Activation of Peptide ions by blackbody radiation: factors that lead to dissociation kinetics in the rapid energy exchange limit

Abstract

Unimolecular rate constants for blackbody infrared radiative dissociation (BIRD) were calculated for the model protonated peptide (AlaGly)(n) (n = 2-32) using a variety of dissociation parameters. Combinations of dissociation threshold energies ranging from 0.8 to 1.7 eV and transition entropies corresponding to Arrhenius preexponential factors ranging from very "tight" (A(infinity) = 10(9.9) s(-1)) to "loose" (A(infinity) = 10(16.8) s(-1)) were selected to represent dissociation parameters within the experimental temperature range (300-520 K) and kinetic window (k(uni) = 0.001-0.20 s(-1)) typically used in the BIRD experiment. Arrhenius parameters were determined from the temperature dependence of these values and compared to those in the rapid energy exchange (REX) limit. In this limit, the internal energy of a population of ions is given by a Boltzmann distribution, and kinetics are the same as those in the traditional high-pressure limit. For a dissociation process to be in this limit, the rate of photon exchange between an ion and the vacuum chamber walls must be significantly greater than the dissociation rate. Kinetics rapidly approach the REX limit either as the molecular size or threshold dissociation energy increases or as the transition-state entropy or experimental temperature decreases. Under typical experimental conditions, peptide ions larger than 1.6 kDa should be in the REX limit. Smaller ions may also be in the REX limit depending on the value of the threshold dissociation energy and transition-state entropy. Either modeling or information about the dissociation mechanism must be known in order to confirm REX limit kinetics for these smaller ions. Three principal factors that lead to the size dependence of REX limit kinetics are identified. With increasing molecular size, rates of radiative absorption and emission increase, internal energy distributions become relatively narrower, and the microcanonical dissociation rate constants increase more slowly over the energy distribution of ions. Guidelines established here should make BIRD an even more reliable method to obtain information about dissociation energetics and mechanisms for intermediate size molecules.

Figure 1

Infrared absorption spectrum of protonated (AlaGly)₂ calculated at the AM1 semiempirical level. Transition dipole moments have been multiplied by 3 (see text). Also shown are the Planck blackbody energy distributions at 300 (dashed line) and 500 K (solid line).

Figure 2

Calculated blackbody infrared radiative dissociation Arrhenius plots for protonated (AlaGly)_n, where n = 4 (•), 8 (▪), 16 (○), and 32 (▴), and for an ion in the rapid energy exchange limit (–). Dissociation parameters of E₀ = 1.5 eV and A^∞ = 10^16.8 s⁻¹ were used. Dashed lines indicate the typical Fourier transform mass spectrometry experimental kinetic window at a magnetic field strength of 2.7 T and for electrospray-generated ions.

Figure 3

Plots of the ratio of calculated blackbody infrared radiative Arrhenius activation energy (E_a) to the calculated rapid energy exchange limit activation energy $(E_a^{\infty })$ as a function of (AlaGly)_n ion size. The E_a is calculated from the master equation model using a rapid energy exchange limit Arrhenius preexponential of (a) 10^9.9, (b) 10^12.4, (c) 10^14.5, and (d) 10^16.8 s⁻¹. Threshold dissociation energies (E₀) and the temperature range necessary to keep the dissociation rate constants within the experimental window are labeled on the graphs.

Figure 4

Boltzmann distributions for (AlaGly)₄ and (AlaGly)₃₂ ions, each determined at 350 (dashed line) and 450 K (solid line) (top). The sum of the absorption (k_1,rad) and emission (k_−1,rad) rate constants for these ions is calculated from the master equation model at 350 (dashed line) and 450 K (solid line); microcanonical dissociation rate constants are calculated from RRKM theory with E₀ = 1.5 eV and transition-state frequencies modeled to fit an A^∞ of 10^16.8 s⁻¹ (bottom).

Figure 5

RRKM dissociation (k_d), sum of the absorption (k_1,rad) and emission (k_−1,rad), and integrated unimolecular dissociation (k_uni) rate constants at 450 K for (AlaGly)₄ (dashed line) and (AlaGly)₃₂ (solid line) ions plotted on an energy scale normalized to a Boltzmann distribution. RRKM dissociation rate constants are calculated for a dissociation process with E₀ = 1.5 eV and A^∞ of 10^16.8 s⁻¹. Integrated k_uni is obtained by integrating the Boltzmann-weighted RRKM dissociation rates over the range from E = 0 to the specified energy fraction of a Boltzmann distribution. The integrated k_uni is equal to the rapid energy exchange limit unimolecular dissociation constant (labeled on graph) when this product is integrated over all energies.