Lecture 10

Question 1

Networks - Abstraction of Cell Regulation

Answer 1

• Construct Gene Regulatory Network
• Networks in general large

  => need computers

Question 2

Network Topology - All Networks are Equal

Answer 2

• All networks have same components: Nodes & Edges
• But dierent topology: dierences in incoming/outgoing edges per node

Question 3

Network Biology

Answer 3

• Genes and proteins interact in a complex network
• Can we gain knowledge from the network analysis?
• All proteins equally important
• Imagine: proteins interact on a regular grid. All proteins have same # of interactors
• All proteins equally important
• True biological Networks look “modular”

Question 4

The Königsberger Bridge Problem

Answer 4

• Recent paper:
• Leonhard Euler, Solutio problematis ad geometriam situs pertinentis,
  in Commentarii academiae scientiarum Petropolitanae 8, 1741, pp. 128-140
• Question:
• Can you walk through the whole city and cross each bridge only once given that
• You cannot swim to the island, bridges must be crossed completely
• Start and end points of the walk need not be the same.
• Solution: Abstract the problem
• The paths on the island do not matter, then
• Consider land mass as vertex or node
• Each bridge as connection, called edge, between nodes
• Graph with 4 nodes, and 7 edges
• Degree: the numbers of edges touching a node
  Solution: graph must be connected and have 0 or 2 nodes of odd degree

Question 5

Networks and Graphs in Biology

Answer 5

• 1000s of genes/proteins interacting in Eucaryotes/Procaryotes
• Disregard kinetics of interaction for now => depict as network
  -> Always possible, if complex system reducible to discrete elements and their relations => possible for most complex system
• Describe dierent things: causal or mechanistic eects
  -> Chemical, logic, functional relatedness
• Inferred from
  -> screening data, such as Yeast 2 Hybrid
  -> text mining
• Highlights topology => might be more important than dynamics!

Network examples:
- The Social Network
- gene Interaction network
- transcription network in E.coli
- protein-protein interaction in yeast
- the human disease network

Question 6

Yeast 2 Hybrid Screening

Answer 6

• Y2H detects the physical interactions of proteins through downstream activation of a reporter gene.
• Modular TFs: DNA binding & activating domain
  -> Tag bait to DBD & prey to activating domain => reside on plasmids in yeast
  -> If proteins interact => gene necessary for survival expressed,
  -> e.g. leucine/ histidine/tryptophan biosynthesis genes
  -> Separate QCs for plasmid transfection/interaction
  -> Finally sequence surviving strains => Interactions
• Drawback: high false positive/negative rates, dierent proteins in yeast and human
• Qualitative data only

Question 7

Erlös-Rényi Network

Answer 7

• A model network, proposed 50 years ago
• Explains certain properties of real networks
• Benchmark real networks Null-model for networks (no such network really exists)
• Dumbest model:
  -> n nodes & draw edges with probability p between pairs
  -> For each n(n-1)/2 edges (can you see this?):
  -> draw edge with prob. p, skip edge with prob. (1-p)
• Elementary random network G(n, p)

Question 8

Network diameter

Answer 8

• Diameter: longest sorgtest path between pairs of nodes
• Equivalently: average distance between two random nodes
  -> n nodes, fully connected: diameter d = 1
  -> n nodes, linear chain d = n-1
• ER network: increase p from 0 -> 1
  -> becomes fully connected
  -> Diameter finite, becomes 1 for p = 1
• How does diameter d depend on p?
• Assume network with identical degrees z=p(n-1)
• How many nodes reached in l steps? 19
• Step 1: z
• Step 2: z(z-1) * Step 3: z(z-1)2

Question 9

Facebook - A Small World Network

Answer 9

• 6 edges between any person in the world
• How close are you to Bill Gates?
• Shortcuts between nodes:
• all nodes are close to each other
• 6 edges between any person in the world

Question 10

Consequences for Cancer Biology

Answer 10

• Few genes frequently mutated
• Oncogenes & Tumor Suppressor Genes
• Mostly hub-proteins
• Rationale on diagnosis & treatment

Question 11

Preferential Attachment

Answer 11

• Structure related to formation process
• Network growth & preferential attachment (The rich get richer) * New nodes are attached to nodes proportional to their degree
• Both processes are necessary for scale-free topology
• Biological Explanations
• Gene Duplication
• High prob. that random new protein attached to a hub node
• Hubs are evolutionary older e.g.
• coenzyme A: oxydation of fatty acids
• Guanosine triphosphate (GTP): signal transmitters
• Nicotinamide adenine dinucleotide (NAD): redox reactions

Question 12

Hierarchy and Modularity

Answer 12

• How to resolve hierarchy in a scale-free network?
• Hubs break layered architecture
• Instead: modularize network into clusters
• Hierarchy: number of modules a node belongs to
  -> Low hierarchy: few functional tasks
  -> High hierarchy: many tasks