Detailed Program and Lectures
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 (link above)
PART I
THEORETICAL BACKGROUND: Stochastic equations and diffusion processes
Lecture 1 27/2/2024
Introduction
Diffusion processes I:
Random walks: diffusion coefficient, drift velocity, distribution p(X,t), standard diffusion vs anomalous diffusion; Langevin equation
Lecture 2 1/3/24
Langevin Equation, FDT theorem, Stores-Einstein relation
Overdamped limit, Wiener process
Diffusion Equation, Fick's law
Lecture 3 5/3/24
Diffusion equation, derivation.
Metabolism in bacteria.
Langevin equation in presence of external forces. Fokker Planck equation, Nerst-Planck formula and membrane potential.
Lecture 4 - 8/3/24
Ornstein Uhlenbeck model - mean-square displacement - different dynamical regimes
Lecture 5 - 12/3/24
Arrhenius law - introduction to the problem as a first passage problem
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. e Arrhenius (cap. 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)
BACTERIAL CHEMOTAXIS
http://www.mit.edu/~kardar/teaching/projects/chemotaxis(AndreaSchmidt)/home.htm
(continuation of Lecture 5)
Chemotaxis - Introduction to the problem
Experiments of Adler - phenomenology
Estimate of thermal effects
Lecture 6 15/3/24
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
Connection between the probability of occupation of the receptor and arrival rate of molecules
Bialek chap 4 (simplified computation)
Lecture 7 20/3/24
Signal-transduction pathway: general description and role of the enzimes
Berg & Purcell, articolo 1977 (physics of chemoreception)
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
Lecture 8 26/3/24
Dynamical equations for chemotaxis: model in d=1 (continue from 24/3)
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)
Bialek chap 4, problems 49-50 (model 1d)
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 3/4/24
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.
Lecture 10 5/4/24
Summary of previous steps. 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 11 9/4/2024
Response at high intensity:
Input-output relations: membrane potential in response to a modulation of light intensity.
Computation of the average potential, of fluctuations, transfer function and SNR.
Comparison with experiments.
Rhodopsin isomerization. BO approximation and retinol absorption spectrum. Simple model with quadratic potential. Fluorescence red-shift. Coupling retinol-opsin---> beyond BO.
Lecture 12 12/4/24
Biochemical amplification I - general scheme
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 16/4/24
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).
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. (see net lecture)
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
Lecture 14 19/4/2024
Optimal non-linear static filter (conclusion) - experiments on bipolar cells.
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)
Lecture 15 23/4/204
Ising model:
Mean-field solution, qualitative description of the ordering transition.
Response functions - fluctuation dissipation theorems.
Variational mean-field free energy; free energy landscape vs transition vs ergodicity breaking.
Lecture 16 24/4/2024
Connection with the Gibbs potential. Phase transitions as points of maximal response (divergence of the susceptibility)
Correlation length and correlated regions.
Lecture 17 30/4/2024
Scale free behavior and long range collective behavior.
Critical exponents and universality classes.
Lecture 18 3/5/2024 - part1
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
PROTEINS
Lezione 18 3/5/24 - part2
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.
Lezione 19 10/5/24
Protein design - minimal model with 2 aminoacids: exhaustive computations of compact folded structures - connection between sequences and structures.
Lezione 20 14/5/24
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
NEURAL NETWORKS
Lezione 21 17/5/24
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
Role of deactivation and Hodgkin-Huxley equations
Lezione 22 22/5/24
Neural networks: memory retrieval and Hopfield model
Learning dynamics and update of synapses - plasticity - comparison with experimental data.
Maximum Entropy Models and role of correlations - 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)
ACTIVE MATTER
Lezione 23 24/5/24
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 24 29/5/24
Vicsek model - general equations.
Vicsek model - d=2.
Kinetic transition to the polar state - comparison with equilibrium orientational models (XY) - predictions.
Lezione 25 31/5/24
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. Flocks: topological interactions - long-range correlations. Maximum Entropy approach to flocks.
Lezione 26 4/6/24
Propagation of information and disperision relation.
Lezione 27 11/6/24
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
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
sugli uccelli,
www.cobbs.it
PNAS 2012 http://www.pnas.org/content/109/13/4786.full
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