THEORETICAL PHYSICS MODELING OF NEUROLOGICAL PROBLEMS

In this thesis we approach different problems in neurobiology using methods from theoretical physics. The first topic that we studied is the mechanoelectrical transduction at the basis of touch sensation, i.e. the process by which a mechanical signal conveyed during touch is transformed into an electric signal. We investigate how the neural response is generated in the C. elegans and propose a channel gating mechanism to explain the activation of touch receptor neurons by mechanical stimuli. The second part of the thesis is related to our ability of orient ourself and navigate in space. The neural system underlying this ability has been extensively characterized in rats, where the activity of different types of neurons has been found to be correlated with the spatial position of the animal. Grid cells in the rat entorhinal cortex are part of this “neural map” of space; they form regular triangular lattices whose geometrical properties have a modular distribution among the population of neurons. We show that some of the features observed in the system may be explained by assuming that grid cells provide an efficient representation of space. We predict a scaling law connecting the number of neurons within a module and the spatial period of the associated grids. The last problem discussed in this thesis concerns the neurodegenerative Parkinson’s disease. Limb tremor caused by the disease is currently treated by administering drugs and by fixed-frequency deep brain stimulation. The latter interferes directly with the brain dynamics by delivering electrical impulses to neurons in the subthalamic nucleus. We develop a theory to describe the onset of anomalous oscillations in the neural activity that are at the origin of the characteristic tremor. We propose a new feedback-controlled stimulation procedure and show that it could outperform the standard protocol.