Systems Biology II - Spatio-Temporal Systems PDF

Systems Biology II spatio-temporal mechanisms underlying pattern formation Kees Weijer  Diffusion-Random walk (Brownian motion) Diffusion equation c(x,t)= ~ 2Dt Mean square displacement is proportional to time. 25 time steps -> displacement ~5 625 time s...

Systems Biology II spatio-temporal mechanisms underlying pattern formation Kees Weijer  Diffusion-Random walk (Brownian motion) Diffusion equation c(x,t)= ~ 2Dt Mean square displacement is proportional to time. 25 time steps -> displacement ~5 625 time steps -> displacement ~25 Steps 8, displacement - 2  Two dimensional random walks Diffusion of molecules, Brownian motion C(x,y,t)= Random Walk Biased random walk Random Walk Biased random walk Bacterial movement (run and tumble Random walk acterial Cell makes a Random Walk ovement of a population of cells can be described as a diffusion Biased random walk  Bacterial chemotaxis, finding food Mechanism based on a biased random walk gradient Find food Low high Biased Random walk in gradient Biased random walk to find food Chemo-attractants control direction of bacterial flagellar rotation CCW(counter clockwise) - Run CW (clockwise) - Tumble  Chemotaxis system of E coli Bacteria swim towards attractants and away from repellents by modulating tumbling frequency Tumbling frequency changes after addition of chemo- attractant Attractants rapidly switch CheA kinase off and suppress tumbling CheR/CheB, add/remove methyl groups to the receptor, increased methylation increases its activity Attractant binding Adaptation reduces demethylase (cheB) activity resulting in an increase in receptor CheyA methylation phosphorylates CheY (CheR) Increasing tumbling CheZand re-activation de-phosphorylates (adaptation). CheY, inhibiting tumbling Binding of attractant inhibits receptor function and decreases CheY phosphorylation, reducing tumbling instantaneously. It also increases methylation at a slower rate through activation of the demethylase CheB (adaptation), resulting in increased CheY phosphorylation and tumbling.  Bacterial movement and chemotaxis Bacterial movement is driven by CCW rotation of the flagella, tumbling is the result of motor reversal and CW rotation of the flagella. In the presence of attractants or repellents, bacteria make a biased random walk, either towards the attractant or away from a repellent. Increasing attractant concentrations increase the probability to continue moving in the direction of the attractant, via a suppression of tumbling. Bacteria perform a biased random walk changing the length of runs towards an attractant via modulation of the tumbling frequency. Adaptation (methylation) ensures that when the attractant concentration does not increase in time anymore, the tumbling frequency returns to normal, increasing the chance to move in a new, possibly more favourable, direction. Amoeboid cell movement is driven by actin polymerisation driving protrusion at the leading edge and a myosin II driven retraction at the rear. actin Myosin II Moving amoeba show random extension and retraction of cellular protrusions in the absence of directional signals They also make a random walk Brightfield Actin GFP  Chemotactic movement of Dictyostelium cells to cyclic AMP involves persistent extension of pseudopodia in the direction of the signal. Cells polarise and move directionally cAMP  Chemotaxis signalling pathways in Dictyostelium cAM P Gγ PIP2 PIP3 Gγ Ras Gβ Gα2 Gβ GDP PI3K PTEN Gα2 Rac GEF GTP Rac PI3 kinase PI4,5P2 PI3,4,5P3 Wasp Scar PTEN Arp2/3 + Actin polymerisation PTEN Actin depolymerisation PI3 kinase Actin polymerisation Pseudopod extension Myosin II filament assembly Myosin filament disassembly PI(3,4,5)P3 (GRP1-PH domain-GFP sensor) PTEN-GFP localisation in back of cell  Models for pattern formation Turing, 1952 Gierer &Meinhardt, 1982 Da< DI concentration A Distance Da> DI t=1 concentration I +ρa t=2 + ρb Distance http://www.eb.tuebingen.mpg.de/research/emeriti/hans-meinhardt  Pattern formation in 1&2D Gradient formation Wave formation and propagation Formation of stripes Cell Cortex Polarisation hemotaxing eukaryotic cells measure gradient along their length. hey amplify the gradient internally to control the spatial organisation o ctin-Myosin activity in the front and back of the cell resulting in rectional movement Model simulation Cells move by extending two pseudopods at front of cell in a random direction. The pseudopod extended better in direction of signal gradient will persist and guide the movement of the cell, while the pseudopod extended in wrong direction is retracted. http://journals.plos.org/plosbiology/article?id=10.1371/journal.p bio.1000618 Bacterial aggregation patterns in E coli cultures growing on a nutrient plate ( petri dish ~10 cm diameter) Collective movement can result in complex spatio-temporal patterns as seen in growing populations of bacteria that Produce and secrete an attractant BUDRENE, E. and BERG, H. (1991). Complex patterns formed by motile cells of Escherichia coli. Nature. 349:630-633. Dictyostelium discoideum Lifecycle g of cAMP to cAMP receptors of aggregation competent Dictyostelium c two responses. 1: Chemotaxis 2: cAMP signal amplification and secretio A 5’AMP receptor Actin polymerisation, Adaptation Adenylyl cyclase Myosin filament assembly ATP cAMP Movement B Gene expression concentration cAMP adaptation  cAMP wave propagation in Dictyostelium discoideum 1. Release of cAMP in aggregation centre 2. Surrounding cells relay cAMP signal 3. Continuing propagation of cAMP wave AMP waves control the chemotactic movement of thousands of cells cAMP concentration adaptation Multicellular Dictyostelium development is controlled by propagating waves of a chemoattractant (cAMP)  Continuous model for Dictyostelium development T h e c e ll’s c A M P r e la y s y s te m is d e s c r ib e d b y th e F itz H u g h -N a g u m o e q u a tio n s  g /  t  D  g  k g ( g  g )( g  g 1 )  k r r g 0 (1 )  r /  t  (g  r ) / (2 ) C e l l m o v e m e n t i s m o d e l l e d a s a fl o w i n a n i n c o m p r e s s i b l e l i q u i d : 0   i (  V i /  t  ( V i div )V i)  F i  F fr   i  V i   i grad p (3 ) T h e c h e m o ta c tic fo r c e is p r o p o r tio n a l to th e g r a d ie n t o f c A M P : F ch  K ch (  g /  t ) grad g (4 ) V o lu m e fr a c tio n s fo r p r e s ta lk a n d p r e s p o r e c e lls a r e d e r iv e d fr o m th e e q u a tio n fo r th e c o n s e r v a tio n o f m a s s :   i /  t   div ( iV i ) w h e r e i= 1 ,2 (5 ) Mathematical modelling of aggregation, mound formation and slug migration Aggregation patterns in Dictyostelium; experimental vs model Wildtype aggregation cAMP relay mutant gating cAMP waves directing chemotaxis control Dictyostelium morphog CJ Weijer Current opinion in genetics & development 14 (4), 392-398  Spatio-temporal pattern formation -Bacterial chemotaxis : Temporal sensing (biased random walk) -Eukaryotic chemotaxis: Spatial Gradient Sensing Patterning requires non-linear reaction dynamics Including at least activation and inhibition that cross talk. -If the activator moves slower than the inhibitor this results in gradients -If the activator moves faster than the inhibitor this results in propagating waves Interactions between signalling and movement result in complex pattern formation and morphogenesis in prokaryotes and eukaryotes This is clearly demonstrated for Dictyostelium, but is important in development of all organism including humans. These complex systems can only be understood through system-based approaches  erences for further reading ward.C. Berg (1983) Random walks in Biology, Princeton University Press s Meinhardt (1982) Models of biological pattern formation ://www.eb.tuebingen.mpg.de/research/emeriti/hans-meinhardt/82-book/bur82.ht