Mathematical and computational methods in natural sciences. 1100-4PM23
Topics. Contemporary trends and research strategies of complex systems in natural sciences using theoretical physics, computational sciences and simulation techniques. Contemporary computer architectures. Classical and quantum computers. World and Polish supercomputing centers and a review of research and services carried out. Methods for determining the structure of complex (bio)molecular systems. Structural databases. Multiscale modeling methods and simulations of complex physical, chemical and biological systems and processes as an indispensable element of research in order to understand their structure and function. Review of the leading methods and computational environments used in (bio)molecular and material sciences. Selected quantum methods for generating potential energy, including ab initio and DFT methods. Hellmann-Feynman theorem and molecular forces. Analytical approximations of the potential energy. Relations of physics of (bio)molecular systems and nanosystems. Dynamical systems. Phase space trajectories. Classification of dynamical systems. Correlation functions, including time correlation functions. Selected molecular dynamics algorithms: classical molecular dynamics (MD), quantum molecular dynamics (QD) and quantum-classical molecular dynamics (QCMD). Numerical stability of MD algorithms. Simulations of systems in thermodynamic equilibrium: basic statistical systems and thermodynamic properties, microscopic models of pressure and temperature, free energy simulations, thermodynamic integration. Microscopic and mesoscopic models of molecular fields. Poisson-Boltzmann equation. Diffusion processes. Fokker-Planck equation. Brown's dynamics. Hydrodynamic interactions. Simulations of kinetic processes, including metabolic and signaling pathways. Physics and evolution. Genetic algorithms. In silico neural networks and their applications. Analysis of signals. Causality relations in the dynamics of complex systems. New challenges.
Main fields of studies for MISMaP
mathematics
chemistry
biology
computer science
Mode
Learning outcomes
The purpose of the lecture and presentations, as well as exercises, is to provide students with a review of methods, trends and strategies for studying complex systems in life sciences using mathematical and computational models, including the use of multi-scale methods of theoretical physics and computational sciences. The lecture should provide a good, substantive background for a better understanding of complex systems and processes, enabling own research.
Assessment criteria
Written exam. 4-problems/questions to solve. 20 points to get. A minimum of 10 points to obtain a positive grade. From 11 points to 20 points, a linear scale for converting points into scores.
Bibliography
• B. Lesyng, Notes to lectures, e-mailed using USOS.
• Molecular Conceptor, computer course available in the laboratory.
• SCIGRESS, a computational environment for studying complex (bio)molecular
and material systems (https://www.fqs.pl/en/chemistry/products/scigress/).
• A. Hinchliffe, Molecular Modeling for Beginers, Wiley, West Sussex, 2008.
• T. Schlick, Molecular Modeling and Simulation. An Interdisciplinary Guide.
Springer, New York, Dordrecht, Heidelberg, London, 2010
• A. H. Zewail, Physical Biology. From Atoms to Medicine, Imperial College Press,
2008.
• K.A. Dill, S. Bromberg, Molecular Driving Forces. Statistical Thermodynamics in
Chemistry and Biology, Garland Science, 2003.
• U. Forys, Mathematics in Biology, WNT, 2005.
• L. Susskind, The Theoretical Minimum. What You Need to Know to Start Doing
Physics, Basic Books, 2013.
• L. Susskind, Quantum Mechanics. The Theoretical Miniumum.
Penguin Random House, UK, 2014.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes: