Course coordination: Prof. Irene Giardina & Prof. Francesco Zamponi
This year Prof. Giardina is on sabbatical and will only teach part of the course. She will however maintain full coordination of the course and of the exam sessions, with the help of Prof. Zamponi.
The course will keep a structure similar to past years, taking advantage of a few visiting professors, who will teach new modular installments.
Course Structure:
Part I: the role of noise, signal/noise discrimination
(brief theoretical background on stochastic processes / chemotaxis /photoreception/other bio examples)
Lecturer: Irene Giardina
Part II: Cell Populations
(introduction to structured populations / growth laws / Simpson's paradox / Phenotypic Switching /Antibiotic persistence/Microbial Game)
Lecturer: Edo Kussel,
Center for Genomics and Systems Biology, New York University
Bio: Prof. Kussell’s work is focused on understanding how bacteria adapt and survive in fluctuating environments. He combines experiments and theory in his lab to address this broad question on several levels, from molecular mechanisms to cellular physiology to population and evolutionary dynamics.
Part III: The Physics of the Immune System
(introduction to the immune system / statistics of immunity / diversity and selection in the immune system)
Lecturer: Federica Ferretti,
National Institute for Theory and Mathematics in Biology, Chicago & Max Planck Institute for the Physics of Complex Systems, Dresden
Bio: Dr Ferretti got her PhD at the Department of Physics, Sapienza, working on irreversibility in active matter. Her research focus then shifted to the adaptive immune system and implicit regularization in population dynamics (MIT & Chicago). She recently moved to MPI-PHS Dresden, as group leader.
Part IV: Interacting biological collectives
(introduction to the physics of interacting systems / introduction to active matter / flocks, swarms and motile cell colonies)
Lecturer: Irene Giardina
Lectures will be held in presence only. The location is
Aula: TBA
Schedule: TBA
Ricevimento: Lun 15-16 - Stanza 504 Ed. Fermi (scrivere per appuntamento / write an email for appointment)
PLEASE NOTE: all students are kindly requested to send an email to irene.giardina@uniroma1.it to subscribe to the course mailing list.
General Program and Texts (to be adjourned)
Past academic years (lectures, program and videorecordings - in english and italian)
Detailed Program and Lectures (to be adjourned)
in black: what has been already done up to the present day
in grey: what will be done in the next lectures
in yellow: last year program that will not be done this year
in pink: new subjects
in green: reference bibliography
video-recordings can be found in the lectures of past academic years, see lectures 21-22 or 20-21 (link above)
PART I
THEORETICAL BACKGROUND: Stochastic equations and diffusion processes
Lecture 1 26/2/2026
Introduction
Diffusion processes I:
Random walks: diffusion coefficient, drift velocity, distribution p(X,t), standard diffusion vs anomalous diffusion; Langevin equation
Lecture 2 3/3/26
Langevin Equation, FDT theorem, Stores-Einstein relation
Overdamped limit, Wiener process
Diffusion Equation, Fick's law
Diffusion equation, derivation.
Lecture 3 5/3/26
Metabolism in bacteria.
Langevin equation in presence of external forces. Fokker Planck equation, Nerst-Planck formula and membrane potential.
Equilibrium limit
Ornstein Uhlenbeck model - effect of confinement
Lecture 4 - 10/3/26
Ornstein Uhlenbeck model (stochastic hamronic oscillator)- mean-square displacement - different dynamical regimes
Arrhenius law, quick derivation
For a more rigorous approach: introduction to the problem as a first passage problem (Gardiner, chap. 5 & 3.6)
Summary and final comments on noise vs inertia vs force
Biblio:
Zwanzig, Non-equilibrium statistical mechanics (Oxford University Press, 2001), chap.3
Gardiner, Handbook of stochastic methods (Springer, 1997) (Fokker-Planck eq. & Arrhenius (chap. 5, cap 3.6)
Nelson, chap. 4 (biological examples)
H. Berg, Random walks in biology (Princeton UP, 1993)
Bouchaud JP & Georges A. "Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications." Physics reports 195.4-5 (1990): 127-293. (introduction)
Lecture 5 - 12/3/26
BACTERIAL CHEMOTAXIS
http://www.mit.edu/~kardar/teaching/projects/chemotaxis(AndreaSchmidt)/home.htm
Chemotaxis - Introduction to the problem
Experiments of Adler - phenomenology
Estimate of thermal effects
Experiments of Berg and Brown and characterization of run & tumble
Phenomenology of chemotaxis
papers Adler 1973; Berg (general) 2005; Berg&Brown 71 (see Dropbox link below); Bialek chap. 4
A few words on bacterial movement on mesoscale: Navier-Stokes and Reynolds number (scallop theorem - flagellar motors NOT DONE - see Di Leonardo in Biophysics)
Berg & Purcell: chemoreception and signal vs noise discrimination in bacteria: What does `counting' mean
Computation of T: signal integration time necessary to discriminate the gradient of the nutrient (using diffusion arguments and assuming chemoreceptor=perfect counter)
Computation of T using correlation functions of the arrival process of molecules on the receptor
Lecture 6 - 17/3/26
Connection between the probability of occupation of the receptor and arrival rate of molecules
Bialek chap 4 (simplified computation)
Berg & Purcell, articolo 1977 (physics of chemoreception)
Signal-transduction pathway: general description and role of the enzimes
Lecture 7 - 19/3/26
Biochemical signal amplification - MWC two model state to explain regulation of flagellar motors (equilibrium computation). Bialek cap 4 - Berg 2005
Dynamical equations for chemotaxis: model in d=1
Bialek chap 4, problems 49-50 (model 1d)
Lecture 8 24/3/26
Coarse grained approach - Keller-Segel model (pdf file on keller-segel)
Tumbling rate as a Response function (linear approximation, comparison to dynamical response in physics)
Review M. Cates (non-linear response kernel)
Relevant papers quoted above can be found in the directory
https://www.dropbox.com/sh/domuijulp605en9/AAA5-M9aPJMlvSygdIweGg4Xa?dl=0
Interesting websites
http://www.mit.edu/~kardar/teaching/projects/chemotaxis(AndreaSchmidt)/home.htm
http://www.rowland.harvard.edu/labs/bacteria/movies/index.ph
PHOTORECEPTION
Lecture 9 26/3/26
Photoreception. First experiments on photoreception at low light intensity
(Hechte-Pirenne). Experiments on single photoreceptor. Intracellular current and response to single photons.
Counting and signal discrimination - optimal threshold values.
From individual photoreceptors back to Hechte-Pirenne. Dark noise and SNR.
Response at high intensity: superposition of independent events and linear response.
Input-output relations: membrane potential in response to a modulation of light intensity.
Lecture 10 28/3/2026
Response at high intensity:
Input-output relations: Computation of the average potential, of fluctuations, transfer function and SNR.
Comparison with experiments.
Lecture 11 30/3/26
Biochemical amplification I - general scheme
Rhodopsin isomerization. BO approximation and retinol absorption spectrum. Simple model with quadratic potential. Fluorescence red-shift. Coupling retinol-opsin---> beyond BO.
Lecture 12 31/3/26
Enzymatic reactions. Michaelis-Menten formula.
Complete enzymatic reactions for cGMP with production and degradation enzymes. Comments on the efficient regime (return time, gain, amplification factor).
Lecture 13 9/4/26
Electric current through an ionic channel.
Statistics of open/closed channels (dynamical model). Connection with the concentration of cGMP (MWC model for the opening statistics of ionic channels).
Lecture 14 23/4/26
Photoreception: final considerations. The problem of filtering: transmission of the signal from photoreceptors to bipolar cells. Optimal non-linear static filter - experiments on bipolar cells.
linear dynamic filters (not done)
All photoreception lectures/material can be found in Bialek chap. 2
PART II
COLLECTIVE PHENOMENA AND INTERACTING SYSTEMS
THEORETICAL BACKGROUND IN STATISTICAL PHYSICS
Brief reminder of Statistical Mechanics of equilibrium processes: canonical ensemble - average quantities -
The Ising model as an archetype of cooperative behavior: order parameter, correlation functions (simple and connected)
Mean-field solution, qualitative description of the ordering transition.
Mean-field free energy; free energy landscape vs transition vs ergodicity breaking.
Lecture 15 21/4/26
Ising model:
Connection with the Gibbs potential. Phase transitions as points of maximal response (divergence of the susceptibility)
Response functions - fluctuation dissipation theorems.
Critical exponents and universality classes.
Computing correlations via response functions.
Lecture 16 23/4/26
Correlation length and correlated regions
Scale free behavior and long range collective behavior.
Models with continuous symmetry. Goldstone modes. Power-laws vs criticality vs soft modes.
Texts: any text on critical phenomena
eg: Binney et al, Critical Phenomena, Oxford Science Publications - chap 1-2-3-6 (only the sections on the Ising model)
Huang, Statistical Mechanics, Wiley, Chap. 14-16-17
Toda-Kubo-Saita Statistical Physics chap.4
NEURAL NETWORKS
Lezione 17 28/4/26
Neurons: ionic channels and single neuron dynamics with activation channels
Neuroni II: il ruolo dei canali calcio voltage-gated - problema della regolazione dei parametri e ruolo del calcio
Example with single leak channel
Role of deactivation and Hodgkin-Huxley equations
Lezione 18 30/4/25
Neural networks: memory retrieval and Hopfield model
Maximum Entropy Models: general approach and derivation of the ME distribution
Lezione 19 5/5/26
Application to neural networks: single-site MEM
MEM: role of correlations - comparison with experimental data.
Learning dynamics and update of synapses - plasticity - comparison with experimental data.
References: Bialek chap. 5.2 (canali ionici e dinamica di singolo neurone - NO), chap. 5.4 (Hopfield and maximum entropy models)
PROTEINS
Proteins: simple modeling of a heteropolymer - link with spin glasses: frustration/complex landscape vs funnel landscape.
Problem of protein folding - Go-models and folding mechanism. NO
Protein design - minimal model with 2 aminoacids: exhaustive computations of compact folded structures - connection between sequences and structures.
Lezione 20 7/5/26
Data analysis of natural protein families: relevance of one point and two points statistics.
Proteins: statistical inference - Maximum Entropy models.
References: Bialek chap. 5.1
Lecture by Prof. Zamponi su Generative Models for protein evolution and design.
Slides at the link below:
https://drive.google.com/drive/folders/1E_MkmnI8WykjT7QpArLSXUcZk6GLpR3K?usp=sharing
ACTIVE MATTER
Lezione 21 12/5/26
Active matter: definition - role of motility - connection with the dynamics of passive particles.
Simple models of active particles: Active Brownian Particles;
Active Ornstein Uhlenbeck.
Lezione 22 14/5/26
Vicsek model - general equations.
Vicsek model - d=2.
Kinetic transition to the polar state - comparison with equilibrium orientational models (XY) - predictions.
Lezione 23 21/5/26
Phase diagram, role of the control parameters (noise and density).
Comparison with experimental results on various kinds of active matter: giant density fluctuations in granular active matter.
Lezione 24 25/5/26
Flocks: topological interactions - long-range correlations.
Lezione 25 26/5/26
Maximum Entropy approach to flocks (Pnas 2012, below)
Lezione 26 28/5/26
Propagation of information and dispersion relation.
Swarms of midges: critical behavior and dynamic scaling
What does it mean to be critical at finite size
Dynamic scaling hypothesis
Scaling in the correlation functions and new dynamic critical exponent
Lezione 27 8/6/26
Questions and Answers on the various topics of the course
Texts:
Vicsek et al, Phys Rev Lett 75 (1995): 1226.
http://rocs.hu-berlin.de/complex_sys_2015/resources/Seminarpapers/Vizcek_Model_2006.pdf
Ginelli F., The Physics of the Vicsek model:
http://link.springer.com/article/10.1140/epjst/e2016-60066-8
nota per gli studenti: articolo di rassegna sul Vicsek model, molto leggibile. c'e' un errore pero' nel calcolo della linea critica rumore/densita' (vedere i miei appunti per il calcolo corretto)
Narayan et al. Science 2007, https://www.researchgate.net/profile/Sriram_Ramaswamy/publication/6223264_Long-lived_giant_number_fluctuations_in_a_swarming_granular_nematic/links/00b7d529d79e592a62000000.pdf
Deseigne et al, PRL 2010
http://iramis.cea.fr/spec/Docspec/articles/s10/035/public/publi.pdf
On flocks and swarms
PNAS 2012 http://www.pnas.org/content/109/13/4786.full
slides on flocks and swarms shown during class
Lezioni - NON FATTE
Flusso di informazione e rappresentazioni efficienti, trasmissione di informazione e risposta collettiva - ruolo dell'entropia come informazione - concetto di efficienza in biologia
esempi biologici
articoli su argomenti interessanti (Infotaxis - neural encoding etc)
problema generico dell'inferenza statistica