Alternative views on gradient sensing Postma and van hastert. 'a diffusion-translocation model for gradient sensing by chemotactic cells Biophys.J.81,1314(2001) Levchenko and Iglesias. Models of eukaryotic gradient sensing: applications to chemotaxis of amoeba and neutrophils Biophys.J.82,50(2002) Main point how to prevent cells to polarize irreversibly?
Alternative views on gradient sensing: - Postma and van Haastert. ‘A diffusion-translocation model for gradient sensing by chemotactic cells.’ Biophys. J. 81, 1314 (2001). - Levchenko and Iglesias. ‘Models of eukaryotic gradient sensing: applications to chemotaxis of amoeba and neutrophils’ Biophys. J. 82, 50 (2002). Main point: - how to prevent cells to polarize ‘inreversibly’? 1
dm=dm omk, m+p Dm-1 umts (membrane protein. lipid) OX D 100 umts (cytosolic small molecule) For a second messenger to establish and maintain a Images removed due to copyright considerations See Postma. M. and P.j. van hastert gradient the dispersion a diffusion-translocation model for gradient sensing rangeλ should be smaller by chemotactic cells. "Biophys J.81, no. 3(Sep, 2001): 1314-23. than cell size k
k m P x m D dt dm m − + ∂ ∂ = 2 −1 2 Dm ~ 1 µm2s-1 (membrane protein. lipid) Dm ~ 100 µm2s-1 (cytosolic small molecule) For a second messenger to establish and maintain a gradient the dispersion range λ should be smaller than cell size Images removed due to copyright considerations. See Postma, M., and P. J. Van Haastert. "A diffusion-translocation model for gradient sensing by chemotactic cells." Biophys J. 81, no. 3 (Sep, 2001): 1314-23. L m k s k Dm µ λ 10 1 1 1 1 = = = − − − 2
Second mesenger production a gradient Dm 2-km+P(x) Dm- 1 umls"(membrane protein. lipid um2s-1 x D~100 P(x)=kR-△R (cytosolic small molecule) Images removed due to copyright considerations See Postma. M. andp.j. van hastert Diffusion flattens internal A diffusion-translocation model for gradient sensing by chemotactic cells. Biophys J.81, no. 3(Sep, 2001): 1314-23. gradient Gain is 1 ( the larger Dm the smaller the gain How to amplify
⎟⎠⎞ ⎜⎝⎛ = − ∆ − + ∂ ∂ = − r x P x k R R k m P x x m D dt dm R m * * 2 1 2 ( ) ( ) Second mesenger production in a gradient Dm ~ 1 µm2s-1 (membrane protein. lipid) Dm ~ 100 µm2s-1 (cytosolic small molecule) Diffusion flattens internal gradient Gain is < 1 (the larger Dm the smaller the gain) How to amplify ? 3 Images removed due to copyright considerations. See Postma, M., and P. J. Van Haastert. "A diffusion-translocation model for gradient sensing by chemotactic cells." Biophys J. 81, no. 3 (Sep, 2001): 1314-23
Amplification by positive feedback A. Before receptor stimulation only a small number of effectors (inactive) bound to membrane B After receptor stimulation membrane bound effectors will be stimulated to produce more phospholipid second mesengers Images removed due to copyright considerations See Postma. M. and P.J. Van hastert C Local phospholipid increase "A diffusion-translocation model for gradient sensing leads to increased translocation of by chemotactic cells. Biophys J effector molecules 81,n0.3(Sep,2001):131423 D receptor can signal to more effectors leading to even more phospholipid production and further depletion of cytosolic effector molecules m k-m+P(x)Em: effector concentration in membrane P(x)=ko+kER (x)Em(x) Ec: effector concentration in cytosol
Amplification by positive feedback 4 A. Before receptor stimulation only a small number of effectors (inactive) bound to membrane B. After receptor stimulation, membrane bound effectors will be stimulated to produce more phospholipid second mesengers C. Local phospholipid inc rease leads to increased transloc ation of effector molecules D. receptor can signal to more effectors leading to even more phospholipid production and further depletion of cytosolic effecto r molecules. E m: effector concentration in membrane E c: effector concentration in cytosol. ( ) ( ) ( ) ( ) * 2 1 2 P x k k R x E x k m P x x m D dt dm o E m m = + − + ∂ ∂ = − Images removed due to copyright considerations. See Postma, M., and P. J. Van Haastert. "A diffusion-translocation model for gradient sensing by chemotactic cells." Biophys J. 81, no. 3 (Sep, 2001): 1314-23
Images removed due to copyright considerations. See Postma, M, and P.J. Van Haastert A diffusion-translocation model for gradient sensing by chemotactic cells. "Biophys J 81,no.3(Sep,2001):131423
5 Images removed due to copyright considerations. See Postma, M., and P. J. Van Haastert. "A diffusion-translocation model for gradient sensing by chemotactic cells." Biophys J. 81, no. 3 (Sep, 2001): 1314-23
Molecules ? Image removed due to copyright considerations. See Levchenko, A, and P A Iglesias Models of eukaryotic gradient sensing: application to chemotaxis of amoebae and neutrophils Biophys J.82(1Pt1)(Jan2002):50-63 receptor binding→ G-protein activation> activation of p13K (activator)-> activation of pten (inhibitor)-> P3-R*(binding Ph domains)
Molecules ?? Image removed due to copyright considerations. See Levchenko, A., and P. A. Iglesias. "Models of eukaryotic gradient sensing: application to chemotaxis of amoebae and neutrophils." Biophys J. 82 (1 Pt 1)(Jan 2002): 50-63. receptor binding → G-protein activation → activation of PI3K (activator) → activation of PTEN (inhibitor) → P3 ~ R* (binding PH domains) 6
Perfect adaptation module R* A kp k R kall k A
Perfect adaptation module: R* A* k R k-R I* k-A kA’ kI’ R k-I 7 A I S
dR kiRThAR k-AAtksa=-k-yA+k,so k_/+k sr=k_/+k s(ltot-l) Main assumption k a&k>>ka&ki(atot >a, lto?>1r) R knⅠR+k,AR dA k A+ks k,=k, =-k11+k
( ) ( ) * ' * ' * * * ' * ' * * * * * * k I k SI k I k S I I dt dI k A k SA k A k S A A dt dA k I R k A R dt dR I I I I tot A A A A tot R R = − + = − + − = − + = − + − = − + − − − − − Main assumption: k-A & k-I >> k’A & k’I (Atot>>A*, Itot>>I*) k I k S dt dI k A k S dt dA k I R k A R dt dR I I A A R R = − + = − + = − + − − − * * * * * * I I tot A A tot k k I k k A = = ' ' 8
Steady state Image removed due to copyright considerations k R R k R 4/I+k R for the rest of the calculations ignoreXfor I and A
Steady state: R ss ss R R ss ss ss I I ss A A ss k A I k k A I R S k k I S k k A − − − + = = = * * * * * * * / / Image removed due to copyright considerations. for the rest of the calculations ignore ‘*’ for I and A ! 9
Now introduce diffusion only I diffuses, other components are local a/(x,) a1(, t) -kI(x, t)+k,s(x, t)+D at assume signal S varies linearly with S S(x)=S。+Sx no flux boundary conditions for a(0,)a/(,2) 0 ax in steady state this system can be solved analytically
Now introduce diffusion: - only I diffuses, other components are local 2 2 ( , ) ( , ) ( , ) ( , ) x I x t k I x t k S x t D t I x t I I ∂ ∂ = − + + ∂ ∂ − - assume signal S varies linearly with S S x s s x o 1 ( ) = + - no flux boundary conditions for I 0 ( 0, ) ( 1, ) = ∂ ∂ = ∂ ∂ x I t x I t in steady state,this system can be solved analytically ! 10
