Functional Genomics and Gene Network Analysis

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Functional Genomics and Gene Network Analysis

• Alexandra Maertens
• Oct. 5, 2004

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Functional Genomics

• The fundamental strategy of functional genomics
  is to expand the scope of biological
  investigation from studying single genes or
  proteins to studying all genes or proteins at
  once in a systematic fashion.
• Functional genomics seeks to narrow the gap
  between sequence and function and to yield new
  insights into the behavior of biological
  systems.
• paraphrased from http//bip.weizmann.ac.il/mb/func
  tional_genomics.html

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How to determine functionally related genes?

• 40 of predicted genes in newly sequenced
  genomes cannot be assigned function based on
  sequence similarity
• Other techniques include data across
  phylogenetic profiles, looking for gene fusion
  events, etc. but all of these techniques are
  inexact

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Does co-regulation imply functional similarity?

• Guilt by association genes sharing a common
  pattern of expression in many different
  experiment are likely to be involved in similar
  processes
• This technique has been used by Tavazoie et al.
  (1999) to identify biologically significant
  DNA-motifs in the promoter region of genes
  clustered based on cell-cycle expression patterns
  in yeast.
• Limited applicability for determining functions
  of genes in a single species

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Co-Expression Can Be Caused By

• Gene A regulates Gene B, or vice versa
• Or, they are both regulated by a third gene, C
• It can just represent a common response to the
  environment of the cell
• And lastly it can be an accident

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Determining Co-Regulation in Large Scale Data Sets

• Euclidean Distance
• Pearson
• Spearman

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Euclidean Distance

• Commonly used
• Not practical for analyzing a large data set with
  a diverse set of microarrays
• Microarrays do not really measure an absolute
  amount of mRNA they should be considered as
  measuring the relative amount of mRNA
• There will be large differences in range of
  values for two microarrays done at different
  times

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• The Pearson Correlation treats the vectors as if
  they were the same (unit) length, and is thus
  insensitive to the amplitude of changes that may
  be seen in the expression profiles.
• Since Euclidean distance measures the absolute
  distance between points in space, the Euclidean
  distance thus takes into account both the
  direction and the magnitude of the vectors.
• From Stanford Microarray Database,

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Pearsons

• How well does a linear function describe the
  relationship between two variables?
• Values ranges between -1 (negative correlation),
  0 (no correlation), and 1 (perfect correlation)

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Pearson(courtesy of Hyperstat.com)
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R 0.778184
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Spearman

• from www.mathworld.com

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Convert each expression value to a value
according to rank in each column (from lowest to
highest)
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• Calculate the difference between the ranks

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Going From Distance Measurements to Networks

• Why do biologists care about networks?

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FromPatrik DhaeseleerHarvard
Universityhttp/genetics.med.harvard.edu/patrik

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Yeast Protein Interaction Network
Uetz, Schwikowski, Fields and co-workers Ito and
co-workers
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Image credit U.S. Department of Energy
GenomicsGTL Program, http//doegenomestolife.org
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A network is simply

• A collection of nodes (vertices)
• Connected by edges (links)

From Barbassi, Nature Review Genetics, Vol. 5
Feb, 2004
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From the layout of the network, you can calculate
a lot of interesting properties.

• Degree the connectivity, k, which is the number
  of links a node has to its neighbours
• Degree distribution P(k) gives the probability
  that a node will have a given k number of links
  (obtained by counting the number of nodes and
  with each value of k and dividing by the total
  number of nodes)

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• From this, you can calculate whether the network
  is scale-free
• This means that P(k) is propertional to k- g
• Usually g is around 2
• This means that the network is organized into a
  hub and spoke system with a small number of
  nodes having a large number of links

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• If there are N nodes in a network, the number of
  possible connections is N2
• Assuming a modest 6,000 genes, that is still more
  than we can hope to experimentally determine
• However, using correlation between two genes (or
  orthologues) across several different experiments
  as a stand-in for links, we can use microarrays
  to develop a basic network that can then be
  refined
• The more experiments, and the more types of
  experiments, that we find the gene co-expressed,
  the more probable they are truly linked.

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Hierarchical clustering vs. non-hierarchical
clustering

• Hierarchical clustering (various agglomerative
  and divisive techniques) treat the data as if we
  have no idea how many clusters there should be.

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K-means clustering

• the user decides in advance how many clusters
  there will be
• this is a good method if you a priori know who
  many clusters you want (for example, three time
  points, you would use three different clusters)
• alternatively, if you visually inspect the data
  you can see if there appears to be certain number
  of clusters
• If all else fails, there are computer programs
  that calculate an ideal k-cluster out of many
  possible values for k
• goal is to divide the objects into K clusters
  such that some distance metric relative to the
  centroids of the clusters is minimized

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• Initial reference vectors are assigned randomly
  or according to previous knowledge
• Assign each object to one of k clusters randomly
• Calculate average expression vectors for each
  cluster (as reference vectors) and the distance
  between clusters
• Iteratively move objects between clusters and the
  objects stay in the new cluster when they are
  closer to the new cluster than to the old
  cluster.
• Repeat steps 3-4 until converge, i.e. moving any
  more objects would increase intra-cluster
  distances

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For every cluster k, sum the differences between
every data point Xn in the cluster and the
geometric mean of the cluster.
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Finding the Center
                                             
so the new cluster centre for A is 19.666 , 21
This process is repeated until successive
iterations cause no overall change in the sum of
distances of each point in each cluster from the
center. (adapted from http//www.ucl.ac.uk/oncolog
y/MicroCore/HTML_resource/KMeans_eq_popup.htm
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http//www-2.cs.cmu.edu/awm/tutorials/kmeans10.pd
f
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• Remember
• Clustering always works.
• There is no guarantee it is the optimal
  partition.

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• Analyze coexpression relationships of homologous
  sets of genes in human, fly, worm, yeast to
  identify conserved genetic modules
• 3182 microarrays over multiple groups of
  homologous genes (metagenes)

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• Metagenes
• Orthologous counterparts in different organisms
• Best reciprocal BLAST hit
• Each gene assigned to at least one metagene

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BLAST

• stands for Basic Local Alignment Search Tool
• Performs a pairwise alignment of two strings
  (either nucleotides or amino acids)
• Amino acids are scored according to their
  similarity chemical similarity and observed
  mutation frequencies
• The probability that this match could have
  occurred by chance is given as an E value

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A Metagene
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Global View of the Data Set
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• They then identified pairs of genes by
  relabeling each gene in each species with its
  metagene, and then comparing expression levels
  across each different array. This provided a
  Pearson correlation.

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Are the data sufficient?

• Divided the data set randomly into half
• Used each half independently to generate a
  network and compared this to the network
  generated by the total data to see how many
  interactions were maintained at the same level of
  statistical significance
• Only 40 of the interactions observed were
  statistically significant in both halves

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• You can interpret this number two ways
• 1) The approach is sensitive to the amount of
  data used
• 2) However, even with only half of the data,
  there was still some signal amidst the noise

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How robust is the constructed network to noise?

• They added increasing amouts of Gaussian noise
  and found that the network was robust with
  realistic levels of noise seen in microarray
  experiments

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• Permutating your data preserves the same
  distribution of your data, but without the labels
• They claim that they randomly permutated gene
  expression data. This is a bit ambiguous
• Probably means they shuffled the expression data
  within the species column, so the consistency of
  the metagenes would cease to hold throughout the
  row
• They repeated this shuffling 10 times. The point
  of shuffling is to get a representative sample of
  the ways you could rearrange your objects 10 is
  a conservative number for this instance.

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Using Several Different Species

• By using more species, are you just providing
  more data or is there a benefit to looking at
  conservation of coexpression across several
  distantly related species

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Using Several Different Species
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How to go from this data to a network?

• For each metagene, m1, they ranked each other
  instance of the metagene in each species by how
  well they correlate, and then compared this
  across species, producing a rank ratios each
  specis for each directed pair
• They calculated a joint probability distribution
  based on order statistics to determine if these
  rankings were statistically significant.

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• They then used this p-value to do to things
• if the p-value was above a cutoff (corrected for
  multiple tests) this defined a link
• The strength of the p-value then provided a
  distance metric that was then used visualize the
  grouping of the data
• From visual inspection of this data, the ydecided
  upon 12 clusters, and then performed k-means
  clustering

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Do these clusters effectively group functionally
related genes?

• The Gene Ontology (or GO) terminology provides a
  controlled vocabulary to describe protein and
  gene function, cellular location and biological
  process
• You can calculate whether you have an
  overrepresentation of certain GO terms in any
  given cluster to characterize the cluster
• The P-value is derived from a a hypergeometric
  distribution (sampling without replacement), as
  the probability of x or more out of n genes
  having a given annotation, given that G of N have
  that annotation in the genome in general.
  (Probably done by GOFinder)

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Do these clusters effectively group functionally
related genes?
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• However, this is a bit suspicious.
• If you look in their supplemental material, you
  find metagenes that were further than d units
  away from their closest center were excluded from
  membership in any of the 12 components. We chose
  d to be 10 of the diameter of the entire
  landscape.
• How many were excluded?

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But are these predictions biologically valid?

• Finding these metagenes in cancer data does
  imply that they are connected to cell
  proliferation, but it is weak proof that they are
  actually cell proliferation genes

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But are these predictions biologically valid?

• RNAi involves feeding small double stranded
  oligonucleotides into cells, tricks cells into
  degrading its own mRNA.
• New technique for quickly knocking out or
  knocking down gene expression.

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Worm gonads stained for DNA wt-type worms show
less nucei
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• Not a properly done RNAi experiment
• How much does one experiment tell you? (Did they
  have to do 10 RNAi experiments based on their
  predictions before one worked?)

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Does this network look like a biological network?

• Count the number of links of each metagene (with
  links being defined by the number of other
  metagenes with coexpressed for a given P-value)
• See if the distribution of links is non-random
  and different from a network generated from
  random data

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Does this network look like a biological network?
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• Does this likely reflect the actual distribution
  of links, or does this data by definition select
  highly linked genes?

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What are the limitations?

• Is has been estimated that in humans 95 of mRNA
  transcripts are expressed at
  lt5 copies/cell
  Velculescu et al.(1997), Cell 88243-251