Course Syllabus
Obiettivi
Le macromolecole organiche e biologiche sono esempi paradigmatici di sistemi complessi: Da un lato, la loro modellizzazione fisica è complicata dalla presenza di interazione su diverse scale di lunghezza. Dall’altro, frustrazione e barriere sia energetiche che entropiche rendono computazionalmente estremeamente costosa l’esplorazione dello spazio conformazionale e lo studio delle proprietà sia dinamiche che di equilibrio di questi sistemi.
Questo corso si propone di condurre lo studente dai principi di base fino alla frontiera dello studio teorico e la simulazione dei sistemi macromolecolari complessi. In particolare, si mostrerà come l’integrazione di tecniche di fisica statistica sviluppate negli ultimi 20 anni con algoritmi di machine learning renda oggi possibile affrontare i principali ostacoli computazionali, offrendo un nuovo strumento di indagine chimico-fisico per lo studio processi fondamentali in biofisica, biologia, scienze dei materiali e ricerca farmacologica.
Il corso e' concepito per adattarsi a due tipologie diverse di studenti:
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studenti provenienti da un percorso teorico in fisica, chimica o scienze dei materiali interessati ad approfondire maggiormente aspetti teorici e concettuali della fisica statistica dei sistemi complessi, della dinamica stocastica ei fondamenti teorici di algoritmi di machine learning che sono utilizzati in questo ambito.
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studenti provenienti da un percorso sperimentale (in biofisica, biochimica, o biotecnologie) interessati ad approfondire gli aspetti pratici, ovvero imparare ad eseguire ed interpretare di tecniche di simulazione molecolare.
Gli studenti potrano scegliere tra due diverse modalità di esame che riflettono questi due diversi obiettivi formativi.
Contenuti sintetici
Dalla dinamica stocastica alle proprietá di equilibrio di sistemi complessi. Tempi di rilassamento. Approcci multi-scala, campi statistici e stocastici, meccanica statistica degli eventi rari e problemi computazionali ad essa collegati. Cenni di fenomenologia delle macromolecole e in particolare di biopolimeri. Algoritmi AI per l'esplorazione, il campionamento e la analisi di dinamica molecolare. Algoritmi per la predizione di strutture molecolari.
Programma esteso
Chapter 1: Biomolecules as complex open systems
The theoretical foundation of physics-based simulation of biomolecules
The concept of multi-scale description of soft and biological matter
Chapter 2: Stochastic dynamics
Dynamics in open macromolecular systems: characteristic scales and fluctuation-dissipation processes
Microscopic derivation of the generalized Langevin equation. Ohmic and overdamped limit.
Rudiments of Stochastic Calculus and stochastic measure.
Fokker-Plank equation and stochastic path integrals
Chapter 3: Statistical mechanics of thermally activated processes
Reactive events and transition path ensamble
Stochastic descriptors of reactive dynamics: committor function, transition path density and transition path current
Kinetics of Mean-first passage times and transition path time
Markov state models
Chapter 4: Molecular Dynamics (MD)
Ergodic Integrators
MD in the NPT and NVT ensembles.
Practical Simulations using GROMACS: set-up, execution and analysis of MD simulations (6 ore)
Chapter 5: Statistical Computing for molecular simulations
Collective variables and potential of mean-force
Diffusive distance and diffusion maps
Configuration clustering and Markov State Model construction
Intrinsic manifold and intrinsic dimensionality
Chapter 5: Enhanced sampling methods and machine learning for molecular simulations
Open challenges in simulating complex biological matter
Enhanced sampling algorithms
Machine Learning for Molecular Simulations
Prerequisiti
Per studenti di indirizzo teorico:
Meccanica analitica Lagrangiana e Hamiltoniana, meccanica statistica (ergodicità e teoria degli ensemble microcanonici e canonici), meccanica quantistica, metodi matematici per la fisica (spazi di Hilbert, distribuzioni, operatori lineari).
Per studenti di indirizzo biofisico e biochimico:
Concetti rudimentali di meccanica statistica (equilibrio termodinamico e sue proprietá, distribuzione di Boltzmann). Equazione di Newton, leggi della termodinamica, elettrostatica e aspetti fenomenologici di meccanica quantistica (quantizzazione dell'energia, concetto di funzione d'onda e di orbitale)
Modalità didattica
Gli argomenti centrali del corso saranno trattati in lezioni frontali alla lavagna.
Gli studenti interessati al percorso teorico svolgeranno un esame orale sugli argomenti teorici e presenteranno un algoritmo AI a scelta.
Gli studenti interessati al percorso teorico svolgeranno un esame orale su rudimenti di meccanica statistica connessi al corso e porteranno un progetto di simulazione di sistema macromolecolare.
Materiale didattico
- Dispense fornite dal docente.
- M. Tuckermann: "Statistical mechanics: Theory and Molecular Simulations", Oxford Graduate Texts
- T. Schlick: "Molecular Modeling and Simulation: An Interdisciplinary Guide (Interdisciplinary Applied Mathematics)" Springer.
Periodo di erogazione dell'insegnamento
Secondo semestre, secondo anno
Modalità di verifica del profitto e valutazione
Il voto verrà assegnato sulla base di una prova orale finale, tenuto anche conto del contributo dello studente alle sessioni tematiche e relative discussioni.
Orario di ricevimento
In qualsiasi momento, previo accordo con il docente via email
Sustainable Development Goals
Aims
Organic and biological macromolecules are paradigmatic examples of complex systems:
On the one hand, their physical modeling is complicated by the presence of interactions at multiple length scales. On the other hand, frustration and both energetic and entropic barriers make the exploration of conformational space, as well as the study of dynamic and equilibrium properties, computationally extremely expensive.
This course aims to guide students from the basic principles to the cutting edge of theoretical study and simulation of complex macromolecular systems. In particular, it will demonstrate how the integration of statistical physics techniques developed over the last 20 years with machine learning algorithms now makes it possible to tackle major computational challenges, offering a new physico-chemical tool for investigating fundamental processes in biophysics, biology, materials science, and pharmaceutical research.
The course is designed to accommodate two different types of students:
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Students with a theoretical background in physics, chemistry, or materials science who are interested in deepening their understanding of the theoretical and conceptual aspects of statistical physics of complex systems, stochastic dynamics, and the theoretical foundations of machine learning algorithms used in this field.
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Students with an experimental background (in biophysics, biochemistry, or biotechnology) who are interested in the practical aspects, namely learning how to perform and interpret molecular simulation techniques.
The students will be able to choose between two different exam formats, reflecting these two distinct learning objectives.
Contents
Relaxation times. Multiscale approaches, statistical and stochastic fields, statistical mechanics of rare events and related computational challenges.
Overview of the phenomenology of macromolecules, with a focus on biopolymers.
AI algorithms for the exploration, sampling, and analysis of molecular dynamics.
Algorithms for molecular structure prediction.
Detailed program
Chapter 1: Biomolecules as complex open systems
The theoretical foundation of physics-based simulation of biomolecules
The concept of multi-scale description of soft and biological matter
Chapter 2: Stochastic dynamics
Dynamics in open macromolecular systems: characteristic scales and fluctuation-dissipation processes
Microscopic derivation of the generalized Langevin equation. Ohmic and overdamped limit.
Rudiments of Stochastic Calculus and stochastic measure.
Fokker-Plank equation and stochastic path integrals
Chapter 3: Statistical mechanics of thermally activated processes
Reactive events and transition path ensamble
Stochastic descriptors of reactive dynamics: committor function, transition path density and transition path current
Kinetics of Mean-first passage times and transition path time
Markov state models
Chapter 4: Molecular Dynamics (MD)
Ergodic Integrators
MD in the NPT and NVT ensembles.
Practical Simulations using GROMACS: set-up, execution and analysis of MD simulations (6 ore)
Chapter 5: Statistical Computing for molecular simulations
Collective variables and potential of mean-force
Diffusive distance and diffusion maps
Configuration clustering and Markov State Model construction
Intrinsic manifold and intrinsic dimensionality
Chapter 5: Enhanced sampling methods and machine learning for molecular simulations
Open challenges in simulating complex biological matter
Enhanced sampling algorithms
Machine Learning for Molecular Simulations
Prerequisites
Analytical mechanics in Lagrangian and Hamiltonian formulation, statistical mechanics (ergodicity and the theory of microcanonical and canonical ensembles), quantum mechanics, and mathematical methods for physics (Hilbert spaces, distributions, linear operators).
For students with a biophysical or biochemical background:
Basic concepts of statistical mechanics (thermodynamic equilibrium and its properties, Boltzmann distribution). Newton’s equation, the laws of thermodynamics and the notion of free-energy, electrostatics, and phenomenological aspects of quantum mechanics (energy quantization, the concept of wavefunction and orbital).
Teaching form
The core topics of the course will be covered through traditional lectures at the blackboard.
Students following the theoretical track will take an oral exam on the theoretical topics and present an AI algorithm of their choice.
Students following the applied/experimental track will take an oral exam on basic concepts of statistical mechanics related to the course and present a simulation project of a macromolecular system.
Textbook and teaching resource
- Typeset notes provided by the lecturer.
- M. Tuckermann: "Statistical mechanics: Theory and Molecular Simulations", Oxford Graduate Texts
- T. Schlick: "Molecular Modeling and Simulation: An Interdisciplinary Guide (Interdisciplinary Applied Mathematics)" Springer.
Semester
Second semester, second year
Assessment method
The grade will be assigned on the basis of a final oral examination, also taking in consideration the student’s contribution to the special topic session (or computational project) and related discussion.
Office hours
The lecturer will be available any time, previous arranging the time and date by email.
Sustainable Development Goals
Staff
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Pietro Faccioli
