Introduction

Lecture #1

Outline

• The systems biology paradigm• What is a (biological) network?• Why build mathematical models for

simulation?• Key concepts in analysis of dynamic states• Fundamental approaches• Sources of data

The Systems Biology Paradigm:components -> networks -> computational models -> phenotypes

Palsson,BO; Systems Biology, Cambridge University Press 2006

What is a network?Networks are made up of chemical transformations

Networks have nodes and linksNetworks produce biological/physiological functions

Levels of knowledge about linksAbstract Specific

relationships(correlations)

influences(directional) mechanisms

chemicalmechanisms

kinetics &thermo.

Some Compounds (nodes) are Found in Many Networks

What is a network?Networks can be a priori defined by function or defined based on High Throughput data

Bottom-up Network Reconstructions Represent a Biochemically, Genetically, and Genomically

(BiGG) Structured Knowledge Base

Global human metabolic network

Methylglyoxal metabolism

Acetone monooxygenase

Acetone

Cytochrome P450, family 2, subfamily E,

polypeptide 1

ReadsBase pairs

Contigs

Chromosomes

ReactionsCompounds

Gene-protein relationships

Pathways

Genome AnnotationComprehensively represents genetic material in all human cells

Network AnnotationComprehensively represents biochemical activities in all human cells

Hierarchical Levels of Detail in the 1D and 2DHuman Annotations

Biological networks operate in the crowded intra-cellular environment

© David Goodsell 1999

There are Many Sources of Information About Biological Networks

Why Build Models?(Jay Bailey, 1998)

1. To organize disparate information into a coherent whole

2. To think (and calculate) logically about what components and interactions are important in a complex system.

3. To discover new strategies4. To make important corrections to the conventional

wisdom5. To understand the essential qualitative features

Biotech Prog 14:8-20 (1998)

“What I cannot create, I do not understand”

Richard Feynman

Reconstructing complex systems

“And that’s why we need a computer”

Networks Have States:steady, dynamic & physiological states

Basic Concepts in Dynamic Analysis:

1. Time constant; t1/2, , …

2. Aggregate variables, multi-scale analysis ATP2ATP+ADP “pools”

3. Transition from one steady state to another4. Graphical presentation of solution

The Two Fundamental Approaches

1. Simulation: 1) formulate equations using well-defined assumptions; 2) specify parameter values; 3) specify IC; 4) use a computer to solve the equations numerically (MatLab, Mathematica); 5) graph and analyze the results

1. Analysis: A model is a formal (mathematical) representation of the data/knowledge that you have about the process/phenomena that you are studying; can analyze model properties to examine how its different components interrelate or contribute to its properties

Assumptions Used in the Formulation of Dynamic Network Models

• Continuum assumption, i.e, do not deal with individual molecules, but treat medium as continuous

• Constant volume assumption• Ignore p/c factors, i.e., electroneutrality or osmotic

pressure• Finer spatial structure of cells and organelles is

ignoredmedium is homogeneous ~100nm• Constant temperature; isothermal (also isobaric)

Mathematical Representation:3 key matrices

S: Network topology/structurelinks between network components(numerically “perfect,” well-behaved and sparse)(biologically genomic origin)

G: Kinetic properties of individual links in the network;reciprocals of time constants(numerically challenging; very different order of magnitudein numerical values—ill conditioned, sparse)(biological origin is genetic)

J: The Jacobian matrix contains the dynamic propertiesof the network, J=S•G

1/1/min

1/1/hr

1, 2,…m

Attributes of the Stoichiometric and Gradient Matrices

Summary

• The systems biology process has four basic steps• Biological networks can be reconstructed using disparate data• Dynamics states are characterized by: time constants, forming

aggregate variables, characteristic transitions• Dynamic analysis is a mathematical subject• Spectrum of times scales and formation of aggregate

variables are key issues• Dynamic models can be simulated or analyzed• There are notable assumptions in building dynamic models

that one needs to understand• The needed data is organized into two matrices