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Probability and Random Processes - M143008

Title:	Pravděpodobnost a náhodné procesy
Guaranteed by:	Department of Informatics and Chemistry (143)
Faculty:	Faculty of Chemical Technology
Actual:	from 2023
Semester:	summer
Points:	summer s.:4
E-Credits:	summer s.:4
Examination process:	summer s.:
Hours per week, examination:	summer s.:2/1, C+Ex [HT]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Level:
Note:	course can be enrolled in outside the study plan enabled for web enrollment

Guarantor:	Lankaš Filip doc. Ing. Ph.D.
Interchangeability :	N143054

Examination dates

Annotation -

The course is focused on computer modelling of biological macromolecules (nucleic acids and proteins) and their interactions. With increasing computer power and development of new algorithms, computer modelling now forms an integral part of research in molecular biology, genetics and biochemistry. The first part of the course comprises an introduction to probability theory and stochastic processes, more solid than usually taught in introductory courses. This knowledge is of broader use well outside the domain of biomolecular modelling. We then use the acquired theoretical background to formulate an important simulation method, Brownian dynamics. We finish by discussing its applications to specific biological problems such as protein-ligand interactions or macromolecular dynamics in the cell. The exercises include theoretical topics as well as simple computations which the students are supposed to programm themselves.

Last update: Hladíková Jana (04.01.2018)

Aim of the course -

Students will:

understand probability and stochastic processes at a more solid level

get insight into the theoretical formulation and algorithmic realization of Brownian dynamics simulations

obtain an overview of applications to specific problems at the border between molecular biology, genetics and bioinformatics

Last update: Hladíková Jana (04.01.2018)

Course completion requirements -

A necessary prerequisite to get the credit is active participation at lectures and exercices. The exam is in oral form.

Last update: Lankaš Filip (16.02.2018)

Literature -

R: I. Nezbeda, J. Kolafa, M. Kotrla, Úvod do molekulárních simulací – Metody Monte Carlo a molekulární dynamiky, Univerzita Karlova, Praha 2002

R: T. Schlick, Molecular Modeling and Simulation, Springer 2010

A: D. Frenkel, B. Smit, Understanding Molecular Simulation, Academic Press 2002

A: J. Šponer, F. Lankaš (eds.), Computational Studies of RNA and DNA, Springer 2006

Last update: Svozil Daniel (29.10.2018)

Requirements to the exam -

Solving homework exercises.

Last update: Lankaš Filip (16.02.2018)

Syllabus -

1. Introduction. Length and time scales in biomolecular modelling

2. Probability

3. Random variables

4. Characteristics of random variables

5. Probability distribution

6. Normal distribution

7. Stochastic processes

8. Langevin equation

9. Brownian motion

10. Brownian dynamics simulations

11. Application I: Diffusion-controlled protein-ligand binding

12. Application II: Dynamics of nucleosomes and of the chromatin fibre

13. Application III: Movement and interactions of biomolecules in the cell

14. Application IV: Bownian simulations of DNA and RNA nanostructures

Last update: Lankaš Filip (26.10.2018)

Learning resources -

Online materials for the course.

Last update: Lankaš Filip (16.02.2018)

Registration requirements -

Basic courses in mathematics, physical chemistry, biochemistry and molecular modelling.

Last update: Lankaš Filip (16.02.2018)

Teaching methods
	Activity	Credits	Hours
	Účast na přednáškách	1	28
	Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi	0.5	14
	Příprava na zkoušku a její absolvování	2	56
	Účast na seminářích	0.5	14
		4 / 4	112 / 112