure to use mass spectrometry to measure the mass of
polypeptides, oligonucleotides (even complete transfer RNAs!) and
saccharides, amongst other complex biomolecules.

A mass spectrometer is usually described by giving to its three main
different ``regions'' a name suggestive of their function:
\begin{itemize}
\item the source, where production of ionized analytes takes place,
\item the analyzer, where the ions are electrically/magnetically
  ``tortured'',
\item the detector, where the ions arrive, are detected and counted.
\end{itemize}

Before letting Mass Spectrometry in, I would like to state once for
all: \emph{mass spectrometry is aware of ionized molecular species
  only}\dots\\

Now, \emph{enter} Mass Spectrometry\\

\renewcommand{\sectitle}{Ion Production: The Source}
\section*{\sectitle}
\addcontentsline{toc}{section}{\numberline{}\sectitle}

Indeed, mass spectrometry cannot do anything as long as the molecule
to analyze (\emph{analyte}) is not in a charged state. The process of
creating an ion from an un-charged analyte is called
\emph{ionization}. Well, most of the times the ionization is favored
by adapting the sample's pH to a value higher/lower than the
isoelectric pH of the analyte, which will elicit the appearance of (a)
charge(s) onto it. In cases where the analyte cannot be charged by
simple pH variations (small molecule that does not bear any ionizable
chemical group), the ionization step might require --on the massist's
part-- use of starker ionization techniques, like electronic impact
ionization or chemical ionization. In biopolymer mass spectrometry,
the pH strategy is usually considered the right way to proceed. The
ionization process might involve complex charge transfer mechanisms
(not fully understood yet, at least for certain ionization/desorption
methods) which tend to ionize the analyte in a way not predictable by
looking at the analyte's chemical structure.

Ion production should not be uncoupled from one important feature of
mass spectrometry: solvent evaporation --in case of liquid sample
delivery to the mass spectrometer-- and sample \emph{desorption} --in
case of solid state sample introduction. The general idea is that mass
spectrometry works on gas phase ions. This is because it is of crucial
importance, for a correct mass measurement to take place, that the
analyte be \emph{totally} freed of its chemical immediate environment.
That is, it should be ``naked'' in the gas phase. Equally important is
the fact that ions must be capable of travelling long distances
without ever encountering any other molecule in their way.  This is
achieved by pumping very hard in the two regions called ``analyzer''
and ``detector''. In this respect, the source is a special region
because, depending on the design of the mass spectrometer, it might be
partially at the atmospheric pressure during mass spectrometer
operation. It is not the aim of this manual to provide insights into
mass spectrometer design topics (I just would not be able to enter
into the physics details!), but the general principle is that mass
spectrometry involves working on gas phase ions. This is why a mass
spectrometer is usually built on extremely reliable pumping technology
aimed at maintaining for long periods of time (with no sudden
interruption, otherwise the detector might suffer seriously) a good
vacuum in the conduit in which ions must flow during operation.

\renewcommand{\sectitle}{The Analyzer}
\section*{\sectitle}
\addcontentsline{toc}{section}{\numberline{}\sectitle}

Once an ion has been generated in the gas phase, its mass should be
measured. This is a complex physical process. Depending on the mass
spectrometer design, the mass measurement is based on more or less
complex physical events. Magnetic mass spectrometers are usually
thought of as pretty complex devices; this is also the case for the
Fourier transform ion cyclotronic resonance devices. An analyzer like
the \emph{time of flight} analyzer is much more simple. I will refrain
from trying to explain the physics of the mass measurement, just limit
myself saying that --at some stage of the mass measurement process--
forces are exerted on the ions by electric/magnetic fields
(incidentally, this explains why it is so important that an analyte be
ionized, otherwise it would not be subject to these fields). The
ionized analytes submitted to these forces have their trajectory
modified in such a way that the detector should be able to quantify
this modification. Roughly, this is the measurement process.

\renewcommand{\sectitle}{What Is Really Measured?}
\section*{\sectitle}
\addcontentsline{toc}{section}{\numberline{}\sectitle}

Prior to entering into some detail, it seems necessary to make a few
definitions\footnote{Interesting posting signed by Ken I. Mitchelhill
  in the \corpname{ABRF} mailing list at
  \url{http://www.abrf.org/archives}, and a document published by the
  California Institute of Technology.}:
\begin{itemize}
\item unified mass scale (u): IUPAC \& IUPAP (1959-1960) agreed upon
  scale with 1 u equal to 1/12 the mass of the most abundant form of
  carbon; the dalton is taken as identical to u (but not accepted as
  standard nomenclature by IUPAC or IUPAP), it is abbreviaed in Da.
\item a former unit was ``a.m.u.'' (\textit{i.e.} ``atomic mass
  unit''). It should be considered obsolete, since based on an old
  1/16 of $\mathrm{^{16}O}$ standard;
\item the mass of a molecule (also ``molecular mass'') is expressed in
  daltons. The symbol commonly used is ``M'' (not ``m''), as in
  ``M+H'' or ``M+Na''\dots\ Symbol ``m'' is already employed for ion
  mass (as in ``m/z'');
\item the mass-to-charge ratio (``m/z'') of an ion is the ion's mass
  (in daltons) divided by the number (z) of elementary charges. Hence
  ``m/z'' is ``mass per charge'' and units of ``m/z'' are ``daltons
  per charge'';
\item nominal mass: the integral sum of the nucleons in an atom (it is
  also the atomic mass number);
\item exact (also known as accurate) mass: the sum of the masses of
  the protons and neutrons plus the nuclear binding energy;
\end{itemize}

In the previous sections I used to say that a mass spectrometer's task
is to measure masses. Well, this is not 100~\% exact. A mass
spectrometer actually allows to measure something else: it measures
the \emph{$m$ to $z$ ratio} of the analyte, which is denoted
\emph{$m/z$}. What is this ``\emph{$m$ to $z$ ratio}'' all about?
Well, we said above that a mass spectrometer has to exert forces on
the ions in order to determine their $m/z$. Now, let us say that we
have an electric field of constant value, $E$. We also have two ions
of identical masses, one bearing one charge ($q$) and the other one
bearing two charges (2$q$) --positive or negative, no matter in this
discussion. These two ions, when put in the same electric field $E$,
will ``feel'' two different forces exerted on them: $F_1$ and $F_2$.
It is possible to calculate these forces ($F_1=qE$ and $F_2=2qE$).
Evidently, the ion that bears two charges is submitted to a force that
is twice as intense as the one exerted on the singly charged ion.

What does this mean? It means simply that the numeric result provided
by the mass spectrometer is not going to be the same for both ions,
since the physics of the mass spectrometer takes into account the
charge level on each different analyte. Our two ions weigh exactly the
same, but the mass spectrometer simply can not know that; all it knows
is how a given ion reacts to the electric field it is put in. And our
two ions, evidently, will react differently.

When we say that a mass spectrometer measures a $m/z$ ratio, the $z$
of this ratio represents the sum of all the charges (this is a net
charge!) that sit onto the analyte. But what does the $m$ stand for?
The molecular mass? No! The $m$ stands for the mass of the whole
analyte ion, which is --in a word-- the \emph{measured mass}. This
is not the molecular mass (which would be $M$), it is the molecular
mass \emph{plus/less} the mass of the chemical entity that brings the
charge to the analyte. When ionizing a molecule, what happens is that
something brings (or removes) a charge. In biopolymer chemistry, for
example, often the ionization is a simple protonation/deprotonation.
If it is a protonation, that means that an electronic doublet (on some
basic group of the analyte) captures a proton. This brings the mass of
a proton to the biopolymer ($\simeq$ 1 Da). Conversely, if it is a
deprotonation (loss of a proton by some acidic group, say a carboxylic
that becomes a carboxylate) the polymer looses the mass of a proton.
Of course, if the ionization involves a single electron transfer the
mass difference is going to be so feeble as to be un-measurable on a
variety of mass spectrometers.

Let us try to formalize this in a less verbose manner by using a sweet
amino acid as an example:
\begin{itemize}
\item the un-ionized analyte (Glycine) has the following formula:
  $\mathrm{C_2H_5O_2N_1}$; \\
  the molecular mass is thus $M = 75.033$ Da;
\item the analyte gets protonated in the mass spectrometer: 
  \[\mathrm{C_2H_5O_2N_1 + H \rightharpoonup\ C_2H_6O_2N_1}\]
  the measured mass of the ion is thus $m = 75.033 + 1.00782$ Da and
  the charge beared by the ion is thus $z = +1$.
\item the peak value read on the mass spectrum for this analyte will
  thus be:\\
  \[\mathrm{value} = \frac{m}{z} = \frac{M + 1.00782}{z} = 76.04\]
  with $z = +1$
\end{itemize}

We see here that the label on the mass spectrum does not correspond to
the nominal molecular mass of the analyte: the ionizing proton is
``weighed'' with the Glycine molecule.

Imagine now that, by some magic, this same Glycine molecule just gets
protonated a second time. Let's do exactly the same type of
calculation as above, and try to predict what value will be printed
onto the mass spectrum:

\begin{itemize}
\item the un-ionized analyte (Glycine) has the following formula:
  $\mathrm{C_2H_5O_2N_1}$; \\
  the molecular mass is thus $M = 75.033$ Da;
\item the analyte gets protonated in the mass spectrometer \emph{two
    times}: \[\mathrm{C_2H_5O_2N_1 + 2H \rightharpoonup\ 
    C_2H_7O_2N_1}\] the molecular mass of the ion is thus $M = 75.033
  + 2.01564$ Da and the charge beared by the ion is thus $z = +2$.
\item the peak value read on the mass spectrum for this analyte will
  thus be:\\
  \[\mathrm{value} = \frac{m}{z} = \frac{M + 2.01564}{z} = 38.52\]
  with $z = +2$
\end{itemize}

Oh! yes!, this time it is absolutely clear that a $m/z$ is not a
molecular mass! By the way, if the Glycine happened to be ionized
\emph{negatively} the calculation would have been analogous to the one
above, but instead of \emph{adding} the mass of the proton(s) we would
have \emph{removed} it. It is that simple.

Summing up all this in a few words: an ionization involves one or more
charge transfer(s) and in most cases (at least in biopolymer mass
spectrometry) also involves matter transfer(s). It is crucial
\emph{not} to forget the matter transfer(s) when ionizing an analyte.
This means that when an ionization process is described, its
description ought to be complete, clearly stating three different
pieces of information:

\begin{itemize}
\item the charge transfer (net charge that is beared by the analyte
  after the ionization has completed);
\item the matter transfer (optional; usually something like ``+H1'');
\item the ionization level (0 means ``no ionization''; usually this
  would be 1 for a single ionization, but might be as large as 30 if,
  for example, you were ionizing myoglobin with electrospray
  ionization (protonation). In this case the $m/z$ value would be
  computed this way:
  \[\mathrm{value} = \frac{m}{z} = \frac{M + 30\cdot\ 1.00782}{30} =
  \frac{16959 + 30.2346}{30} = 566.30\] with $z = +30$
\end{itemize}

By now, the reader should have grasped the importance of understanding
well the ionization formalisms for accurately predicting/analyzing
mass spectrometric data!
  
In the next chapters of this manual we will describe how \pxm\ works
and how the user might take advantage of its powerful capabilities.
In a first chapter I will introduce some general concepts around the
way the program behaves. Next, in the remaining part of this manual, a
chapter will be dedicated to each important \pxm\ function or
characteristic.

\cleardoublepage



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