Quantum Theory on Glucose Transport Across Membrane

After a brief review of the protein folding quantum theory and a short discussion on its experimental evidences the mechanism of glucose transport across membrane is studied from the point of quantum conformational transition. The structural variations among four kinds of conformations of the human glucose transporter GLUT1(ligand free occluded, outward open, ligand bound occluded, and inward open)are looked as the quantum transition. The comparative studies between mechanisms of uniporter (GLUT1) and symporter (XylE and GlcP) are given. The transitional rates are calculated from the fundamental theory. The monosaccharide transport kinetics is proposed. The steady state of the transporter is found and its stability is studied. The glucose (xylose) translocation rates in two directions and in different steps are compared. The mean transport time in a cycle is calculated and based on it the comparison of the transport times between GLUT1,GlcP and XylE can be drawn. The non-Arrhenius temperature dependence of the transition rate and the mean transport time is predicted. It is suggested that the direct measurement of temperature dependence is a useful tool for deeply understanding the transmembrane transport mechanism. *Email : [email protected] Recently, the crystal structures of several bacterial and human monosaccharide transporters were reported [1-4]. Through sequential and structural comparison with other members of the sugar porter subfamily, the basic transport mechanism of the human glucose GLUT1 is clarified [4]. It was proposed that the successive conformational changes of the transporter occur in the glucose transport process and form a complete cycle, from ligand free occluded conformation (A), changed to outward open (B), ligand bound occluded (C), and inward open (D), then to the ligand free occluded of the next cycle. The conformation A is connected to the intracellular side and the conformation C to the extracellular side. The above picture provides a basis for understanding the general transport dynamics for sugar porter subfamily. However, more detailed and quantitative analysis is necessary. Since the glucose transport is essentially a process associated with a series of conformational changes of the porter protein we shall discuss the problem by using the quantum theory of protein 2 conformation transition which was developed in recent years by the author [5][6][7]. 1 Quantum transition between conformational states 1.1 Conformational change as torsion transition Considering that the torsion vibration energy 0.03-0.003 ev is the lowest in all forms of biological energies, even lower than the average thermal energy per atom at room temperature and easily changed at physiological temperature, we can look upon the torsion as the slow variable of the macromolecule. Following Haken’s synergetics, the slow variables always slave the fast ones of a complex system. By taking a general form of the torsion Hamiltonian H1 and the fast variable Hamiltonian H2 and by the adiabatically elimination of fast variables we obtained a Hamiltonian describing the conformational transition of the macromolecule and deduced a general formula for the conformational transition rate [5].