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

2

2

x

c

t

c

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

1

2

0

falls c > cT

nach τ Zeiteinheiten

nach tR

Zeiteinheiten

falls c < cT

τ : Dauer der ErregungtR : Refraktärzeitc : cAMP Konzentration an der ZellecT: Erregungs- schwellenwert

Diffusion

• Standard-Diffusionsgleichung 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 usingmean-field theory

• The equation with production by the cells

• Travelling wave

Analytical solution to mean-field - Variables

• =cell packing density

• c=cAMP amount released per cell

• cT=minimum exciting conc.

• =degradation factor (Abbau)

• =time cells remain excited

• tR=time cells remain refractory

Analytical solutionto mean-field

There are three regions

• z>0

• -<z<0

• z<-

zkTecc

zkzk BeAec

c

zkDec

Wave velocity vs

c=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

– A.S. Mikhailov, V. Calenbuhr, Sections 2.1, 2.2• “Mathematical Biology-Spatial Models and Biomedical Applications”

– Murray, J.D., University of Washington, Seattle, WA, USA / Pp. 436-439• “Pattern formation in Dictyostelium via the dynamics of cooperative

biological entities”– 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”

– 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

– http://www.sigmaaldrich.com/Brands/Fluka___Riedel_Home/Bioscience/Microbiology/Signaling_Compounds.html

• “Antibiotic resistance of bacteria in biofilms”– 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 App 9521 - 9526; (Article) DOI: 10.1021/jp9920949