Course teached as: B031982 - FISICA DEI SISTEMI COMPLESSI CON APPLICAZIONI Second Cycle Degree in PHYSICAL AND ASTROPHYSICAL SCIENCES Curriculum ASTROFISICA
Teaching Language
Italian / English
Course Content
Advanced statistical physics, stochastic processes, various applications in the physics of biological systems
NG Van Kampen, Stochastic Processes in Physics and Chemisry, Horth Holland
L. Peliti and S. Pigolotti, Stochastic thermodynamics: an introduction, Princeton University Press
R. Phillips, The molecular switch, Princeton University press
P. Nelson, Physical models of living systems, Chiliagon Science
Original research articles provided by lecturers
Learning Objectives
Acquire awareness for modelling, and appropriate analytical and numerical tools to study complex systems of various kinds. The course is decidedly oriented towards the physics of living systems, where 'living' is to be understood in a general sense. It thus ranges from the study of the functioning of biological circuits underlying thermodynamics and the processing of information and life on the molecular and cellular scales, to the interaction of sets of 'active' agents. This last notion encompasses very diverse cases, from the functioning of cellular clusters (many cells interacting with each other), with important applications for example in the understanding of tumours, to the organisation, evolution and exchange of information within sets of organisms that are progressively more complex: from bacterial colonies to societies of human beings.
Particular attention will be paid to fluctuation aspects (deterministic evolution of complex systems vs. their stochastic evolution) and non-equilibrium aspects (the effect in terms of temporal evolution and organisation of populations and information in complex living (active) systems in a general sense, i.e. under the action of various driving forces).
Prerequisites
Statistical mechanics, numerical analysis/computational physics, basic elements of dynamical systems
Teaching Methods
Lectures, collaborative work sessions, seminars
Further information
Type of Assessment
Individual project report to be agreed with instructors and oral examination
Course program
In the first part of the course (Prof. D. Fanelli), an overview of dynamic systems will be given. Reaction-diffusion systems and the concept of pattern formation (à la Turing) will be introduced and discussed. Stochastic processes will be dealt with, with particular emphasis on techniques around the development of van Kampen. The Fokker Planck and Langevin equations will be derived and discussed. Finally, we will introduce and study quasi-cycles.
In the second part of the course (Prof. F. Piazza) we will focus on the study of statistical and computational physics techniques and models in connection with specific practical examples. These will be chosen as far as possible so as to start the study systematically from observational data in the life sciences, both through more recent examples (hot topics) and through more historical topics (insights of fundamental importance). We will systematically revolve around the concepts of thermodynamic equilibrium and out-of-equilibrium, in particular systematically illustrating the importance of thermodynamic consistency in out-of-equilibrium problems for calculating the energy and information cost of non-equilibrium processes. We will also insist on the need to formulate theoretical and computational methods of investigation that are inherently multi-scale.
The topics covered will be a selection (varying from year to year) inspired by the following themes.
Statistical inference methods
Bayesian inference, asymptotic inference and Information. Inference in many dimensions, dimensional reduction and principal component analysis.
Biological circuits, gene and cell regulatory feedbacks, how cells decide who to be, what to do and how to organise themselves.
Introduction to stochastic thermodynamics
Equilibrium vs. non-equilibrium. Local detailed balance. Stochastic entropy, open chemical systems and formulation of network theory of non-equilibrium steady states. Free energy and information transduction in biological systems. The problem of sensitivity in the reading of a chemical signal by a cell. Fluctuation theorems, Jarzynski and Crooks inequalities.
Reaction diffusion in complex spatially extended systems
Multi-scale investigation methods and particle-based simulations. The problem of phase separations in cellular dynamics. The dilemma between equilibrium and non-equilibrium scenarios.
Passive, active diffusion and persistent transport
Energy-consuming movement to follow a gradient. Chemotaxis in bacteria, unicellular organisms and the cells of multicellular organisms. Durotaxis: moving following gradients of mechanical rigidity: the paradox of metastatic invasion. Run and tumble model, computational models of active transport
Paradigmatic examples that will be analysed from various aspects and with various techniques among those listed above and studied in the first part of the course:
Catalytic acceleration of (bio)chemical reactions, enzyme kinetics and The ultra-sensitivity phenomenon. The original Goldbeter-Koshland model and its thermodynamically consistent formulation.
The phosphorylation-dephosphorylation switch: a write/read module underlying cellular information flow.
Kinetic proofreading (Hopfield), original model and thermodynamically consistent formulation. The energy cost of precision in fundamental processes of cellular kinetics.
Brownian ratchet and molecular motors. Entropic pulling. Active transport within the cell.
Signalling switches: excitation-inhibition mechanisms and the concept of balanced inactivation.