### Events and News

#### News

Systems Biology Journal club has restarted for the this term. First meeting 29 September >>more

Information about the BBSRC e-Learning for Systems Approaches programme now available >>more

#### New PhD Programme

UCL has developed a new Interdisciplinary PhD Programme in bioscience and bioengineering. The programme covers all levels of biology, from molecules through to cells and whole animal physiology, and provides training in cutting edge techniques, including bioengineering, data analysis, computational and mathematical modelling, imaging, structural biology and systems approaches >>more

#### Recent Publications

Jennifer Rohn and Buzz Baum (LMCB) "Comparative RNAi screening identifies a conserved core metazoan actinome by phenotype"

Jennifer Rohn and Buzz Baum (LMCB) "Identification and characterization of a set of conserved and new regulators of cytoskeletal organization, cell morphology and migration"

## Module 1

**Basic
quantitative skills for systems biology**

Students will be introduced to course software, which will be used to illustrate the implementation of basic operations (initially at the level of preliminary material). Mathematica and MATLAB are excellent packages having rich ranges of palettes, templates etc for inputting expressions, and a wide variety of output capabilities including animated graphics. The use of this package of tools will be developed through hands-on application by the students as the module progresses.

**1. Review &
expansion of key concepts (functions, graphs, rates of change)**

*1.1** Dependent and independent variables. What are rates of change?
Derivatives as slopes of tangent lines. Exponential growth and decay – constant
rate of growth/decay – exponential growth/decay differential equation.
Properties of the exponential function. Inverse functions – natural logarithms.
Properties of logarithms. Real powers – properties, graphs. Logistic functions
– constrained growth. Hill functions – Michaelis-Menten; co-operative
activation. *

*1.2** Finding derivatives using Mathematica
or MATLAB. Higher order derivatives. Local maxima and minima of functions of
one variable; points of inflexion. Maximum rates of change for logistic
function and Hill functions. *

*1.3** Equilibria and local stability
analysis of 1-dimensional ODE systems. Examples using growth equations and
chemical reaction equations.*

*1.4** Describing periodic processes.
General sine, cosine and tangent functions and graphs. Circadian rhythms and
heart beat examples. Oscillators: Simple Harmonic oscillator (SHO) defined by
2nd order differential equation. Damped and reinforced oscillators. *

**2. Linear systems: the
basics (first steps to working with systems of equations) **

There is no doubt that it will be critical for SysMIC graduates to appreciate the inherent and almost universal non-linearity of biological systems at all scales. However to approach this concept sensibly and to appreciate some of the methods and simplifications required to analyse these process mathematically it is necessary to first be familiar with linear methods and systems.

*2.1** Systems of linear equations.
Examples. Vector and matrix representation. Composition of systems and matrix
multiplication. Solving systems of linear equations by Gaussian elimination
using mathematical software. Examples using stochiometric matrices of metabolic
networks.*

*2.2** Square matrices. Identity matrices,
diagonal matrices, upper and lower triangular matrices. Inverse matrices. When
do they exist? Determinant of 2x2 matrices and relation to the existence of
inverses. Determinants and inverses for diagonal and triangular matrices. How
determinants can be defined for arbitrary square matrices. Finding matrix
inverses using Mathematical software.*

**3. Networks (methods
for describing and handling complicated interactions)**

Systems biology is about the interaction of parts. Students must understand how these parts and their relations one to another can be described graphically and unambiguously and then analysed.

*3.1** What is a network? Biological
networks – metabolic, transcriptional, signalling, neural and food webs.
Directed and undirected networks. Neighbours. Cluster measures. Paths and path
length. Diameter. Random, small world and scale free networks. Simple association
rules for constructing networks.*

*3.2** Introduction to the logic of
networks: “and”, “or”, “xor”, feedforward, feedback, functional motifs.
Examples from gene transcription networks in yeast and intracellular protein
signalling networks. *

**4. Probability and
Statistics (working with data)**

*4.1.** Review of basic material
(optional): Discrete probabilities. Simple examples using permutations and
combinations. Distributions: binomial, negative binomial, Poisson,
hypergeometric. How they arise in biological applications – sampling with and
without replacement. Continuous distributions. Density functions. Exponential
distribution; Normal distribution; LogNormal distribution; Power law
distributions. Simple biologically relevant examples. Review of available Mathematica or MATLAB
resources.*

*4.2** Further probability and statistics:
Small course in basic R. Sampling, hypothesis testing, data fitting. *

**5. Modelling
(introducing a systematic approach)**

*The 5-step modeling
cycle – purpose, creation, implementation, interpret results, evaluate
outcomes. Input-output models, sensitivity analysis, dimensional consistency. *

**6. Modelling
challenges I: (First steps in model making) **

A set of substantial mini-projects in which the student creates a model of a biological system using the ideas and techniques taught in Module 1. Only suitably simplified models can be expected at this stage and they will lack realism though they will be (often very) simplified versions of real systems.

Page last modified on 22 jul 11 15:02