Download spore cells

Wechselwirkung
zwischen Zellen
Amöben und chemische
Signalen
DICTY-a special amoeba
• Dictyostelium
Discoideum
• Phagocytosis – they
feed on soil bacteria
Picture: © Ron Neumeyer - microimaging.ca
Movie: © dictybase.org
Dicty
• Amoebae are protozoans, much larger
than bacteria.
• Dicty live as single amoebae on soil
surfaces where they eat bacteria and
increase in number by fission.
• When the food becomes scarce, Dicty
aggregate to form a multicellular
organism.
• The goal of the starving cells is to get to
another patch of soil, hopefully where
there is plenty of food so a new colony
can be formed.
Chemotaxis / Chemoattraction
•cells detect and migrate towards chemical signals
•up to 100,000 form a multi-cellular organism
•cAMP – cyclic adenosine 3,5 monophosphate
Picture: © Wikipedia.org (GNU Encyclopedia)
Movie: © G. Gerisch, Max-Planck-Institut fur Biochemie, Martinsried, Germany
Chemotaxis in microorganisms
• Dicty aren’t the only ones doing
aggregation using chemotaxis
– Gram negatives and plankton
phototrophic bacteria use N-Acyl
homoserine lactones (ASL’s) as general
signaling components.
– In the sea, Plankton and bacteria
aggregate to transparent exopolymer
particles, the so-called sea snow.
Chemotaxis / Chemoattraction
Digitized
Dicty
© D. Wessel and D.
Soll, Unv. of Iowa
Lapse: 18
seconds
© K. Barisic, M. Ecke,
C. Heizer, M. Maniak,
M. Westphal, R.
Albrecht, G. Gerisch, /
Max-Planck-Institut fur
Biochemie /
Martinsried, Germany.
Dicty aggregation as a model
for multicellular processes
• Chemotaxis and signal transduction
by chemoattractant receptors play a
key role in
– Inflammation and arthritis
– Asthma
– Axon guidance
– Sperm movement.
Differentiation
• Distinct phenotypes
– Spore cells
– Stalk cells
Movie: © R. Chisholm,
Northwestern University.
Differentiation
• The amoebae cooperate and form a
fruiting body made up of a mass of spore
cells held off the ground by a thin column
of stalk cells. The spore cells can then be
dispersed by wind or water to another
area where hopefully conditions are better
and a new colony can form.
• This can serve as a model for:
– Embryogenesis
– Cell-type determination and cell sorting
– Pattern formation
Biofilms in infections
• Bacteria aggregate and
form a hydrated matrix
of polysaccharide and
protein. This slimy layer
is known as biofilm.
• They are present in:
–
–
–
–
Implanted devices
Periodontitis
Chronic Lung Infection
Catheter infection
Resistance to antibiotics
• Usual mechanisms of resistance in
bacteria are:
– Plasmids
– Transposons
– Mutations.
• Biofilms employ other mechanisms. In
vitro, biofilms survive antibiotic
concentrations
– 100x or even
– 1000x the minimum inhibitory concentration
for bacteria in suspension
Resistance to antibiotics
Figure: © Philip S.
Stewart and J. William
Costerton / Center for
Biofilm Engineering /
Montana State University
Fick’s Law of Diffusion
c  c
 2
t x
2
Erregbares Medium mit
Diffusion (Modell I)
• Approximiere Zellen als zelluläre
Automaten
• Zellen zufällig verteilt auf Gitter
mit Dichte ρ
• Zustände:
– 0: Ruhezustand
– 1: Erregt
– 2: Refraktär
Zellcyclus im Modell I
falls c > cT
1
falls c < cT
nach τ
Zeiteinheiten
0
nach tR
Zeiteinheiten
2
τ : Dauer der Erregung
tR : Refraktärzeit
c : cAMP Konzentration
an der Zelle
cT: Erregungsschwellenwert
Diffusion
• StandardDiffusionsgleichung mit
Abbau
Travelling Wave Annahme
• Welle wandert mit konstanter
Geschwindigkeit unter Beibehaltung
der Form =>
Lösung der Gleichung
• Lösung der Gleichung
Matlab Model 1 – Feste Zellen
– cAMP wird produziert,
difundiert und abgebaut
Analytical solution using
mean-field theory
• The equation with
production by the
cells
• Travelling wave
Analytical solution to meanfield - Variables
•
•
•
•
•
•
r=cell packing density
Dc=cAMP amount released per cell
cT=minimum exciting conc.
g=degradation factor (Abbau)
t=time cells remain excited
tR=time cells remain refractory
Analytical solution
to mean-field
There are three regions
• z>0
c  cT e
• -ut<z<0
rDc
k z
k z
c
 Ae  Be
t
• z<-ut
k z

c  De
k z

Wave velocity vs r
rc=0.015
Solutions to mean-field
With A=1E-10
and v=3.5
Modellierung der Aggregation
(Modell 2)
• Biologisches Vorbild:
– Aggregationsphase bei Dictyostelium
– Zellen wandern in Richtung höherer
cAMP Konzentration
– Ausprägung netzartiger Strukturen
Modellierung der
Aggregation
• Automatenmodell
– nur erregte Zellen können wandern
– Zelle kann nur einmal pro
Erregungsphase wandern
– Zelle misst [cAMP] Gradient zu
Nachbarfeldern
=> wandere wenn Δc > cT‘
Matlab Model 2 –
Sich bewegende Zellen –
cAMP wird produziert, difundiert und abgebaut
Dicty Waves – actual
microscope images
Lapse: 36
seconds
© F. Siegert and C. J.
Weijer, J. Cell Sci. 93,
325-335 (1989).
Lapse: 10
seconds
© F. Siegert and C. J.
Weijer, J. Cell Sci. 93,
325-335 (1989).
Further models
•Because diffusion happens so fast, some question
whether it is really possible for the cell to trace the
gradient.
•It has been proposed that when Dicty first detects
cAMP on a receptor, all other receptors on the cell
become refractory.
•This way, Dicty knows where cAMP came from.
Take-Home Message
• Microorganisms have communication
and are not as primitive as they look.
• Complex behavior like spirals and
streams can be described with
simple rules…
• …but correct parameters are not
easy to choose.
Bibliography
•
"From Cells to Societies“ – The Games of Life
–
•
“Mathematical Biology-Spatial Models and Biomedical Applications”
–
•
http://www.sigmaaldrich.com/Brands/Fluka___Riedel_Home/Bioscience/Microbi
ology/Signaling_Compounds.html
“Antibiotic resistance of bacteria in biofilms”
–
•
Nature 419, 244 - 246 (2002); doi:10.1038/419244a
19 September 2002 doi:10.1016/S0140-6736(01)05321-1
“New Signaling Compounds for Quorum Sensing or how Bacteria talk to
each other” - © 2003 Sigma-Aldrich Co
–
•
David A Kessler and Herbert Levine, Physical Review E, Vol 48 No. 6 December
1993, Pp. 4801-4804.
“Physics meets biology: Bridging the culture gap”
–
–
•
Murray, J.D., University of Washington, Seattle, WA, USA / Pp. 436-439
“Pattern formation in Dictyostelium via the dynamics of cooperative
biological entities”
–
•
A.S. Mikhailov, V. Calenbuhr, Sections 2.1, 2.2
Philip S. Stewart and J. William Costerton - The Lancet & Center for Biofilm
Engineering and Department of Chemical Engineering, Montana State
University, Bozeman, MT 59717-3980, USA
“Dimensional Strategies and the Minimization Problem: Barrier-Avoiding
Algorithms”
–
Daniel B. Faken, A. F. Voter, David L. Freeman, and J. D. Doll - Journal of
Physical Chemistry A
pp 9521 - 9526; (Article) DOI: 10.1021/jp9920949