GProteins and Polarity

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G-Proteins and Polarity

• Systems Cell Biology (Winter 2008)
• Module II, Lecture 2

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Outline (Lecture II-2)

• Introduction to spatial dynamics
• Microscopy
• Cell polarization
• Amplification and positive feedback
• Small G-proteins
• Readings
• Alberts (p. 969 978)
• Angeli and Sontag (Fig. 3 optional, resource for
  homework)

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Spatial Dynamics

• State variables are varying in time and space
• Species may be moving
• Dynamics may depend on location
• Spatial structure is important

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Examples of Spatial Dynamics in Cell Biology

• Calcium diffusion in cells
• Protein trafficking
• Protein complexes
• Receptor endocytosis
• Lipid rafts
• Cytoskeletal motors
• Morphogen gradients
• Metastasizing tumor cells

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Mathematical Representation of Spatial Dynamics

• Not explicitly represented in ODEs
• Explicitly represented in PDEs
• Represent using compartmental ODE model
• Dynamics in different compartments are described
  by different variables
• PDEs represent the extreme case of many, many
  compartments
• PDEs are more accurate but more difficult to
  simulate and analyze

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Cell Biology and Spatial Dynamics

• Cells have lots of structure
• This structure is dynamic
• Harvard Animations (http//multimedia.mcb.harvard.
  edu/media.html)

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Light Microscopy

• The microscope is the best friend of the
  (systems) cell biologist
• Spatial resolution
• 0.2 mm (1.4 N.A. objective)
• Temporal resolution
• Detectors have exposure times as short as 1 ms

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Transmitted Light versus Fluorescence Imaging

• Transmitted light
• Light passes through sample
• Less destructive to the cell
• Fluorescence
• Excite fluorescent probe at one wavelength
  observe emission at another wavelength
• Advantage of labeling specific cellular components

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Green Fluorescent Protein (GFP)
Protein

• Fuse GFP to the protein of interest

DNA
YFG
GFP
Your Favorite Gene
Promoter
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Spectra of GFP variants

• Label multiple proteins at the same time

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Quantitative Imaging
Ste2p-GFP

• Average intensity
• Image processing to integrate intensity
• Subtract background autofluorescence
• Standard curve to relate intensity to s of
  molecules
• Fluctuations in intensity
• Fluorescence Correlation Spectroscopy (FCS),
  Image Correlation Spectroscopy (ICS)
• Numbers of molecules, complexes, diffusion
  coefficients
• http//www.lfd.uci.edu/workshop/agenda/

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Symmetry

• Object looks same after symmetry operation
  (reflection, inversion, rotation, etc.)
• Example Egg/Stem Cell
• Simple
• Genotype (Gene)
• Potential

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Loss of Symmetry

• There is still some symmetry, but not as much
• Example Adult
• Complex
• Phenotype (Behavior)
• Function

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Cell Polarization

• Process of breaking symmetry
• Unpolarized cell has isotropic (independent of
  direction) distribution of components
• Polarized cell has anistropic distribution of
  components
• Fundamental to life
• Creates complexity of function and form
• Challenge is to polarize at the right place, at
  the right time, to the proper extent, etc.
• Response to internal or external cue
• Polarized structures include
• Actin cytoskeleton, microtubules
• Secretory apparatus, endocytosis apparatus
• Nucleus, organelles
• Signaling complexes
• Lipids

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Examples of Cell Polarization
Internal cue
Budding
External cue
Mating Projection
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More Examples of Cell Polarity

• Neural
• Par

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All Aspects of Cellular Structure Become Polarized

• Cytoskeleton
• Actin, microtubules, intermediate filaments, etc.
• Lipids
• Organelles
• Mitochondria, nucleus, vacuole, etc.
• Signaling complexes
• Secretion and protein trafficking
• Endocytosis

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Polarization of Specific Proteins is Essentially
All-or-None in Yeast Pheromone Response
a-factor gradient
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Amplification of Spatial Cue
External Cue
Internal Cue
Polarization
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Amplification Can Occur in Stages
Uniform
Slightly more at front
Uniform
Slightly more at front
Localized at front
Localized at back
Tightly localized at front
Tightly localized at front
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Cell Polarity

• Amplification of shallow external gradient to a
  steep all-or-none internal gradient
• How is this amplification achieved?
• Positive feedback?

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Basic Feedback Control System
Goal Robust performance in the presence of
disturbances
Closed-Loop Control System
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Positive Feedback Causes Instability
e
Ac
Negative Feedback versus Positive Feedback
Positive feedback produces an increase in output
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Example Positive Feedback and Instability
k 1
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Polarization (Amplification) Via Positive Feedback

• Slightly more Gbg (Gbg) at front versus back
• Slightly more Cdc24 (C24m) at front versus back
• Slightly more active Cdc42 (C42a) at front
• Slightly more Bem1 (B1m) at front
• Recruits even more Cdc24 at front
• Activates even more Cdc42 at front
• Recruits even more Bem1 at front
• Etc.

C42a
Positive feedback loop
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Small G-Protein (Ras) Superfamily

• Ras
• Signal transduction (e.g. Ras activates Raf
  kinase which activates MAPK signaling)
• Rho
• Regulation of cytoskeleton (e.g. Cdc42)
• Rab
• Intracellular vesicular transport (i.e. protein
  trafficking)
• Arf
• Vesicle coating
• Ran
• Nucleocytoplasmic transport

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Small G-Protein Cycle
Active
GEF
GAP
Inactive
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More Detailed View of G-Protein Cycle
Guanine Dissociation Inhibitor (stabilizes GDP
form)
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Rho Family
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Cdc42 is a Master Regulator of Polarization in
Yeast

• In Cdc42 loss-of-function mutants, actin
  cytoskeleton is disorganized and not polarized
• Constitutively active Cdc42 causes polarization
  in the absence of mating pheromone
• A number of proteins are known to bind and be
  activated by Cdc42
• Signaling proteins (e.g. PAK kinases Ste20p,
  Cla4p)
• Actin cytoskeleton (e.g. formin Bni1p)
• Scaffold proteins (e.g. Gic1p, Bni1p, Bem1p)
• Secretory apparatus (e.g. Sec3p)

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Sensing and Polarization Response in Yeast
Pheromone input
Sensing (heterotrimeric G)
Response (Cdc42)
Active Cdc42
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Sensing and Polarization Response in Eukaryotes
Sensing (heterotrimeric G)
Response (small G)
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Adding the Small G-Protein (sg) Dynamics
Reaction
Reaction Rate
Gai gGEFc Gai gGEFi gGEFi sgi gGEFi
sgai sgai gGEFc sgai gGEFi
k5GaigGEFc k6gGEFisgi
gGEFi gGEFc sgai sgi
k8gGEFi k9sgai
Note gGEFc cytoplasmic Guanine Exchange Factor
for small G-protein
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Two Membrane Compartment Model
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Cytoplasm

• There are 3 total compartments
• Membrane compartment 1 (front)
• Membrane compartment 2 (back)
• Cytoplasm

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Compartment ModelSimple View of Spatial Sensing
Normalized output (comparment i)
u1
Normalized input (comparment i)
y1
Input slope
y2
u2
Amplification
u0 average input
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Homework Problem II-2(20 points 5
points/question)

• Using the two compartment version of the generic
  receptor system (G2.nb), calculate the
  amplification for an input slope of 1 and u0
  0.1, 1, 10, 100.
• L is the input Ga is the output
• Modify the model so that it possesses a positive
  feedback loop (that is different from the example
  in class). Add as many additional dynamics as you
  require.
• You can define a new output that is downstream
  of Ga
• Turn in the Mathematica notebook of the model
• Calculate the amplification of the model with the
  positive feedback loop for an input slope of 1
  and u0 0.1, 1, 10, 100.
• Design the feedback so that the amplification is
  bigger than the original model without positive
  feedback
• Hint see Angeli and Sontag paper, Fig. 3 (2004)

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Figure 3 (Angeli Sontag)
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Summary (Lecture II-2)

• Spatial dynamics of cell polarization
• Polarization, amplification and positive feedback
• Rho family small G-proteins
• Compartment modeling of spatial dynamics
• Homework II-2
• Homeworks II-1, -2, and -3 are due Feb. 15.
• You may work together, but what you turn in must
  represent your own understanding.