Approximate solution of the time-dependent Kratzer plus screened Coulomb potential in Feinberg-Horodecki equation
Mahmoud Farout, Ramazan Sever, Sameer M Ikhdair
Chinese Physics B, 2020
We obtain the quantized momentum eigenvalues, P n, together with space-like coherent eigenstates for the space-like counterpart of the Schr&# 246; dinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.
The interaction between metabolism and the plasma membrane potential, and intracellular pH
Lancaster University, 2019
Hodgkin and Huxley won a Nobel Prize for their passive model of the squid axon. Their model describes the voltage across a cell plasma membrane, based on measurements in the squid axon. The model explains the generation of action potential. It was published over 60 years ago, however, their model still represents the paradigm in neurobiology . Hodgkin and Huxley used the voltage-clamping method to do their measurements of currents across the membrane of the axon. All measured currents are caused by the diffusion of ions due to their electrochemical gradients. Due to the voltage-clamping method that they used, there was no need to include active transport in their model, therefore, metabolism was ignored in their study. In reality, metabolism is required to produce ATP, which is required to operate the ATPases that regenerates the electrochemical gradient of the cations Na+ and K+ and results in maintenance of the plasma membrane potential . Therefore, it is still unknown how the energy state of a cell is involved in the generation of the plasma membrane potential, and what is the origin of the fluctuations in the voltage across the membrane of a cell. Here we discuss results of free-running whole-cell patch-clamp recordings of the resting membrane potential of jurkat T cells . Since the voltage was not clamped in these experiments, it is plausible to assume that a metabolism is required to pump the cations against their electrochemical gradients. These pumps have been shown to be crucial in maintenance of the plasma membrane potential . To study the interactions between the plasma membrane potential and metabolism, we analysed data recorded in yeast cells in suspension [4, 5]. The measurements include the energy state of the cell evaluated from the intracellular level of ATP in the yeast population, and the mitochondrial membrane potential obtained by a fluorescent recording . In addition, nicotinamide adenine dinucleotide NAD and hydrogen H substance (NADH), plays a role in the chemical process that generates energy for the cell, as well as the intracellular pH were measured. All measured parameters were oscillating over time under aerobic/anaerobic shift. The results were analysed using time series analysis methods that allow for time-localised analyses of the underlying dynamics [7, 8, 9]. We will present results of analysis of interaction between cellular functional processes and argue that the metabolism is driving them. The results suggest that the mitochondrial F0F1-ATPase might be involved in the mechanism by which glycolytic oscillations are driving the oscillations in the mitochondrial membrane potential and the cytosolic pH. The results were modelled as phase oscillators of glycolysis, cytosolic pH and the mitochondrial membrane potential. This model regenerates the signals measured from yeast cells and show approximately the same main mode frequency as the original data.