Mathematical Sciences for Artificial Intelligence

Module I - The cell: nucleic acids, organelles, cell membranes. - The neuron and its functional domains; non neuronal cells (glia) and neuron-glia interplay. - Membrane potentials; ionic equilibrium; Nernst equation; Gibbs-Donnan equilibrium; electrochemical equilibrium and Goldman equation. - Structure and function of ionic channels; techniques for measuring ionic currents; passive properties of cell membranes: capacitance and conductance. - Electrophysiological recordings; membrane potentials and currents: patch clamp, intracellular recordings, extracellular recordings, multi electrode array (MEA). - Passive propagation of electrical signals: the cable theory, time constant, space constant. Electrotonic potentials (graduated). - Active properties of membranes: action potential, its ionic basis and modality of propagation; voltage-activated ionic channels; Action potential propagation and factors modulating its velocity; voltage clamp. - Electrical synaptic transmission. - Chemical synaptic transmission; mechanism of neurotransmitter release: proteins involved in the neurotransmitter liberation, depolarization-release coupling, quantal release; role of calcium; “classical” neurotransmitters and neuromodulators. - Neurotransmitter receptors: Ionotropic receptors (ligand-activated ionic channels); gating mechanisms. Metabotropic receptors: transduction signaling pathways. - Postsynaptic potentials; Inversion potential; Excitatory and inhibitory synapses. - Reticular theory and neuron doctrine: Golgi, Cajal and Sherrington. Synaptic integration. Temporal and spatial summation of postsynaptic potentials. Active properties of dendrites.

Although the course will begin with an introduction to the cell, its organelles, and nucleic acids, it is strongly recommended that students review these topics in advance, as well as the basic concepts of physics, by referring to the textbooks used during high school. This preliminary preparation will allow students to engage more effectively with the course content and to better grasp its interdisciplinary connections.

TEXTBOOKS For in-depth study and review of the topics covered in the lectures, the following textbook is recommended: - Neuroscience (5th American Edition), edited by Purves, Augustine, Fitzpatrick, Hall, LaMantia, Mooney, Platt, and White. Alternatively, the following textbooks are recommended: - Neuroscience: Exploring the Brain, by Bear, Connors, and Paradiso. - Principles of Neural Science (6th American Edition), edited by Kandel, Koester, Mack, and Siegelbaum. Additional teaching materials, including lecture notes, will be available on the course webpage on Sapienza's e-learning site.

The course includes a series of lectures, through which students will learn the basic fundamentals of neuroscience. To this end, the first part of the course will focus on the study of the animal cell in general (structure and function of cell organelles, nucleic acids, cell membranes; protein synthesis; physico-chemical characteristics of intra- and extra-cellular environments), for then address the nerve cell, its biophysical characteristics, electrical and functional properties. The second part of the course will introduce the student to the study of complex neuronal circuits, which imply specific brain functions. Between one module and the next, you can decide to insert an ongoing test in agreement with the students

Attendance is not mandatory, but it is strongly recommended in order to gain a more thorough and informed understanding of the subject.

The exam is designed to assess both the level of knowledge and understanding of the topics covered in the syllabus, as well as the student’s reasoning skills. The exam consists of a written test made up of multiple-choice questions. Each question includes four answer options, with only one correct answer. The final grade is expressed in thirtieths: the minimum passing grade is 18/30, and the maximum grade is 30/30 with honors. Students may choose between two exam formats: - A single exam at the end of the course - Two midterm exams: one halfway through the course and one at the end. In this case, the final grade will be the arithmetic average of the two scores. If the final score of the written test is 27/30 or higher, students may request an optional oral question to potentially improve their grade. The final increment will be determined based on the oral performance.

Teaching will be carried out with face-to-face lectures. The presentation of the topics will be supported by the projection of explanatory slides. The slides of the lessons, as well as any didactic material that the teacher deems useful to provide for individual study, will be made available to students on the Moodle platform.