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An SU(5) grand unified theory model is used to show how the degeneracy between vacua with different spontaneously broken charge parity can be dynamically lifted by a condensate of heavy fermion pairs. This drives a phase transition to a unique vacuum state with definite charge parity. The transition eliminates the domain walls in a matter antimatter symmetric domain cosmology.
A computational approach that has been used extensively in the last two decades for Hall thruster simulations is to solve a diffusion equation and energy conservation law for the electrons in a direction that is perpendicular to the magnetic field, and use discrete-particle methods for the heavy species. This "hybrid" approach has allowed for the capture of bulk plasma phenomena inside these thrusters within reasonable computational times. Regions of the thruster with complex magnetic field arrangements (such as those near eroded walls and magnets) and/or reduced Hall parameter (such as those near the anode and the cathode plume) challenge the validity of the quasi-one-dimensional assumption for the electrons. This paper reports on the development of a computer code that solves numerically the 2-D axisymmetric vector form of Ohm's law, with no assumptions regarding the rate of electron transport in the parallel and perpendicular directions. The numerical challenges related to the large disparity of the transport coefficients in the two directions are met by solving the equations in a computational mesh that is aligned with the magnetic field. The fully-2D approach allows for a large physical domain that extends more than five times the thruster channel length in the axial direction, and encompasses the cathode boundary. Ions are treated as an isothermal, cold (relative to the electrons) fluid, accounting for charge-exchange and multiple-ionization collisions in the momentum equations. A first series of simulations of two Hall thrusters, namely the BPT-4000 and a 6-kW laboratory thruster, quantifies the significance of ion diffusion in the anode region and the importance of the extended physical domain on studies related to the impact of the transport coefficients on the electron flow field.
The transport of protons across membranes is an essential process for both bioenergetics of modem cells and the origins of cellular life. All living systems make use of proton gradients across cell walls to convert environmental energy into a high-energy chemical compound, adenosine triphosphate (ATR), synthesized from adenosine diphosphate. ATR, in turn, is used as a source of energy to drive many cellular reactions. The ubiquity of this process in biology suggests that even the earliest cellular systems were relying on proton gradient for harvesting environmental energy needed to support their survival and growth. In contemporary cells, proton transfer is assisted by large, complex proteins embedded in membranes. The issue addressed in this study was: how the same process can be accomplished with the aid of similar, but much simpler molecules that could have existed in the protobiological milieu? The model system used in the study contained a bilayer membrane made of phospholipid, dimyristoylphosphatidylcholine (DMPC), which is a good model of the biological membranes focusing cellular boundaries. Both sides of the bilayer were surrounded by water which simulated the environment inside and outside the cell. Embedded in the membrane was a fragment of the Influenza-A M2 protein and enough sodium counterions to maintain system neutrality. This protein has been shown to exhibit remarkably high rates of proton transport and, therefore, is an excellent model to study the formation of proton gradients across membranes. The Influenza M2 protein is 97 amino acids in length, but a fragment 25 amino acids long, which contains a transmembrane domain of 19 amino acids flanked by 3 amino acids on each side, is sufficient to transport protons. Four identical protein fragments, each folded into a helix, aggregate to form small channels spanning the membrane. Protons are conducted through a narrow pore in the middle of the channel in response to applied voltage. This channel is large enough to contain water molecules, and is normally filled with water. In analogy to the mechanism of proton transfer in some other channels, it has been postulated that protons are translocated along the network of water molecules filling the pore of the channel. This mechanism, however, must involve an additional, important step because the channel contains four histidine amino acid residues, one from each of the helices, which are sufficiently large to occlude the pore and interrupt the water network. The histidine residues ensure channel selectivity by blocking transport of small such as sodium or potassium. They have been also implicated in gating protons due to the ability of each histidine to become positively charged by accepting an additional proton. Two mechanisms of gating have been proposed. In one mechanism, all four histidines acquire an additional proton and, due to repulsion between their positive charges, move away from one another, thus opening the channel. The alternative mechanism relies of the ability of protons to move between different atoms in a molecule (tautomerization). Thus, a proton is captured on one side of the gate while another proton is released from the opposite side, and the molecule returns to the initial state through tautomerization. The simulations were designed to test these two mechanisms. Large-scale, atomic-level molecular dynamics simulations of the channel, in which the histidine residues were in different protonation states revealed that all intermediate states of the system involved in the tautomerization mechanism are structurally stable and the arrangement of water molecules in the channel is conducive to the proton transport. In contrast, in the four-protonated state, postulated to exist in the gate-opening mechanism, the electrostatic repulsion between the histidine residues appears to be so large that the channel looses its structural integrity and one helix moves away from the remaining three. This result indicates that such a mechanism of proton transport is unlikely. The simulations revealed that translocation along a network of water molecules in the channel and tautomerization of the histidine residues in the M2 proteins in the most likely mechanism of proton transport. The results not only explain how a remarkably simple protein system can efficiently aid in the formation of proton gradients across cell walls, but also suggest how this system can be genetically re-engineered to become a directional, reversible proton pump. Such a pump can provide energy to laboratory-built models of simple cellular systems. If they were successfully constructed it would greatly advance our understanding of the beginnings of life and find important applications in medicine and pharmacology.
The transport of protons across membranes is an essential process for both bioenergetics of modern cells and the origins of cellular life. All living systems make use of proton gradients across cell walls to convert environmental energy into a high-energy chemical compound, adenosine triphosphate (ATP), synthesized from adenosine diphosphate. ATP, in turn, is used as a source of energy to drive many cellular reactions. The ubiquity of this process in biology suggests that even the earliest cellular systems were relying on proton gradient for harvesting environmental energy needed to support their survival and growth. In contemporary cells, proton transfer is assisted by large, complex proteins embedded in membranes. The issue addressed in this Study was: how the same process can be accomplished with the aid of similar but much simpler molecules that could have existed in the protobiological milieu? The model system used in the study contained a bilayer membrane made of phospholipid, dimyristoylphosphatidylcholine (DMPC) which is a good model of the biological membranes forming cellular boundaries. Both sides of the bilayer were surrounded by water which simulated the environment inside and outside the cell. Embedded in the membrane was a fragment of the Influenza-A M$_2$ protein and enough sodium counterions to maintain system neutrality. This protein has been shown to exhibit remarkably high rates of proton transport and, therefore, is an excellent model to study the formation of proton gradients across membranes. The Influenza M$_2$ protein is 97 amino acids in length, but a fragment 25 amino acids long. which contains a transmembrane domain of 19 amino acids flanked by three amino acids on each side. is sufficient to transport protons. Four identical protein fragments, each folded into a helix, aggregate to form small channels spanning the membrane. Protons are conducted through a narrow pore in the middle of the channel in response to applied voltage. This channel is large enough to contain water molecules. and is normally filled with water. In analogy to the mechanism of proton transfer in some other channels, it has been postulated that protons are translocated along the network of water molecules filling the pore of the channel. This mechanism, however, must involve an additional important step because the channel contains four histidine amino acid residues, one from each of the helices, which are sufficiently large to occlude the pore and interrupt the water network. The histidine residues ensure channel selectivity by blocking transport of small ions, such as sodium or potassium. They have been also implicated in gating protons due to the ability of each histidine to become positively charged by accepting an additional proton. Two mechanisms of gating have been proposed. In one mechanism, all four histidines acquire an additional proton and, due to repulsion between their positive charges, move away from one another, thus opening the channel. The alternative mechanism relies of the ability of protons to move between different atoms in a molecule (tautomerization). Thus, a proton is captured on one side of the gate while another proton is released from the opposite side, and the molecule returns to the initial state through tautomerization. The simulations were designed to test these two mechanisms. Large-scale, atomic-level molecular dynamics simulations of the channel with the histidine residues in different protonation states revealed that all intermediate states of the system involved in the tautomerization mechanism are structurally stable and the arrangement of water molecules in the channel is conducive to the proton transport. In contrast, in the four-protonated state, postulated to exist in the gate-opening mechanism, the electrostatic repulsion between the histidine residues appears to be so large that the channel loses its structural integrity and one helix moves away from the remaining three. Additional information is contained within the original extended abstract.