BT8118 – Adv. Topics in Systems Biology Prof. Eivind Almaas Dept. of Biotechnology, NTNU

Course overview 3 double-day meetings: 23&24/9, 14&15/10, 28&29/10 Grade: based on project presentation (50%) and oral examination (50%) Final exam: 18/11 15-20 min project presentations in plenum Individual projects handed out 14/10: A metabolic reconstruction

Intended Learning Outcomes At the completion of this course, the student should be able to: Explain the principles and central methods of linear programming, as well as formulate and solve linear programming problems using pen and paper or MatLab Discuss the steps involved in metabolic network reconstruction, and describe how to evaluate a model’s fidelity Explain the principles of constraint-based modeling, and discuss its strengths and weaknesses, as well as using computer analysis to determine a model’s phenotypic behavior Use FBA, MoMA, and dynamic FBA to analyze a metabolic model and further modify it to achieve a predetermined objective To achieve the Intended Learning Outcomes, class sessions will be based on active discussions & participation, not solely on lectures.

Introduction

Cellular networks: GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

Bacterial cells are complex dynamical systems They interact nonlinearly with their environments through e.g. - movement (chemotaxis) - quorum sensing - hysteretic response Display functional stability — they generally behave predictably e.g. - cell cycle progression - measured growth - substrate uptake and excretion rates

Metabolic chart from Roche Applied Science Point out TCA cycle (tricarboxylic acid cycle) …not only networks in biology…

Metabolism: Flux Balance Analysis (FBA) FBA input: List of metabolic reactions Reaction stoichiometry Impose mass balance Impose steady state Optimize goal function FBA ignores: Fluctuations and transients Enzyme efficiencies Metabolite concentrations / toxicity Regulatory effects Cellular localization … Standard form linear program formulation:

FBA idea Most used (and only currently realistic) method for modeling genome-scale metabolism Based on: List of all possible reactions Mass conservation Steady-state Optimization of a cellular objective

Example: Cartoon metabolism Optimal growth curve 1 2 6 3 4 5 7 1 1 2 6 4 3 4 5 7 2 3 Optimization of objective function 1 2 3 optimal growth line Edwards et al, Biotechn. Bioeng. 77, 27 (2002)

Experiment: E. coli growth on glycerol Study adaptive growth of E. coli on glycerol: 60-day experiment Three independent populations: E1 & E2 @ T=30C; E3 @ T=37C Initially sub-optimal performance glycerol R.U. Ibarra, J.S. Edwards & B.O. Palsson, Nature 420, 186 (2002)

FBA calculations Metabolic flux map Metabolic flux statistics Some possibilities: Predict single- and double-knockout mutants, test experimentally Identify possible minimal genomes Identify high-flux reaction sets Identify reasons for enzyme dispensability and gene-dosage Mechanisms for bacterial adaptation to growth environment, test experimentally

How do we get “there”? Need to understand WHAT a metabolic network is Have a good grasp of what goes into MAKING a metabolic reconstruction Understand the modeling PRINCIPLES and METHODS to know their strengths and pitfalls Know state-of-the-art COMPUTATIONAL tools, so that you do not have to re-invent the wheel!!

Metabolic network representations E. Almaas, J. Exp. Biol. 210, 1548 (2007)

Effect of network representation E. Almaas, J. Exp. Biol. 210, 1548 (2007)

Effect of network representation E. Almaas, J. Exp. Biol. 210, 1548 (2007)

Metabolic networks scale-free in all domains of life Large-scale Metabolic Network Structure Nodes: chemicals (substrates) Links: chem. reaction Archaea Bacteria Eukaryotes Metabolic networks scale-free in all domains of life H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature 407, 651 (2000).

How do we get “there”? Need to understand WHAT a metabolic network is Have a good grasp of what goes into MAKING a metabolic reconstruction Understand the modeling PRINCIPLES and METHODS to know their strengths and pitfalls Know state-of-the-art COMPUTATIONAL tools, so that you do not have to re-invent the wheel!!

What is a metabolic reconstruction? 2. What steps should go into a metabolic reconstruction process?

Thiele & Palsson, Nature Protcols, 5:95 (2010)

Refinement of reconstruction

Gene-protein relations (GPR)

Biomass function

Cellular (bacterial) composition Growth-associated maintenance

Confidence score to assess quality of model reconstruction pieces

Thiele & Palsson, Nature Protcols, 5:95 (2010)

Mathematical representations of metabolic networks

Stoichiometric Matrix: “Container” for reaction information What is missing?

Metabolite vs. Reaction centric view

Why / how is the S-matrix relevant Why / how is the S-matrix relevant?  Represent metabolism as dynamical system in steady state

Linear Programming

Simple example

Basic Feasible solutions

Solution space Synonymous: Null space or (Right) null space Rows of A correspond to constraints (metabolite mass conservation) on the variables (fluxes) Columns of A correspond to reactions

Solution space Synonymous: Null space or (Right) null space What is A? Null space of A?

In and out of Null space Stoichiometric matrix: S = [-1 -1 2] - x - y + 2 z = 0 Normal vector to plane: [-1, -1, 2] /√6 Possible null space (2-d) basis vectors: a = [1,1,1] /√3 b = [-1,1,0] /√2 Corresponding projection matrix: √(2/5), -√(3/5) √(2/5), √(3/5) 1 , 0 b a

Fundamental Theorem of Linear Optimization

Simplex algorithm

Simplex example