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Density of one-particle states for 2-D electron gas in magnetic field
Dubrovskyi
Condensed Matter Physics , 2013,
Abstract: The density of states of a particle in a 2-D area is independent both of the energy and form of the area only at the region of large values of energy. If energy is small, the density of states in the rectangular potential well essentially depends on the form of the area. If the bottom of the potential well has a potential relief, it can define the small eigenvalues as the discrete levels. In this case, dimensions and form of the area would not have any importance. If the conservation of zero value of the angular momentum is taken into account, the effective one-particle Hamiltonian for the 2-D electron gas in the magnetic field in the circle is the Hamiltonian with the parabolic potential and the reflecting bounds. It is supposed that in the square, the Hamiltonian has the same view. The 2-D density of states in the square can be computed as the convolution of 1-D densities. The density of one-particle states for 2-D electron gas in the magnetic field is obtained. It consists of three regions. There is a discrete spectrum at the smallest energy. In the intervening region the density of states is the sum of the piecewise continuous function and the density of the discrete spectrum. At great energies, the density of states is a continuous function. The Fermi energy dependence on the magnetic field is obtained when the field is small and the Fermi energy is located in the region of continuous spectrum. The Fermi energy oscillates and in the average it increases proportionally to the square of the magnetic induction. Total energy of electron gas in magnetic field also oscillates and increases when the magnetic field increases monotonously.
Density of one-particle states for 2D electron gas in magnetic field
I. M. Dubrovskyi
Physics , 2013, DOI: 10.5488/CMP.16.13001
Abstract: The density of states of a particle in a 2D area is independent both of the energy and form of the area only at the region of large values of energy. If energy is small, the density of states in the rectangular potential well essentially depends on the form of the area. If the bottom of the potential well has a potential relief, it can define the small eigenvalues as the discrete levels. In this case, dimensions and form of the area would not have any importance. If the conservation of zero value of the angular momentum is taken into account, the effective one-particle Hamiltonian for the 2D electron gas in the magnetic field in the circle is the Hamiltonian with the parabolic potential and the reflecting bounds. It is supposed that in the square, the Hamiltonian has the same view. The 2D density of states in the square can be computed as the convolution of 1D densities. The density of one-particle states for 2D electron gas in the magnetic field is obtained. It consists of three regions. There is a discrete spectrum at the smallest energy. In the intervening region the density of states is the sum of the piecewise continuous function and the density of the discrete spectrum. At great energies, the density of states is a continuous function. The Fermi energy dependence on the magnetic field is obtained when the field is small and the Fermi energy is located in the region of continuous spectrum. The Fermi energy has the oscillating correction and in the average it increases proportionally to the square of the magnetic induction. Total energy of electron gas in magnetic field also oscillates and increases when the magnetic field increases monotonously.
Identification of a New Epitope in uPAR as a Target for the Cancer Therapeutic Monoclonal Antibody ATN-658, a Structural Homolog of the uPAR Binding Integrin CD11b (αM)
Xiang Xu, Yuan Cai, Ying Wei, Fernando Donate, Jose Juarez, Graham Parry, Liqing Chen, Edward J. Meehan, Richard W. Ahn, Andrey Ugolkov, Oleksii Dubrovskyi, Thomas V. O'Halloran, Mingdong Huang, Andrew P. Mazar
PLOS ONE , 2014, DOI: 10.1371/journal.pone.0085349
Abstract: The urokinase plasminogen activator receptor (uPAR) plays a role in tumor progression and has been proposed as a target for the treatment of cancer. We recently described the development of a novel humanized monoclonal antibody that targets uPAR and has anti-tumor activity in multiple xenograft animal tumor models. This antibody, ATN-658, does not inhibit ligand binding (i.e. uPA and vitronectin) to uPAR and its mechanism of action remains unclear. As a first step in understanding the anti-tumor activity of ATN-658, we set out to identify the epitope on uPAR to which ATN-658 binds. Guided by comparisons between primate and human uPAR, epitope mapping studies were performed using several orthogonal techniques. Systematic site directed and alanine scanning mutagenesis identified the region of aa 268–275 of uPAR as the epitope for ATN-658. No known function has previously been attributed to this epitope Structural insights into epitope recognition were obtained from structural studies of the Fab fragment of ATN-658 bound to uPAR. The structure shows that the ATN-658 binds to the DIII domain of uPAR, close to the C-terminus of the receptor, corroborating the epitope mapping results. Intriguingly, when bound to uPAR, the complementarity determining region (CDR) regions of ATN-658 closely mimic the binding regions of the integrin CD11b (αM), a previously identified uPAR ligand thought to be involved in leukocyte rolling, migration and complement fixation with no known role in tumor progression of solid tumors. These studies reveal a new functional epitope on uPAR involved in tumor progression and demonstrate a previously unrecognized strategy for the therapeutic targeting of uPAR.
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