A method for moving charges in a coarse-grained simulation of gas-phase proteins is presented which uses a Monte Carlo approach to move charges between charge sites. The method is used to study the role of charge movement in the dissociation mechanism of protein complexes in order to better understand experimentally observed mass spectra from CID studies. The charge hopping process is analyzed using energy distributions and a pair correlation plot. Hopping rates, charge distributions, and structural parameters (radius of gyration and RMSD) are also calculated. The importance of charge movement for the unfolding of protein complexes is demonstrated. The algorithm is implemented in the GROMACS molecular dynamics software package. In this study, transthyretin (TTR) tetramer is used with the MARTINI force field as a model system, and comparisons to experiments are made. The hopping and unfolding are found to be controlled by the Coulomb repulsion among the charges in the complex.

A series of calculations, varying from simple electrostatic to more detailed semi-empirical based molecular dynamics ones, were carried out on charged gas phase ions of the cytochrome c dimer. The energetics of differing charge states, charge partitionings, and charge configurations were examined in both the low and high charge regimes. As well, preliminary free energy calculations of dissociation barriers are presented. It is shown that one must always consider distributions of charge configurations, once protein relaxation effects are taken into account, and that no single configuration dominates. All these results also indicate that in the high charge limit, the dissociation of protein complex ions is governed by electrostatic repulsion from the net charges, the consequences of which are enumerated and discussed. There are two main trends deriving from this, namely that charges will move so as to approximately maintain constant surface charge density, and that the lowest barrier to dissociation is the one that produces fragment ions with equal charges. In particular, it is shown that the charge-to-mass ratio of a fragment ion is not the key physical parameter in predicting dissociation products. In fact, from the perspective of the division of total charge, many dissociation pathways reported to be "asymmetric" in the literature should be more properly labelled as "symmetric" or "near-symmetric". The Coulomb repulsion model assumes that the timescale for charge transfer is faster than that for protein structural changes, which in turn is faster than that for complex dissociation. One challenge in using mass spectrometry for the general analysis of protein complexes is understanding the dissociation mechanism of these complexes in the gas phase. Many groups [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have reported asymmetric dissociation behaviour for large multimeric proteins. A small subunit, typically a protein monomer, is ejected from the complex during dissociation, with the monomer carrying away a disproportionate amount of charge for its relative mass. Understanding the cause of this phenomenon will help to improve our understanding of the structural properties of noncovalent complexes.It is important to investigate how these dissociations occur and the factors that influence them. Using Fourier-transform mass spectrometry (FTMS), Jurchen and Williams [6] have conducted a number of studies in order to understand the origin of these charge distributions. In these experiments, isolated charge states of cytochrome c dimer were dissociated by sustained off-resonance irradiation collisionally activated dissociation (SORI-CAD). According to Jurchen and Williams [6], the asymmetric charge distribution depends upon charge state, dissociation energy, and conformational flexibility. These studies showed that higher charge states lead to symmetric charge products while lower charge states lead to an asymmetric charge dissociation pathway. Further, their results with different excitation energies show ...

Avoided crossings, conical intersections, and low-lying excited states with a single reference method: The restricted active space spin-flip configuration interaction approach J. Chem. Phys. 137, 084105 (2012); 10.1063/1.4747341Quantum-classical Liouville approach to molecular dynamics: Surface hopping Gaussian phase-space packets A semiclassical approach to intensefield abovethreshold dissociation in the long wavelength limit This paper is a companion to our recently published semiclassical formalism for treating time-dependent Hamiltonians ͓J. Chem. Phys. 105, 4094 ͑1996͔͒, which was applied to study the dissociation of diatomic ions in intense laser fields. Here two fundamental issues concerning this formalism are discussed in depth: conservation principles and coherence. For time-dependent Hamiltonians, the conservation principle to apply during a trajectory hop depends upon the physical origin of the electronic transition, with total energy conservation and nuclear momentum conservation representing the two limiting cases. It is shown that applying an inappropriate scheme leads to unphysical features in the kinetic energy of the dissociation products. A method is introduced that smoothly bridges the two limiting cases and applies the physically justified conservation scheme at all times. It is also shown that the semiclassical formalism can predict erroneous results if the electronic amplitudes for well-separated hops are added coherently. This is a fundamental problem with the formalism which leads to unphysical results if left unattended. Alternative schemes are introduced for dealing with this problem and their accuracies are assessed. Generalization of the well-known Landau-Zener formula to the time-dependent Hamiltonian case is derived, which allows one to significantly decrease the computational overhead involved with the numerical implementation of the semiclassical method. Finally, we show that in strong-field molecular dissociation a trajectory can ''surf'' a moving avoided crossing. In this case the hopping probability is a sensitive function of the interference between two closely spaced avoided crossing regions.

A new semiclassical formalism has been developed to treat Hamiltonians having explicit time dependence, with particular application to the dissociation of diatomic ions in intense laser fields. Based on this formalism, a hopping algorithm is presented which specifies how classical trajectories should be moved between coupled electronic surfaces. The theory is laid out in a rigorous, general form and an analysis is also presented for the case where only two electronic surfaces are strongly coupled. In addition, valuable physical insight into the hopping process is obtained by considering the theory in a number of physically relevant limiting cases. From this insight a number of guidelines are proposed which detail the manner in which trajectory hopping should be implemented when time-dependent potential energy surfaces are present, including the effects of phase coherence and conservation principles.

Free energies are calculated for the protonated cytochrome c' dimer ion in the gas phase as a function of the center of mass distance between the monomers. A number of different charge partitionings are examined as well as the behavior of the neutral complex. It is found that monomer unfolding competes with complex dissociation and that the relative importance of these two factors depends upon the charge partitioning in the complex. Symmetric charge partitionings preferentially suppress the dissociation barrier relative to unfolding, and complexes tend to dissociate promptly with little structural changes occurring in the monomers. Alternatively, asymmetric charge partitionings preferentially lower the barrier for monomer unfolding relative to the dissociation barrier. In this case, the monomer with the higher charge unfolds before the complex dissociates. For the homodimer considered here, this pathway has a large free energy barrier. The results can be rationalized using schematic two-dimensional free energy surfaces. Additionally, for large multimeric complexes, it is argued that the unfolding and subsequent charging of a single monomer is a favorable process, cooperatively lowering both the unfolding and dissociation barriers at the same time.