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
click on the lecture name to access the video-recording
PART I
THEORETICAL BACKGROUND: Stochastic equations and diffusion processes
Lecture 1 25/2/2022
Introduction
Diffusion processes I:
Random walks: diffusion coefficient, drift velocity, distribution p(X,t), standard diffusion vs anomalous diffusion; Langevin equation
Lecture 2 1/3/22
Langevin Equation, FDT theorem, Stores-Einstein relation
Lecture 3 4/3/22 - we did not record but you can look at lecture 3 of last year
Overdamped limit, Wiener process
Diffusion Equation, Fick's law
Diffusion equation, derivation.
Metabolism in bacteria.
Lecture 4 - 8/3
Langevin equation in presence of external forces. Fokker Planck equation, Nerst-Planck formula and membrane potential.
Lecture 5 - 11/3
Ornstein Uhlenbeck model - mean-square displacement.
Arrhenius law - introduction to the problem as a first passage problem
Lecture 6 - 15/3
Arrhenius law - derivation
Summary and final comments on noise vs inertia vs forces
NOTE: at time ~42:44 there is a T missing in the last integral i.e. <T>= - int dt dG/dt T (as in a few lines before)
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
Lecture 7 18/3
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 cap. 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)
Lecture 8 22/3/22
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 cap 4 (calcolo semplice)
Lecture 9 25/3/22
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
Lecture 10 29/3
Dynamical equations for chemotaxis: model in d=1
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 11 1/4/22
Photoreception. First experiments on photoreception at low light intensity
(Hechte-Pirenne). Experiments on single photoreceptor. Intracellular current and response to single photons.
Lecture 12 5/4/22
Counting and signal discrimination - optimal threshold values.
Summary of previous steps. From individual photoreceptors back to Hechte-Pirenne. Dark noise and SNR.
Lecture 13 8/4/22
Response at high intensity: superposition of independent events and linear response.
Input-output relations: membrane potential in response to a modulation of light intensity.
Computation of the average potential, of fluctuations, transfer function and SNR).
Lecture 14 12/4/22
Response at high intensity: 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 15 22/4/21
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 16 26/4/22
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. (vedi prossima lezione inizio)
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 17 29/4/22
Optimal non-linear static filter - 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,
Lecture 18 3/5/22
correlation functions (simple and connected) and response functions - fluctuation dissipation theorems.
Mean-field solution, qualitative description of the ordering transition.
Lecture 19 6/5/22
Ising model: variational approach and mean field free energy; free energy landscape vs transition vs ergodicity breaking. Connection with the Gibbs potential. Phase transitions as points of maximal response (divergence of the susceptibility)
Lecture 20 10/5/22
Correlation length and correlated regions. Scale free behavior and long range collective behavior. Critical exponents and universality classes. 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 21 17/5/22
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.
Protein design - minimal model with 2 aminoacids: exhaustive computations of compact folded structures - connection between sequences and structures.
Lezione 22 20/5/22
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 23 24/5/22
Neurons: ionic channels and single neuron dynamics with activation channels -
Lezione NON FATTO
Neuroni II: il ruolo dei canali calcio voltage-gated - problema della regolazione dei parametri e ruolo del calcio
Lezione 24 27/5/22
Role of deactivation and Hodgkin-Huxley equations
Neural networks: memory retrieval and Hopfield model
Lezione 25 31/5/22
Learning dynamics and update of synapses - plasticity - comparison with experimental data.
Maximum Entropy Models and role of correlations - comparison with experimental data.
Active matter: definition - role of motility - connection with the dynamics of passive particles.
References: Bialek chap. 5.2 (canali ionici e dinamica di singolo neurone - NO), chap. 5.4 (Hopfield and maximum entropy models)
ACTIVE MATTER
Lezione 26 3/6/20
Active matter: definition - role of motility - connection with the dynamics of passive particles. (see lecture 25)
Simple models of active particles: Active Brownian Particles;
Active Ornstein Uhlenbeck.
Vicsek model in d=2,
Lezione 27 7/6/20
Kinetic transition to the polar state - comparison with equilibrium orientational models (XY) - predictions. Phase diagram, role of the control parameters (noise and density)
Lezione 28 8/6/20
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.
Propagation of information and disperision relation. (not done)
Swarms of midges: critical behavior and dynamic scaling (NOT DONE)
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