Example of Modeling Signal Transduction Systems

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Example of Modeling Signal Transduction Systems

• Julie Dickerson

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References and Readings

• P53 Models and data Oscillations and variability
  in the p53 system. Geva-Zatorsky N, Rosenfeld N,
  Itzkovitz S, Milo R, Sigal A, Dekel E, Yarnitzky
  T, Liron Y, Polak P, Lahav G, Alon U., Mol Syst
  Biol 200622006.0033.
• Biomodels.net database of models from
  publications
• SBML.org systems biology markup language
  definitions links to tools and models

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Biological Problem

• In the p53 system, p53 transcriptionally
  activates mdm2. Mdm2, in turn, negatively
  regulates p53 by both inhibiting its activity as
  a transcription factor and by enhancing its
  degradation rate
• The concentration of p53 increases in response to
  stress signals, such as DNA damage. The main
  mechanism for this increase is stabilization of
  p53 due to reduced interaction with Mdm2.
• Following stress signals, p53 activates
  transcription of several hundred genes that are
  involved in growth arrest, apoptosis, senescence,
  and DNA repair.
• Isogenic cells in the same environment behaved in
  highly variable ways following DNA-damaging gamma
  irradiation some cells showed undamped
  oscillations for at least 3 days (more than 10
  peaks).
• Reference Oscillations and variability in the
  p53 system. Geva-Zatorsky N, Rosenfeld N,
  Itzkovitz S, Milo R, Sigal A, Dekel E, Yarnitzky
  T, Liron Y, Polak P, Lahav G, Alon U., Mol Syst
  Biol 200622006.0033.

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Modeling Problem

• The amplitude of the oscillations was much more
  variable than the period. Sister cells continued
  to oscillate in a correlated way after cell
  division, but lost correlation after about 11 h
  on average. Other cells showed low-frequency
  fluctuations that did not resemble oscillations.
• Why does this occur? Can models help us
  understand this?
• Different families of mathematical models of the
  system point to the possible source of the
  variability in the oscillations low-frequency
  noise in protein production rates, rather than
  noise in other parameters such as degradation
  rates.
• Models available at biomodels.net (numbers
  154-159, curated models)

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Transcriptional activation
Negative regulation Inhibits transcription Enhance
s degradation
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Also activates 100s of genes DNA
repair Apoptosis Growth arrest
Transcriptional activation
Stress signals DNA Damage
Negative regulation Inhibits transcription Enhance
s degradation
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Feedback loops

• Oscillatory dynamics, changing dynamics

monotone
Damped Oscillations
Sustained oscillation
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P53 system

• Studies with this system that used averages of
  cell responses showed damped oscillations
  following DNA damage.
• Individual cell studies show a variation in
  responses in cells
• Amplitudes changed, frequency did not change much

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Fluorescent Microscopy

• Fluorescence microscopy is one of the most used
  approaches in studying the location and movement
  of molecules and subcellular components in the
  cell.
• Sample is itself the light source.
• Based on the phenomenon that certain material
  emits energy detectable as visible light when
  irradiated with the light of a specific
  wavelength.
• Samples can either be fluorescing in their
  natural form like chlorophyll and some minerals,
  or treated with fluorescing chemicals.
• Usually, cellular components do not fluoresce
  themselves. Fluorescent markers are therefore
  introduced.

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• Fluorescent DyesFluorescent dyes are directly
  taken up by the cells. They are incorporated and
  concentrated in specific subcellular
  compartments. The living cells are then mounted
  on a microscope slide and examined.
• ImmunofluorescenceImmunofluorescence involves
  the use of antibodies to which a fluorescent
  marker has been attached. Antibodies are
  molecules that recognize and bind selectively to
  specific target molecules in the cell. The
  fluorescent signal can be amplified by using an
  unlabelled primary antibody and detecting it with
  labelled secondary antibodies.
• Tagging of ProteinsProtein molecules are tagged
  with a fluorescing marker. When a specific
  protein is modified in this way, the location of
  that protein can be studied. It is also possible
  to watch the movements of the proteins and its
  interactions with other cellular components
  inside the cell.

http//nobelprize.org/educational_games/physics/mi
croscopes/fluorescence/preparation.html
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C. Elegans Nervous System The image shows the
brain region of a living C. elegans animal.
Different classes of neurons are labelled with
different colors. Photo H. Hutter, Max Planck
Institut, Heidelberg
Fluorescence triple-labeling of human cells. The
DNA in two interphase cell nuclei (left and
right) and in metaphase chromosomes from a third
cell (middle) are shown in blue. Specific DNA
sequences are labeled in red and green. Photo
Petra Björk, Stockholm University
Fluorescence triple-labeling of human cells.
Cytoplasmic fiber structures (microfilament) are
shown in red. Components of the cell nuclei are
shown in blue (nucleoli) and green (splicing
factor). Photo Petra Björk, Stockholm University
Epithelium Cells Immunofluorescence staining of
epithelium cell (Hep-2) mitochondria. (Zeiss)
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Time Lapse microscopy of cells
From supplementary data Oscillations and
variability in the p53 system. Geva-Zatorsky N,
Rosenfeld N, Itzkovitz S, Milo R, Sigal A, Dekel
E, Yarnitzky T, Liron Y, Polak P, Lahav G, Alon
U., Mol Syst Biol 200622006.0033.
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• Prolonged oscillations in the nuclear levels of
  fluorescently tagged p53 and Mdm2 in individual
  MCF7, U280, cells following gamma irradiation.
  (A) Time-lapse fluorescence images of one cell
  over 29 h after 5 Gy of gamma irradiation.
  Nuclear p53-CFP and Mdm2-YFP are imaged in green
  and red, respectively. Time is indicated in
  hours.
• (B) Normalized nuclear fluorescence levels of
  p53-CFP (green) and Mdm2-YFP (red) following
  gamma irradiation. Top left the cell shown in
  panel A. Other panels five cells from one field
  of view, after exposure to 2.5 Gy gamma
  irradiation.
• Mol Syst Biol. 2006 2 2006.0033.
• Published online 2006 June 13. doi
  10.1038/msb4100068.

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Signal Analysis

• Used Fourier analysis and spectrograms to
  estimate period of signals

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Pitch (characteristic period) of Mdm2-YFP signals
of cells at various gamma irradiation doses. (A)
Histogram of the pitch values from movies of
cells exposed to 0, 0.3, 5, and 10 Gy, and from
all the movies together. For each movie, the
total number of cells is indicated, and the
number of oscillating (osc.) cells that had a
detectable pitch. (B) Fraction of cells (out of
the total number of cells) with a pitch value of
47 h, for different gamma doses. Black line is a
guide to the eye. Mol Syst Biol. 2006 2
2006.0033. Published online 2006 June 13. doi
10.1038/msb4100068.
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Average amplitude, width, and time delay of
oscillation peaks and their variance. (AC)
Average values of the first five p53-CFP (green
triangles) and Mdm2-YFP (red squares) oscillation
peaks in 146 cells exposed to 5 Gy of gamma
irradiation, shown with their standard errors.
(A) Average oscillation amplitude of each of the
first five peaks (peak to trough). (B) Average
width (full-width half-maximum). (C) Average time
delay between the p53 peaks and the consecutive
Mdm2 peak. Mol Syst Biol. 2006 2 2006.0033.
Published online 2006 June 13. doi
10.1038/msb4100068.
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Modeling

• Find simplest models that can explain these
  different behaviors
• Negative feedback
• Delay oscillators with delay in response to
  signals
• Relaxation oscillators negative feedback loop is
  supplemented with a positive loop on p53
• Checkpoint model, two negative feedback loops,
  direct and an effect on an upstream regulator of
  p53.

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Describing Models

• Systems Biology Markup Language (SBML) is a
  computer-readable format for representing models
  of biochemical reaction networks in software.
  It's applicable to models of metabolism,
  cell-signaling, and many others. (sbml.org)

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• Function definition
• A named mathematical function that may be used
  throughout the rest of a model.
• Unit definition
• A named definition of a new unit of measurement,
  or a redefinition of an existing SBML unit.
• Compartment Type
• A type of location where reacting entities such
  as chemical substances may be located.
• Species type
• A type of entity that can participate in
  reactions. Typical examples of species types
  include ions such as Ca2, molecules such as
  glucose or ATP, and more.
• Compartment
• A well-stirred container of a particular type and
  finite size where species may be located. A model
  may contain multiple compartments of the same
  compartment type. Every species in a model must
  be located in a compartment.
• Species
• A pool of entities of the same species type
  located in a specific compartment.
• Parameter
• A quantity with a symbolic name. In SBML, the
  term parameter is used in a generic sense to
  refer to named quantities regardless of whether
  they are constants or variables in a model.

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• Initial Assignment
• A mathematical expression used to determine the
  initial conditions of a model.
• Rule
• A mathematical expression added to the set of
  equations constructed based on the reactions
  defined in a model. Rules can be used to define
  how a variable's value can be calculated from
  other variables, or used to define the rate of
  change of a variable. The set of rules in a model
  can be used with the reaction rate equations to
  determine the behavior of the model with respect
  to time.
• Constraint
• A means of detecting out-of-bounds conditions
  during a dynamical simulation and optionally
  issuing diagnostic messages. Constraints are
  defined by an arbitrary mathematical expression
  computing a true/false value from model
  variables, parameters and constants.
• Reaction
• A statement describing some transformation,
  transport or binding process that can change the
  amount of one or more species. For example, a
  reaction may describe how certain entities
  (reactants) are transformed into certain other
  entities (products). Reactions have associated
  kinetic rate expressions describing how quickly
  they take place.
• Event
• A statement describing an instantaneous,
  discontinuous change in a set of variables of any
  type (species quantity, compartment size or
  parameter value) when a triggering condition is
  satisfied.

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Example

• Identifier EnzymaticReaction.
• Compartment (with identifier cytosol)
• four species (with identifiers ES, P, S, and E)
• Reactions (veq and vcat).
• Veq
• listOfReactants (E and S) and listOfProducts
  (ES). kinectic law
• listOfParameters kon and koff
• Vcat
• listOfReactants (E S) and listOfProducts (E and
  P). kinectic law, not reversible.
• listOfParameters kcat

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Model I

• Delay Oscillator
• Action of Mdm2 on p53 is linear, first-order
  kinetics

x
y0
y
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Model III

• Delay Oscillator
• Action of Mdm2 has a delay term, production rate
  of Mdm2 depends on earlier value of p53

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Parameter sensitivity
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Model IV

• Delay Oscillator
• Action of Mdm2 on p53 is nonlinear, saturating
  Michaelis-Menten

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Model II

• Relaxation operator, positive feedback loop to
  upregulate p53

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Model V

• Relaxation operator, positive feedback loop to
  upregulate p53

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Model VI
S

• Checkpoint
• Mdm2 also affects a p53 precursor signaling
  protein, S, e.g., Phosphorylated ATM

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Effect of cooperativity, n
n increasing
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Noise model

• Periodic noise that varied in phase for protein
  production
• Not white high frequency noise

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Model VI Simple
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Model VI active/inactive p53
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Model VI