1. Lecture #1
Introduction

2. 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

3. The Systems Biology Paradigm: components -> networks -> computational models -> phenotypes
Note the one bubble for the reconstruction here, as there is only network for each organism
This subtle transition requires mathematical and programming skills and it the bridge between a data containing reconstruction and a model suitable for computation
Palsson,BO; Systems Biology, Cambridge University Press 2006

4. What is a network? Networks are made up of chemical transformations Networks have nodes and links Networks produce biological/physiological functions

5. Levels of knowledge about links
Statistical modeling
Bayesian networks
Boolean models
Markov chains
Chemical reactions
Kinetics
Levels of knowledge about links
Abstract
Specific
relationships
(correlations)
influences
(directional)
chemical
mechanisms
kinetics &
thermo.
mechanisms

6. Some Compounds (nodes) are Found in Many Networks

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

8. Bottom-up Network Reconstructions Represent a Biochemically, Genetically, and Genomically (BiGG) Structured Knowledge Base
Acetone monooxygenase
Acetone
Methylglyoxal metabolism
Global human metabolic network
Cytochrome P450, family 2, subfamily E, polypeptide 1

9. Hierarchical Levels of Detail in the 1D and 2DHuman Annotations
Genome Annotation
Comprehensively represents genetic material in all human cells
Contigs
Reads
Base pairs
Chromosomes
Compounds
Reactions
Pathways
Network Annotation
Comprehensively represents biochemical activities in all human cells
Gene-protein relationships

10. Biological networks operate in the crowded intra-cellular environment
© David Goodsell 1999

11. There are Many Sources of Information About Biological Networks

12. Why Build Models? (Jay Bailey, 1998)
To organize disparate information into a coherent whole
To think (and calculate) logically about what components and interactions are important in a complex system.
To discover new strategies
To make important corrections to the conventional wisdom
To understand the essential qualitative features
Biotech Prog 14:8-20 (1998)

13. Why Build Models?
Organizing Disparate Information into a Coherent Whole (ie. Context for Content)
To Think (and Calculate) Logically About What Components and Interactions are Important in a Complex System
To Discover New Strategies
To Make Important Corrections in the Conventional Wisdom
To Understand the Essential, Qualitative Features
Bailey, J.E., Biotech Prog 14:8-20 (1998)

14. “What I cannot create, I do not understand” Richard Feynman

15. Reconstructing complex systems
“And that’s why we need a computer”

16. Networks Have States: steady, dynamic & physiological states
Basic Concepts in Dynamic Analysis:
Time constant; t1/2, t, …
Aggregate variables, multi-scale analysis
ATP2ATP+ADP “pools”
Transition from one steady state to another
Graphical presentation of solution

17. The Two Fundamental Approaches
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
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

18. 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 ignoredmedium is homogeneous ~100nm
Constant temperature; isothermal (also isobaric)
Need more icons on this slide

20. Mathematical Representation:
3 key matrices
S: Network topology/structure
links 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 magnitude
in numerical values—ill conditioned, sparse)
(biological origin is genetic)
J: The Jacobian matrix contains the dynamic properties
of the network, J=S•G
1/t-1/min
1/t-1/hr
l1, l2,…lm

21. Attributes of the Stoichiometric and Gradient Matrices

22. S and G as Mapping Operations
G and S are structurally similar
S~-GT (location of non-zero elements is the same)
i.e., if sij=0, then gji=0; and if sij≠0, then gji ≠0
S contains chemistry
S=(||||)
reaction vectors are columns in S
G contains kinetics and thermodynamics
reactions form rows in G b
ki is the “length” of gi
kinetics; diagonal matrix
thermodynamics =
G=( ) = k G

23. 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

24. Summary
Networks have dynamic states that are characterized by time constants, pooling of variables, and characteristic transitions.
Dynamic states are difficult to analyze mathematically and therefore the subject matter of this book is mathematically challenging.
The basic dynamic properties of a network come down to analyzing the spectrum of time scales associated with a network and how the concentrations move on these time scales.
Sometimes the concentrations move in tandem at certain time scales leading to the formation of aggregate variables. This property is key to the hierarchical decomposition of networks and the understanding of how physiological functions are formed.
There are significant assumptions leading to an ordinary differential equations formalism to describe dynamic states. Most notably is the elimination of molecular noise, considering volumes and temperature to be constant, and considering spatial structure to be insignificant.
The study of the dynamic states of networks comes down to the study of three matrices: the stoichiometric matrix, that is typically well-known, the gradient matrix, whose elements are harder to determine, and the Jacobian matrix, that is the product of the two.