3.2.2 Computational methods
3.2.2.4 Collision simulation and analysis
The following computational method (Table 3.4) was adopted in order to simulate the CID within the ESI instrument. Once parent clusters are obtained, as described previously, these are used as starting points for collision simulations, without further optimisation. This simulates the experimental process, as the gas- phase parent clusters would not be expected to be at an energetic minimum.
Table 3.4 – Collision simulation (molecular dynamics) conditions.
Times (ps) Temperatures (K)
Heat time 0.5 Starting Temp 300
Run time 25 Run Temp Varied
Cool time 5 Final Temp 300
Step size 0.0005 Temperature step 15
Collision simulations were carried out by performing molecular dynamics calculations, at a range of run temperatures, on all parent clusters from n = 3 to n = 10, for both ligand systems. These simulations ranged from temperatures where there was no dissociation, through to temperatures where the remaining cluster is approximately 25% of the initial size. This sampling regime led to a wide range of simulation energies, with some parent clusters sampled at more than 20 different energies, all at 50K intervals.
Each collision simulation was analysed individually to determine the size of the daughter (referred to as n`) cluster that remained after each simulation is ‘cooled’. Appropriate non-bonding interactions were accounted for when determining the size of the remaining n` cluster, as the dG residues were required to be interacting (directly or indirectly) with the platinum-containing moiety.
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This extensive range of internal energies allowed for the accumulation of a sufficient data set for statistical analysis.
3.2.2.4.1 Statistical analysis
A probabilistic analysis was used to determine the relative proportion of each of the different n` clusters arising from all of the simulations of each parent cluster, whereby the most abundant n` cluster (the ‘magic number’) can be identified. The analysis utilizes a linear approximation of a Gaussian distribution curve, Fig. 3.8.
Figure 3.8 – Linear approximation (red) of a Gaussian Probability Curve (black)
The analysis of the simulation results required some assumptions to be made, which were drawn purely from the experimental procedure before the statistical analysis was carried out. The assumptions used were:
1. Due to the degree of randomness regarding the collisions in the ion trap of the ESI-MS/MS, a range of collision energies is produced that would be reasonably expected to follow a standard Gaussian probability curve. Whilst some clusters would receive passing blows and other clusters may be involved in secondary collisions, most clusters would be expected to receive an ‘average’ amount of energy. As these collisions occur many times in the instrument, an approximation of a Gaussian-type curve would reasonably be expected to arise, Fig 3.9. Pr ob ability Internal Energy
0 0.2 0.4 0.6 0.8 1 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 Simulation Temperature (K) P
Figure 3.9 – The assignment of P values to simulation temperatures for the n = 5 dien example. The black area estimates the range of energies available in the CID of the ESI- MS/MS, and the red lines represent the discrete sampling by the computational collisions, where the ‘Simulation Temperature’ is equivalent to the ‘Run Temp’ in Table 3.4 above.
2. The increase in internal energy experienced by the clusters at the time of, and immediately after, collision in the instrument has been modelled as an appropriate increase in the in silico simulation temperature, Fig 3.9. With this assumption, the ‘temperature’ of simulation is a representation of the internal energy of the cluster, rather than the actual temperatures reached within the ion trap. Also, the relatively long ‘run time’ of the simulation (25 ps) where the cluster is held at a particular temperature, is designed to account for secondary collisions within the ion trap. Secondary collisions imply that when some clusters, which have collided once, may further collide within the ion trap, hence leading to a delay in energy dissipation.
3. The range of possible internal energies of the clusters within the ion trap increases as the size of the cluster increases. This is due to the fact that a larger cluster has a larger surface to be collided, and therefore has a higher probability of receiving a “passing blow” (a lower amount of energy). Also, a larger surface also increases the probability of secondary or multiple collisions, leading to energies greater than the ‘normal’ being received.
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The value used to define the probability in the remainder of the Chapter is Sum(P), where the probability of that particular energy occurring in the ion trap is P, an arbitrary value representative of an approximation of Gaussian behaviour. Sum(P) is the addition of all P values for like n¢ clusters. Fig. 3.10 and Tables 3.5 and 3.6 illustrates an example of this method using the n = 5 collision data for the dien ligand, including a graphical representation of the assignment of P.
Table 3.5 – Probability data for the n = 5 dien collisions, determined computationally.
Simulation Temp. (K) n¢ P 850 5 0.2 900 4 0.4 950 4 0.6 1000 5 0.8 1050 5 1 1100 4 0.8 1150 3 0.6 1200 3 0.4 1250 3 0.2
Table 3.6 – Sum (P) values for the data from the above table. Note the parent cluster size, in this case n¢ = 5, is not included in the Sum (P) table.
Cluster size (n¢) Sum (P)
1 0
2 0
3 1.2
4 1.8
At this point, a note regarding the nomenclature used in the following discussion needs to be made. When referring to parent cluster size, i.e. clusters before collisions, n shall refer to the number of dG residues in that particular cluster. For clusters that have been subjected to the collision method, the number of dG residues in that cluster is denoted by n¢.
0 0.2 0.4 0.6 0.8 1 1.2 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 Simulation Temperature (K) P n' = 3 n' = 4 n = 5 Gaussian approximation
Figure 3.10 – A plot of the data from Tables 3.5 and 3.6, including a representation of the Gaussian approximation. The Sum (P) values for this data are presented below.
This method is repeated for all parent cluster sizes for both carrier ligands. The results of this method, compared to the ESI-MS/MS results, are presented in the results and discussion section.