Lecture 10 Flashcards
1
Q
Networks - Abstraction of Cell Regulation
A
- Construct Gene Regulatory Network
- Networks in general large
=> need computers
2
Q
Network Topology - All Networks are Equal
A
- All networks have same components: Nodes & Edges
- But dierent topology: dierences in incoming/outgoing edges per node
3
Q
Network Biology
A
- 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”
4
Q
The Königsberger Bridge Problem
A
- 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
5
Q
Networks and Graphs in Biology
A
- 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
6
Q
Yeast 2 Hybrid Screening
A
- 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
7
Q
Erlös-Rényi Network
A
- 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)
8
Q
Network diameter
A
- 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
9
Q
Facebook - A Small World Network
A
- 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
10
Q
Consequences for Cancer Biology
A
- Few genes frequently mutated
- Oncogenes & Tumor Suppressor Genes
- Mostly hub-proteins
- Rationale on diagnosis & treatment
11
Q
Preferential Attachment
A
- 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
12
Q
Hierarchy and Modularity
A
- 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