 Learning objectives
After passing the course, the student has insight in:
 Models of simple grow processes and can set up ordinary differential equations (ode’s).
 Different chemical kinetics and can translating biochemical processes with given kinetics into the corresponding ode’s.
 Elementary solution methods, phase planes, stability analysis of ode’s, and can solve ode’s and perform a stability analysis.
 Different numerical methods and can solve (stiff) ode’s.
 Basicprinciples of molecular dynamics and is able to perform molecular simulations.
 Statistical mechanics, in particular microcanonic and canonic ensemble, correlation particle velocity and temperature radial distribution function and can calculate with regard to statistical mechanics.
 Content
 Modeling with differential equations: exponential growth and decay, logistic growth, massspring systems, LotkaVolterra equations.
 Reaction kineticsn: massaction, MichaelisMenten, Repressilator kinetics, Hill kinetics, modeling of gen regulation, cooperativity, more complicated enzyme kinetics, examples from synthetic biology.
 Analytic solutions of differential equations: separation of variables, equations with constant coefficients.
 Stability analysis: Phase planes, Stability of stationary points, Jacobians.
 Numerical methods for ode's: Onestepmethods, explicite (Euler, ..., RungeKutta) and implicite (CranckNicholson), truncation errors, numerical stability. Multistep methods with larger stability. Praktical aspects, error estimates, ode solvers, Matlab implementation.
 Introduction Molecular Dynamics: Newton's laws, conservative forces, potentials, dynamical equations for 1,2 and N particles.
 Potentials: LennardJones, Morse, harmonic binding potentials.
 Numerical solutions: Special numerica methods for equations of motion (e.g. Verlet), periodic boundary conditions, truncating potentials.
 Introduction statistical mechanics, microcanonical and canonical ensemble, relation between particle velocities and temperature, radial distribution functions.
 Stochastics simulations: simulated annealing.
 Entrance requirementsEntrance requirements tests Assumed previous knowledgeKennis van Calculus, Wiskunde II (lineaire algebra) en Toegepaste natuurwetenschappen. Basiskennis op het gebied van biochemie en moleculaire biologie.  Previous knowledge can be gained by• 3NBB0  Applied physical sciences • 8RA00  Biochemistry • 8VB40  Systems in time and space • 8RB00  Molecular cell biology  Resources for self studyShort promotional description of the course 
Simulaties van biochemische systemen worden gebruikt om moleculaire mechanismes in de cel te begrijpen. In dit college worden basis simulatiemethoden besproken. Eerst worden modellen in termen van concentraties behandeld. Naast chemische kinetieken worden numerieke oplossingsmethoden en stochastische simulaties besproken. Daarna worden, inzoomend op individuele moleculen, Moleculaire Dynamica simulaties behandeld voor het bestuderen van de structuur en/of aggregatie van biomoleculen. 
Short promotional description of the course 
Simulations of biochemical systems are a basis for the unraveling of the molecular mechanisms in the cell. In this course the basic simulation methods are presented. First, models in terms of the concentrations are considered. Besides chemical kinetics also attention is given to numerical solutions and stochastic simulations. Second, zooming in to individual molecules, Molecular Dynamics simulations are treated for the prediction of structure and/or aggregation of biomolecules. 
  Required materialsRecommended materialsCollegedictaat (wordt uitgereikt) 
 Instructional modesGuided selfstudy General Remark  Lecture General Remark 
 TestsAssignment 2Test weight   15 
Minimum grade    
Test type   Interim examination 
Number of opportunities   1 
Opportunities   Block 3 
Test duration in minutes    
Assessment Remark
 Assignment 1Test weight   15 
Minimum grade    
Test type   Interim examination 
Number of opportunities   1 
Opportunities   Block 3 
Test duration in minutes    
Assessment Remark
 Written examinationTest weight   70 
Minimum grade   5 
Test type   Final examination 
Number of opportunities   2 
Opportunities   Block 3, Block 4 
Test duration in minutes    
Assessment Remark


 