**Introduction**

Matrix-assisted laser desorption ionization (MALDI) time-of-flight mass spectrometry (TOF MS) is a powerful technique in the study of polar macromolecules such as peptides, proteins, and DNA. The ionization technique, MALDI, was introduced by Karas and Hillenkamp in 1988 and is a method of producing ions of large polar molecules like peptides and proteins. The analyzer, TOF MS, is most commonly coupled to a MALDI ion source. TOF MS has several advantages over other analyzers (*e.g*., quadrupoles, sectors) for the analysis of MALDI formed ions. For example, the m/z range is unlimited, all m/z values are recorded in each acquisition, and the pulsed lasers used to form the ions couples well with the TOF measurement. Initially, the mass resolution of MALDI TOF MS was very poor and the accuracy of the mass measurements was not very good either. The typical resolution was 100 m/Δm and the accuracy of the mass measurements was no better than 0.1% (1 in 1000). The resolution and signal-to-noise ratio (S/N) ultimately limit the most important feature of mass spectrometry, the mass measurement accuracy. If two signals coalesce the resolution and accuracy of each signal is distorted. Until a few years ago, the variables of the MALDI process limited the S/N, resolution, and ultimately, the mass measurement accuracy of the TOF analyzer. However, when the time-lag focusing principles of Wiley and McLaren are incorporated into today’s mass spectrometers, the deleterious effects of the MALDI process on the performance of a TOF analyzer are reduced, if not completely removed, and mass resolution increases dramatically.

The general procedure of time-lag focusing is to introduce a time delay between ionization and extraction of the ions out of the ion source into the drift tube of the analyzer. Ions are extracted from the source by pulsing and electric potential (voltage) after the time delay expires. The time delay and extraction potential are tuned to minimize the arrival time distribution of the ions at the detector. The following discussion is directed toward gaining an understanding of the affect of the time delay and extraction potential on the arrival time distribution of the ions so that the user can perform resolution optimization.

It is important to have a basic understanding of the events that occur during the MALDI process to appreciate how time-lag focusing affects resolution in TOF analysis. Optimization of the experimental operating parameters can be easily obtained as soon as the user knows the basics. The MALDI process has numerous variables, both physical and chemical, that limit the performance of the TOF analyzer. Figure 1 contains a picture of the MALDI process that we think represents the major events that occur during desorption and ionization. The sample (matrix and analyte) is deposited onto a surface and introduced into the vacuum system of the mass spectrometer. To form ions, the sample is irradiated with a pulsed laser beam. The light energy absorbed by the sample results in a rapid heating and expansion. The rapid heating and expansion against the vacuum results in a supersonic jet that carries matrix and analyte away from the surface. The molecules and ions move away from the surface with some velocity, v_{o}. The initial velocity of ions was determined by numerous research groups and ranges from ~200 to 1000 meters per second (m/s). That is, ions of the same m/z have different initial velocities. Also, the initial velocity is not dependent on the mass of the ion; therefore, as mass increases so does the energy of the ion. At first the is may not seem so important, but as you become more familiar with TOF MS, the problem of a mass independent initial velocity will be obvious.

Ions gain energy from the electric potential used to extract them from the source. The potential energy, U, is converted to kinetic energy and the ions accelerate to a velocity proportional to the potential energy. The velocity is determined by Equation 1 which is just a rearrangement of the equation for kinetic energy, KE = ? m v^{2}. The initial velocity gained from desorption adds to the velocity gained from the acceleration such that the drift velocity, *v*_{drift}, is the sum of acceleration velocity, *v*_{acc}, and the initial velocity, *v*_{o}. Thus, ions of the same m/z with different initial velocities will arrive at the detector at different times. The affect of the initial velocity on the arrival time distribution of ions is illustrated in Figure 2. Ions with a larger initial velocity have a larger final velocity after being accelerated. Therefore, the ions with higher initial velocity travel faster down the tube of the TOF MS and arrive at the detector first. Ions with lower initial velocity travel slower down the tube of the TOF MS and arrive at the detector later in time than the ions of higher initial velocity. The time difference between the arrival of the fastest ion and the slowest ion of the same m/z determines the peak width.

The concept of time-lag focusing is simple. The sample is irradiated with the pulsed laser in a region free of an electric field. During the time delay, the ions drift with the initial velocity imparted by the desorption event. Ions with a greater initial velocity drift faster than ions of lesser initial velocity; therefore, ions of greater initial velocity move farther away from the point of desorption than ions with lesser initial velocity. After some time, *t*_{delay}, a voltage pulse is applied to create an electric field and accelerate the ions (see Figure 3). If we treat the electric fields as slopes, the ions with greater initial velocity are at a lower point on the slope than ions with lesser initial velocity and obtain less energy from the electric field. Conversely, ions with lesser initial velocity are a higher point on the slope than ions of greater initial velocity and obtain more energy from the electric field. For this experiment to work such that the ions arrive at the detector at the same time, the ion with less initial velocity must gain enough energy from the electric field to catch up to the ion with greater initial velocity. If the delay time and voltage pulse are chosen correctly, the two ions will arrive at some point in space at exactly the same time. Ideally, this focal point is the detector surface. This is where the “tuning” of the instrument is important.

Manipulating the position of the detector to the focal point of the ion source would be impractical. Fortunately, we can fix the detector position and use the time delay and voltage pulse to tune the focal point of the ion source. In general, for a given m/z and initial velocity distribution, greater voltage pulses require shorter time delays and vice versa. A greater voltage pulse creates a greater electric field gradient. With a greater electric field gradient, less spatial separation is required for ions to obtain the energy difference needed for focusing. Likewise, the time delay is directly proportional to the initial velocity and required spatial distribution. So, if a smaller spatial distribution is needed, a shorter time delay is required.

**Simulating Time-Lag Focusing**

A TOF simulation is useful to the user to introduce the effect of modifying the delay time and pulse voltage of the time-lag focusing experiment. Also, a simulation that contains accurate description of the instrument used in an experiment can be used to predict the necessary operating parameters (*e.g*., delay time and pulse voltage) required to obtain high resolution spectra. An accurate mathematical description of the MALDI-TOF MS experiment can be used to construct a simulation experiment. One method of deriving the mathematical expressions for simulating the MALDI-TOF MS experiment is the subject of the remainder of this guide.

Any MS can be broken into two parts: (1) the ion source and (2) the analyzer. The basic Wiley-McLaren type TOF MS has three regions: two regions in the ion source and the field free drift region. Figure 4 contains an illustration of a typical Wiley-McLaren type TOF MS. The important features necessary to simulate the TOF MS experiment are the lengths of the regions and the voltages applied to the electrodes. Knowledge of the exact distances between the electrodes of the ion source is especially critical for the simulation to accurately reflect an actual instrument. In Figure 4, Region I of the ion source is where the ions are formed or introduced into the mass spectrometer and is the first stage of acceleration. The length of Region I is denoted with the letter “s”. Region II is the second stage of acceleration and the length is denoted with the letter “d”. Region III is the field free drift region and the length is denoted with the letter “L”. Standard metric units are used for all constants and variables (*e.g.*, length = meters, mass = kilograms, time = seconds).

The equations used to calculate the TOF of an ion are derived from the standard physics equations of motion. For example, the time in a region of the mass spectrometer containing an electric field can be calculated using Equation 2, where, *v*_{f }is the velocity of the ion as it exits the region, *v*_{i} is the velocity of the ion as it enters the region, and *a* is the acceleration of the region. The velocity is calculated using Equation 1. The acceleration is defined in Equation 3, where, *E* is the electric field strength, *q* is the charge of an electron, and *m* is the mass. The electric field, *E*, is assumed to be linear and is the voltage difference between the electrodes defining the region divided by the length of the region.

The experiment begins with ion formation in Region I of the mass spectrometer. Ions drift away from the sample surface with the initial velocity from desorption. The delay time expires and the ions are accelerated by the applied electric field. The time in Region I, *t*_{s}, is the time it takes the ions to reach Region II and is given in Equation 4. Note: the delay time is omitted from the time in Region I because the TOF clock does not start until the extraction potential is applied to Region I.

The velocity of the ion as it exits Region I, *v*_{s}, is a function of the energy the ion received from the electric field and the initial velocity from the desorption. The velocity, vs, is calculated from using Equation 5. To determine the energy gained from the electric field it is necessary to determine the position of the ion in Region I when the delay time expires. The position of the ion in Region I as the delay time expires is a function of the initial velocity and the delay time and is calculated using Equation 6. The distance traveled is subtracted from the length of Region I to determine the remaining distance the ion will travel in that region. The distance remaining multiplied by the field strength of Region I gives the energy gained by the ion from Region I.

The same procedure is used to calculate the time in Region II. The time in Region II is calculated using Equation 7. The velocity of the ion as it exits Region I is used as the initial velocity in Region II. The velocity exiting Region II, *v*_{d}, is the sum of the velocity with which the ion entered and the velocity gained from the electric potential of Region II and is calculated with Equation 8.

The time in Region III, also known as the drift time, is calculated using Equation 9. The equation is simple because no electric fields are present to accelerate or decelerate the ions.

The total flight time of the ion in the mass spectrometer is the sum of the times in the individual regions and is defined in Equation 10. This simple equation is a function of the initial velocity of the ions, the delay time, electric potentials, and lengths of the regions of the mass spectrometer. Therefore, the complete TOF MS experiment can be simulated.

Ideally, some graphical output is used to plot a variety of flight times based on the variation of instrument parameters. A plot of flight time versus delay time for a single m/z with different initial velocities is useful to illustrate the arrival time distribution of the ions given a set of electric potentials. Figure 4 contains a plot of flight time (microseconds) versus delay time (nanoseconds) of an ion of 1000 m/z that has a range of initial velocities from 500 to 900 m/s. Electric field strengths of 166.7 V/mm and 900 V/mm for Regions I and II, respectively, were used in the calculation. At a delay time of approximately 600 nanoseconds the flight times converge, this is the optimum delay time to obtain the smallest arrival time distribution.

Additional plots of flight time versus delay time can be made where the pulse voltage is modified to illustrate how the flight time and arrival time distribution changes. Iteration of this experiment provides a graphical representation of the “tuning” required to obtain high resolution spectra.