# Course Details

#### Name:

**Computer modelling and simulations of biomolecules / Computer Modelling And Simulations Of Biomolecules**

### Basic information

##### Credits:

*Master Degree in Mathematical Engineering:* 6 Ects (d)

##### Degree(s):

Elective 2^{nd} year Master Degree in Mathematical Engineering curriculum Comune

##### Language:

English

### Course Objectives

At the end of the course, students should be able to understand and use the basic concepts of the
(bio)chemistry and thermodynamics, being able to solve problems connected with the molecular
modelling that requires the use of the tools introduced during the course (Poisson-Boltzmann
equation, Molecular Dynamic simulations, Monte Carlo techniques).

### Course Content

- Chemistry basics. The chemical bond. Free energy and equilibrium constant. The peptide bond. Amino acids properties and structure. Secondary structures in proteins. Ramachandran plot. Nucleic acids structure. The genetic code and protein synthesis. Protein folding. Protein internal dynamics. Protein flexibility and biological functions. Experimental methods in structural biology. The Protein Data Bank.
- Introduction to molecular modelling. Molecular interactions and force fields. Empirical force-field energy terms involving bonds, angles, dihedrals and non-covalent interactions. Partial point charges. Charges derived by electrostatic potential, ESP charges. Energy minimization algorithms. Descent algorithms and Newton’s methods.
- From classical mechanics to statistical mechanics. The postulate of statistical mechanics and the microcanonical ensemble. The canonical ensable. Ergodic hypothesis.
- Newtonian dynamics. The position Verlet and the velocity Verlet algorithms. Equivalence and time reversibility. Structure of a molecular dynamics program. Dynamics in the phase space. Simulations in the NVT ensamble. Periodic systems. Simulations in NPT ensamble. Molecular dynamics with constraints. Long range interactions. Truncating two body potentials with cut-off. Ewald sums
- Static and dynamical properties. Pair distribution functions. Coordination numbers. Time correlation functions and their calculation in molecular dynamics. Diffusion coefficient by root mean square distance and by velocity autocorrelation function.
- Basics of Monte Carlo simulations. The Metropolis algorithm.
- Numerical simulations.

### Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

- Have knowledge of biomolecular structures, molecular visualization programs and biological data bases.
Understanding the theory at the basis of molecular dynamics simulations, Poisson-Boltzmann equation and Monte Carlo methods.
- Demonstrate skills in molecular simulations and ability to set up and to interpret classical molecular dynamics simulations in the light of the knowledge acquired on principles of the statistical mechanics.
- Demonstrate capacity for reading and understand other texts on related topics

### Prerequisites and Learning Activities

Basic notions of classical physics and mathematical analysis.

### Teaching Methods

**Language**: English

Lectures and exercises

### Assessment Methods and Criteria

At the end of the course the student has to hand over a report on the practical exercises carried out. The exam
will take place after the evaluation of the report and it will consist on a oral examination.

### Textbooks

- - A.R. Leach,
** Molecular Modelling Principles and Applications, 2nd edition**. Addison Wesley Longman. 2001. *LEA (Chapters: 3.1-3.7, 3.8.3, 3.8.4, 3.9, 3.13.1) *
- L. Stryer,
**Biochemistry**. Freeman . 2002. *STR (Chapters 3 and 4) *
- T. Schlick,
**Molecular Modelling and Simulation**. Springer-Verlag. 2002. *SCH (Chapters 1-5) *
- M.S. Silberberg,
**Principles of General Chemistry**. McGraw Hill. *SIL (chapters from 7 to 12) *
- K. Huang,
**Statistical mechanics**. John Wiley & Sons. 1987. *(Chapters: 6.1-6.6, 7.1,7.2) *
- F-S - D. Frenkel & B. Smit,
**Understanding Molecular Simulations**. Academic Press. 2002. *Chapters: 1, 2, 3.1, 3.2, 4.1-4.4.1, 6.1-6.2, 7.1, 12.1, 12.3, 15.1, 15.3, D1, D2. *

### Course page updates

This course page is available (with possible updates) also for the following academic years:

*Course information last updated on: 23 dicembre 2016, 14:07*