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Higher Order Systems


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Title: Higher Order Systems

  • Higher Order Systems

In this presentation
  • Part 1 Genetic Regulatory Networks
  • Part 2 Molecular Pathways
  • Part 3 Protein Interactions
  • Part 4 Modeling Regulatory Networks

Part 1
  • Genetic Regulatory Networks

Genetic regulatory networks
Higher order systems
  • Although genes and proteins can be studied
    individually, more insight into their functions
    can be gained by studying higher-order systems,
    that is, molecular pathways and networks, cells,
    tissues, organs and whole organisms
  • This allows their physical and functional
    interactions to be determined in the widest
    possible context

  • The work of Tavazoie et al (1999) is vividly
    known for systematic determination of genetic
    network architecture
  • Cell signaling pathways are linked to genetic
    regulatory pathways in ways we are just beginning
    to unscramble
  • The most enormous bioinformatics project in front
    of the scientists is unscrambling this regulatory
    network, which controls cell development from the
    fertilized egg to the adult

  • It would become possible to know which gene to
    perturb or which sequence of genes to perturb,
    and in what order to guide a cancer cell to
    nonmalignant behaviour or to apoptosis
    programmed to cell death
  • Or to guide the regeneration of some tissues, so
    that if someone has lost half of the pancreas,
    the damaged portion could be regenerated
  • Or to regenerate the beta cells in people who
    have diabetes

  • Suppose about 10 genes are picked out that are
    known to regulate one another, then a circuit
    could be built about their behaviour. It is a
    good thing and one should do this but the down
    side will be that those 10 genes have inputs from
    other genes outside that circuit. Therefore, it
    is like taking a little chunk of the circuitry
    that is embedded in a much larger circuit of
    thousands of genes in it. The behaviour can not
    be then properly assessed as to how and what
    impact the outside genes would create

  • It is known for years that every neuron in the
    lobster gastric ganglia a nerve bundle going to
    the animals digestive system, all the synaptic
    connections and the neurotransmitters
  • There would be 13 or 20 neurons in the ganglion
    and still its behaviour cannot be figured out
  • No mathematician would ever think that
    understanding a system with 13 variables is going
    to be an easy thing to do

  • In the human genome case, there would be more
    than 100,000 variables i.e. there would be
    2100,000 states, which is roughly 1030,000
  • So even if genes are treated to be on or off,
    there are 1030,000 states (which is false as
    genes show graded level of activity)
  • It is mind boggling because the number of
    particles in known universe is 1080

Types of pathways
  • Molecular pathways
  • Metabolic pathways
  • Signaling and regulatory pathways
  • Protein interaction networks

Part 2
  • Molecular Pathways

Representation of pathways and networks
  • Molecular pathways and networks can be
    represented by graphs, with molecules at the
    nodes and relationships shown by links
  • In metabolic pathways, nodes represent substrates
    or intermediates and links represent their
    catalytic interconversion by enzymes
  • In signaling and regulatory pathways, nodes
    represent proteins and links indicate the
    transfer of information
  • Graphs of molecular pathways are generally
    directional and can show positive and negative

Reconstruction of molecular pathways
  • Pathways and networks can be mapped directly by
    substrate feeding experiments and in vitro enzyme
  • More recently, a number of indirect but
    high-throughput methods have been developed
    thanks to the advent of functional genomics
  • These methods include pathway reconstruction from
    expression data, protein interaction and
    comprehensive mutagenesis programs

Modeling molecular pathways
  • Mathematical models of biochemical reactions are
    often based on differential equations that
    predict the change in concentration of particular
    molecules over time
  • Simultaneous differential equations can be used
    to model entire pathways and several software
    applications are available for this task,
    including GEPASI and BioQuest

  • There are limitations to the use of simultaneous
    differential equations and these have been
    addressed through the development of stochastic
    models based on the Gillespie algorithm, which is
    incorporated into programs such as StochSim

Subgraph with main interactions between GAD and
GABA-receptors, derived from the linear model. P.
D'haeseleer, X. Wen, S. Fuhrman, and R. Somogyi
(1999) Linear Modeling of mRNA Expression Levels
During CNS Development and Injury
Overview of Procedures for Preparing and
Analyzing Microarrays of Complementary DNA (cDNA)
and Breast-Tumor Tissue. As shown in Panel A,
reference RNA and tumor RNA are labeled by
reverse transcription with different fluorescent
dyes (green for the reference cells and red for
the tumor cells) and hybridized to a cDNA
microarray containing robotically printed cDNA
clones. As shown in Panel B, the slides are
scanned with a confocal laser scanning
microscope, and color images are generated for
each hybridization with RNA from the tumor and
reference cells. Genes up-regulated in the tumors
appear red, whereas those with decreased
expression appear green. Genes with similar
levels of expression in the two samples appear
yellow. Genes of interest are selected on the
basis of the differences in the level of
expression by known tumor classes (e.g.,
BRCA1-mutationpositive and BRCA2-mutationpositiv
e). Statistical analysis determines whether these
differences in the gene-expression profiles are
greater than would be expected by chance. As
shown in Panel C, the differences in the patterns
of gene expression between tumor classes can be
portrayed in the form of a color-coded plot, and
the relations between tumors can be portrayed in
the form of a multidimensional-scaling plot.
Tumors with similar gene-expression profiles
cluster close to one another in the
multidimensional-scaling plot. As shown in Panel
D, particular genes of interest can be further
studied through the use of a large number of
arrayed, paraffin embedded tumor specimens,
referred to as tissue microarrays. As shown in
Panel E, immunohistochemical analyses of hundreds
or thousands of these arrayed biopsy specimens
can be performed in order to extend the
microarray findings.
  • The two basic clusters of a) early and b) late
    upregulated genes as identified by percolation
    clustering. Color coding of the expression
    profiles is as follows black means gene
    expression is the same as it was at 2 hours of
    development increasing tint of red color means
    increasing expression relative to 2 hours and
    increasing tint of green color means decreasing
    expression relative to 2 hours
  • The bottom portions of the figure display
    expression profiles of the corresponding genes
    the red curves are the mean expression. Only
    genes whose connectivity to the cluster origins
    is greater than 20 were included in these plots.

Templates for Looking At Gene Expression
Clustering By Daniel B. Carr, Roland Somogyi and
George Michaels
Gene co-expression pairs in CNS development and
Mutual information tree for genes expressed in
rat spinal cord. Michaels G, Carr DB, Wen X,
Fuhrman S, Askenazi M, Somogyi R (1998) Cluster
Analysis and Data Visualization of Large-Scale
Gene Expression Data
Gene expression waves. (a) Normalized gene
expression trajectories from Fig. 2 are shown
grouped by waves determined by Euclidean
distance clustering. Graphs show average
normalized expression pattern or wave over
the nine time points for all the genes in each
cluster (the time of birth is marked by a
vertical line). Within each wave, genes are
grouped according to gene families, not according
to proximity as determined by Euclidean distance.
(b) Euclidean distance tree of all gene
expression patterns (for annotated tree, see
). Major branches correspond to waves in a. (c)
Plots of all normalized time series, highlighting
wave 3 (Left, white lines) and a subcluster of
wave 3 (Right, white lines plotted on top of
remaining genes of wave 3 in red). Subclusters
(secondary branching) were selected by visual
inspection from tree in b e.g., the plotted time
series of the wave 3 subcluster correspond to
branchlet highlighted in white within wave 3 in
b. (d) PCA. Principal components projection
viewed as a three-dimensional stereo plot. Each
point mapped in three-dimensional space
represents an expression time series
corresponding to a gene in Fig. 2. Highlighted
points correspond to Euclidean distance wave 3
(red triangles), wave 4 (green squares), and the
remaining genes (blue octagons)
Molecular pathway resources
  • There are many resources for viewing molecular
    pathways on the Internet
  • One of the most comprehensive for metabolic
    pathways is KEGG and this also shows a selected
    range of regulatory pathways
  • An important feature of such resources is that
    the contents of the maps are integrated with
    other databases by way of hyperlinks

Part 3
  • Protein Interactions

Interactions and pathways
  • Proteins that physically interact with each other
    may be involved in the same molecular pathway or
    network, or may form part of a multi-subunit
  • Using this principle, pathways can be
    reconstructed based on evidence of protein
  • However, information from other sources e.g.
    gene expression patterns and mutant phenotypes
    may also be useful

Handling Y2H data
  • Yeast two-hybrid (Y2H) screens produce large
    amounts of protein interaction data, but there is
    a relatively high level of spurious results
    (false positives and false negatives)
  • This problem can be addressed by scoring
    interactions for reliability, based either on the
    repeatability of interactions over multiple
    experiments, or by the number of times a given
    bait will trap independent clones representing
    the same prey
  • Even so, similar large-scale screens tend to
    identify different (although) overlapping sets of

Protein interaction databases
  • Several databases have been set up to store the
    interaction data arising from large-scale Y2H
  • However, much more information on protein
    interactions is available in the scientific
    literature and a current challenge in
    bioinformatics is the assimilation of these
    interaction data from diverse sources

The interactome
  • It is sum of all protein interactions in the cell
  • The simplest way to represent protein
    interactions is a graph with proteins as nodes
    and interactions as links
  • However, when large numbers of proteins are
    considered, the graphs become too complex
  • They can be simplified by clustering functionally
    similar proteins, resulting in a functional
    interaction map that links fundamental cellular

Part 4
  • Modeling Regulatory Networks

The cell
  • It can be regarded as a compartmentalized set of
    molecular pathways and networks distributed in
    space and restricted by membranes
  • Any model of a cell must incorporate these
  • A useful modeling resource is Virtual Cell, in
    which the cell is defined as a collection of
    structures, molecules, reactions and fluxes
  • The user can define biological or mathematical
    models for cell function

Modeling tissues and organs
  • Tissues and organs comprise organized population
    of interdependent cells
  • Modeling depends on an accurate description of
    the geometry of the tissue and must include any
    time-dependent processes
  • For example, modeling the heart requires a
    description of its anatomy and the way in which
    action potentials are propagated
  • The model must take into account the fact that
    cardiac muscle is an anisotropic system

Modeling organisms
  • In order to model an entire organism, it is
    necessary to have a sound understanding of the
    principles underlying development
  • For most multicellular organisms there is too
    little information and the developmental program
    too complex for this to be achieved

Nematode C. elegans modeled
  • The nematode has a number of features that make
    it an ideal system upon which to base a
    developmental model
  • It is a simple organism (it has about 1000
    somatic cells) whose somatic cell lineage is
    invariant, making perturbations in development
    very easy to identify
  • The genome has been sequenced indeed, it was the
    first genome of a multicellular organism to be
  • It also relatively easy to study the physiology
    of this organism, and hence a complete wiring
    diagram of C. elegans nervous system is available

Modeling spaces
  • Models of C. elegans development have been
    generated based on the concept of three spaces
  • Genomic space
  • Cellular space
  • Developmental space

Relationships among three spaces
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