1. 1. Fibroblast Chemotaxis: more about positive feedback loops. 2. Autoregulatory Mechanisms of Eukaryotic Chemotaxis System Components: Receptors, G- proteins, GEFs, PI3K, Kinases, phosphatases. How evolution has selected for components with autoregulation and integral feedback control.

2. Fibroblasts chemotax toward growth factors 0 3 hrs 8 hrs 12 hrs 21 hrs PDGF-stimulated wound healing in mouse embryo fibroblasts

3. PI3K p110 Family Members 110     Kinase PIK C2 Ras binding p85 binding Class Ia Class Ib Tissue All Blood Cells Blood Cells Regulation Tyr Kinase +  Tyr Kinase 

4. 0 3 hrs 8 hrs 12 hrs 21 hrs WT PI3K-Ia Deletion Deletion of Class Ia PI3K genes in mouse embryo fibroblasts impairs PDGF-dependent cell migration. Brachmann et al., 2005 Mol. Cell. Biol. 25, 2593.

5. Woundhealing 10ng/ml PDGF 0 10 20 30 40 50 60 70 80 PI3K Ia deletion Migrated Cells 3h8h15h 21h P85  -/-;p85  -/- Wild type Ly294003 PI3K inhibitor

6. unstimulated PI3K Ia deletion PDGFPDGF + WM Wild Type Defect in PDGF-induced lamellipodia formation in MEFs defective in class Ia PI3K Brachmann et al., 2005 Mol Cell Biol 25, 2593

7. SH3 Cdc42 binding SH2 Membrane Catalytic Ras Binding GTP Ras GTP CDC42 P-Tyr Class Ia PI 3-Kinase PIK Tyr Kinase C2 Class Ia PI3K has multiple domains for signal input, allowing it to act as an ‘AND GATE’ or possibly an ‘OR GATE’ p85 regulatory p110 catalytic  GPCR p110  can also be activated by  subunits of G proteins, but only when bound to a phosphoTyr protein (AND GATE).

8. AKT PH PIP 3 Class Ia PI3K mediates growth factor- dependent cortical actin formation Tyr Kinase p110 PI3K p85 SH2 Receptor Growth Factor P-Tyr GTP Ras Rac GEF? PTE N GTP Rac Cell Migration Cortical Actin PIP 2

9. Wild Type MEFs PI3K Ia deleted 5 min PDGF [ng/ml]: 0 1 3 10 0 1 3 10 Erk-P Erk Deletion of class Ia PI3K genes appears to impair (but not eliminate) Ras activation (as judged by impaired activation of the downstream protein kinase, Erk) Brachmann et al., 2005 Mol Cell Biol. 25, 2593 Thus, as in Dictyostelium, there appears to be a positive feedback loop between PI3K and Ras in fibroblasts.

10. Erk-P Erk Control Double KO PDGF: - + - + Rac GTP Rac p85  GST-CRIB pulldown Reduced PDGF-induced Rac activation in MEFs lacking class Ia PI3K Brachmann et al., 2005 Mol Cell Biol. 25, 2593

11. Overexpression of a Rac GEF (Vav2) induces lamellipodia formation in MEFs lacking Class Ia PI3K Brachmann et al., 2005 Mol Cell Biol. 25, 2593 Rhodamine- Phalloidin (Actin) Vav2 Wild Type PI3K Ia deleted

12. PI3K is involved in both local Ras and local Rac positive feedback loops + + Rac GTP p85 p110 PIP 3 GEF PH ? Ras GTP ? PDGF Receptor

13. Conclusions 1. Growth Factor Receptors stimulate Class Ia PI3K through PhosphoTyr residues of receptors binding to SH2 domains, while GPCRs stimulate Class Ib PI3K through  subunits binding to the catalytic subunit. 2. In both cases, PI-3,4,5-P 3 is in a local positive feedback amplification loop involving Rac (and Ras?) that allows non- isotrophic localization of cortical actin, providing directionality to chemotaxis.

14. How is perfect adaptation achieved in eukaryotic chemotaxis? Shutoff mechanisms must exist to adapt the system to a given level of stimulation, allowing a temporal increase in receptor stimulation to be sensed. The adaptation should be slow compared to the stimulation to insure significant directional migration prior to adaptation. What is known about shutoff mechanisms of GPCRs and Receptor Tyr Kinases?

15. Receptor  GDP  Hormone Receptor  GDP  GPCR ACTIVATION

16. Receptor  GDP  attractant Receptor   Effector 2 PI 3-kinase etc. Ligand-induced Conformational Change <100 msec GDPGTP Receptor  GTP   GTP Receptor  Effector 1 (Phospholipase C, etc.) msec to sec GPCR ACTIVATION

17. Receptor  GTP  Signal Termination, Downregulation and Reset to Basal State Effector 1 Effector 2 Minutes  GDP RGS Seconds

18. Receptor  GTP  Signal Termination, Downregulation and Reset to Basal State Effector 1 Minutes  GDP RGS Seconds G-Receptor Kinase (GRK)

19. Receptor  GTP  Signal Termination and Reset to Basal State G-Receptor Kinase (GRK) P P P Receptor P P P Inactive Minutes  GDP RGS Seconds Arrestin Receptor  Dephosphorylation And rebinding of G  and . (minutes)  GDP Basal State Effector 1 Phosphatase Only activated receptors are phosphorylated and downregulated. This effect is slow (minutes) compared to activation (seconds). During this perturbation from steady state, PI3K activation occurs, driving directional motility.

20. Integral Feedback Control Analogous to model in Yi, Huang, Simon&Doyle 2000 PNAS 97, 4649 If we assume that only activated receptors are phosphorylated (and thus inactivated) and that the phosphatase that dephosphorylates the GPCR operates at saturation and is less active than the G-protein Receptor Kinase (GRK), then the model is analogous to integral control of bacterial chemotaxis receptors. Inhibition of active chemotaxis receptors by demethylation is analogous to inactivation of active GPCRs by phosphorylation. This is a consequence of the fact that GRKs only phosphorylate receptors associated with active  proteins. The rate of receptor phosphorylation is: dR P /dt = V P max - V K max (A)/(K K +A) (where A is the concentration of activated receptors, K K is the K M of the GRK for activated receptors, V P max is the maximal activity of the phosphatase and V K max is the maximal activity of the kinase, GRK ). Thus, the activity at steady state will be: A st = K K V P max /(V K max -V P max ) This is the set point (y 0 in the model above). y is defined as the difference between the activity at time t (y 1 ) and the activity at steady state (y 0 ). Thus, at steady state, y = 0.

21. Increased ligand binding acutely increases u and elevates y 1 to a value above y 0, giving a transient positive value for y (resulting in PI3K activation). At steady state, (y = 0) the rate of phosphorylation and dephosphorylation are equal. If one assumes that GRK only acts on active receptors (whether or not ligand is bound) then the net rate of phosphorylation at any instantaneous time will be directly proportional to y (the transient excess in active receptors over the steady state value). When y = 0 phosphorylation and dephosphorylaiton cancel out. The fraction of phosphorylated receptors (x) at any time t is then determined by the number of receptors in the phosphorylated state at time zero, x 0 (e.g. prior to the perturbation due to increased ligand binding) plus the number of receptors that get phosphorylated during the interval in which the system was perturbed. This latter term is the integral from the time at which the perturbation (e.g. ligand unbinding) occurred t=0 to time t of ydt. So x(t) = x 0 + ydt Notice that y can be + or - depending on whether ligand decreases or increases. Thus dx/dt = y = k(u-x) - y 0 At steady state, dx/dt=y=0 and y 1 =y 0 Notice that since k and y 0 are constants, an increase in u (rapid binding of ligand) is ultimately offset by a slow decrease in x so that at steady state k(u-x) = y 0. 0 t

22. Kinase P-Tyr Tyr-P Kinase Autopho-transphorylation of low activity monomeric protein kinases in the ligand-induced dimer stabilizes the active state of each monomer, allowing further transphosphorylation at sites that recruit signaling proteins. SH2 PI3K Tyr-PP-Tyr Regulation of protein-Tyr kinases

23. Kinase SH2 containing phosphoTyr phosphatases (e.g. SHP2) are preferentially recruited to activated receptors and play a dual role of transmitting additional signals (Ras activation) and turning off receptors. SH2 SHP2 P-Tyr Tyr-P P-Tyr

24. Prior to stimulation, protein-Tyr kinases have floppy activation loops (region containing Tyr 1157, 1162 and 1163 of the insulin receptor). As a consequence the enzyme has a low probability of being in the active conformation (~1%). Despite this low activity, when brought in proximity with a another low activity Tyr kinase (due to growth factor binding), cross- phosphorylation of respective activation loops can occur. Phosphorylation of the residues on this loop stabilizes the active conformation of the protein giving a ~100 fold increase in activity.

25. Activated Insulin Receptor Peptide substrate

26. Integral Control of Receptor Protein-Tyr Kinases The preferential dephosphorylation of activated Protein-Tyr kinases by SH2- containing phosphatases provides a potential mechanism for integral control. In response to an acute elevation in the level of ligand, the receptor will be rapidly activated, but in the continuous presence of the ligand, the phosphatase will ultimately return the kinase to a steady state activity that is determined by the affinity of the phosphatase for the activated kinase, the Vmax of the phosphatase and the Vmax of the kinase for transphosphorylation. Analogous to the set point for bacterial chemotaxis receptors one can show that: A st = K M-SHP2 V Kin max /(V SHP2 max - V Kin max ) This simplified system does not reset to the same steady state as prior to receptor stimulation since V Kin max is dependent on receptor ligation. Modeling predicts an overshoot followed by return to a steady state that depends on ligand occupation. This is in agreement with observations at intermediate times (0 to 30 min.) following PDGF stimulation Exclusive ubiquitinylation, of activated protein-Tyr kinases (due to SH2-containing E3 ligases (e.g cbl)), leads to receptor internalization, providing a second mechanism of longer term shut-off that also models as integral feedback control.

27. Integral Control of PI3K PI3K, when activated, phosphorylates lipids at a high rate but also autophosphorylates (on regulatory and catalytic subunits) at a slow rate, leading to inactivation. Assuming that the phosphatase that dephosphorylates PI3K is saturated by substrate, this could also lead to integral control of this enzyme.

28. Ras-GDPRas-GTP GEF (SOS) GDP/GTP Exchange Factor (GEF) activate: analogous to GPCR Effector GAP GTPase Activating Protein Analogous to RGS Effectors such as Raf (Ser/Thr kinase) or PI3K bind to activated Ras Parallels between low molecular weight G protein (Ras, Rac Rho) regulation and heterotrimeric G protein regulation basal slow Heterotrimeric and low molecular weight GTP binding proteins have been retained and expanded during evolution because they have unstable activated states and can spontaneously return to inactive states. Inactivation can also be accelerated by GAPs.

29. Signal Transduction in Eukaryotic cells is usually initiated by recruitment of signaling proteins to the plasma membrane. We have discussed three major mechanisms for acute and reversible protein relocation in response to cell stimulation. These mechanisms have the potential to amplify small signals. More importantly, recruiting signaling proteins from a 3-dimensional space (cytosol) to a 2-dimensional space (membrane) provides a mechanism for facilitating unfavorable multimeric interactions. Activation of GTP-binding proteins Protein phosphorylation to create docking site Generation of lipid second messengers PI3K GDP-Ras SH2 Ras GEF PI-4,5-P 2 AKT PH PI-3,4,5-P 3 Membrane GTP-Ras Membrane Tyr P-Tyr Membrane Large Amplification Stochiometric Small Amplification

30. Plasma Membrane Sarraste The PH domain of BTK binds the head group of PI-3,4,5-P 3 and crystallizes as a dimer with the two binding pockets on the same surface. However, in solution, it behaves as a monomer.

31. Moving signaling proteins from the three dimensional environment of the cytosol to the two dimensional environment of the plasma membrane decreases the entropy difference between a monomeric and dimeric state. Many signaling proteins may have evolved very weak free energies of homo or hetero-dimerization to insure that dimerization only occurs when confined on a two dimensional surface. Membrane Monomers Dimers Signal

32. Pólya's Random Walk Constants http://mathworld.wolfram.com/PolyasRandomWalkConstants.html Let p(d) be the probability that a random walk on a d-D lattice returns to the origin. Pólya (1921) proved that (1) p(1) = 1; p(2) = 1 but (2) p(d) < 1 for d > 2. Watson (1939), McCrea and Whipple (1940), Domb (1954), and Glasser and Zucker (1977) showed that (3) p(3) = 1 - 1/u(3) = 0.340537…. where u(3) = 3/(2  ) 3     _____dxdydz______ 3-cosx-cosy-cosz Finch, S. R. "Pólya's Random Walk Constant." §5.9 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 322- 331, 2003. Domb, C. "On Multiple Returns in the Random-Walk Problem." Proc. Cambridge Philos. Soc. 50, 586-591, 1954. Glasser, M. L. and Zucker, I. J. "Extended Watson Integrals for the Cubic Lattices." Proc. Nat. Acad. Sci. U.S.A. 74, 1800-1801, 1977. McCrea, W. H. and Whipple, F. J. W. "Random Paths in Two and Three Dimensions." Proc. Roy. Soc. Edinburgh 60, 281-298, 1940. Montroll, E. W. "Random Walks in Multidimensional Spaces, Especially on Periodic Lattices." J. SIAM 4, 241-260, 1956. Sloane, N. J. A. Sequences A086230, A086231, A086232, A086233, A086234, A086235, and A086236 in "The On-Line Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/. Watson, G. N. "Three Triple Integrals." Quart. J. Math., Oxford Ser. 2 10, 266-276, 1939. Eric W. Weisstein. "Pólya's Random Walk Constants." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolyasRandomWalkConstants.html

33. http://www.rwc.uc.edu/koehler/biophys.2ed/java/walker.html http://www.krellinst.org/UCES/archive/modules/monte/node4.html Further websites for random walks