Lecture #1 Introduction

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 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

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

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

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 Acetone monooxygenase Acetone Methylglyoxal metabolism Global human metabolic network Cytochrome P450, family 2, subfamily E, polypeptide 1

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

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) 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)

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)

“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: 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

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

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

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

Attributes of the Stoichiometric and Gradient Matrices

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

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

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.