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.

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Fibroblasts chemotax toward growth factors

0

3 hrs

8 hrs

12 hrs

21 hrs

PDGF-stimulated wound healing in mouse embryo fibroblasts

PI3K p110 Family Members

110

110

110

110

KinasePIKC2Rasbinding

p85binding

Class Ia

Class Ib

Tissue

All

All

BloodCells

Blood Cells

Regulation

Tyr Kinase

Tyr Kinase + Tyr Kinase

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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.

Woundhealing 10ng/ml PDGF

0

10

20

30

40

50

60

70

80

PI3K Ia deletion

Mig

rate

d C

ells

3h 8h 15h 21h

P85-/-;p85-/-Wild type

Ly294003PI3K inhibitor

unstimulated

PI3K Iadeletion

PDGF PDGF + WM

Wild Type

Defect in PDGF-induced lamellipodia formationin MEFs defective in class Ia PI3K

Brachmann et al., 2005 Mol Cell Biol 25, 2593

SH3 Cdc42binding

SH2 SH2

Membrane

CatalyticRasBinding

GTPRas

GTPCDC42 P-TyrP-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 regulatoryp110 catalytic

GPCR

p110 can also be activated by subunits of G proteins, but only when bound to a phosphoTyr protein (AND GATE).

AKT

PH

PIP3 PIP3

Class Ia PI3K mediates growth factor-dependent cortical actin formation

TyrKinase p110

PI3Kp85SH2

Receptor

GrowthFactor

P-Tyr

GTPRas

RacGEF?

PTEN

GTPRac

Cell Migration

Cortical Actin

PIP2

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.

Erk-P

Erk

Control Double KO

PDGF: - + - +

Rac GTP

Rac

p85

GST-CRIB pulldown

Reduced PDGF-induced Rac activationin MEFs lacking class Ia PI3K

Brachmann et al., 2005 Mol Cell Biol. 25, 2593

Overexpression of a Rac GEF (Vav2) induces lamellipodia formationin MEFs lacking Class Ia PI3K

Brachmann et al., 2005 Mol Cell Biol. 25, 2593

Rhodamine-Phalloidin

(Actin)

Vav2

Wild Type PI3K Ia deleted

PI3K is involved in both local Ras and local Rac positive feedback loops

+

+

RacGTP

p85 p110 PIP3

GEFPH

?

RasGTP

?PDGF

Receptor

Conclusions1. 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-P3 is in a local positive feedback amplification loop involving Rac (and Ras?) that allows non-isotrophic localization of cortical actin, providing directionality to chemotaxis.

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?

Receptor

GDP

Hormone

Receptor

GDP

GPCR ACTIVATION

Receptor

GDP

attractant

Receptor

Effector 2

PI 3-kinase etc.

Ligand-inducedConformationalChange <100 msec

GDP GTP

Receptor

GTP

GTP

Receptor

Effector 1

(Phospholipase C, etc.)

msec to sec

GPCR ACTIVATION

Receptor

GTP

Signal Termination, Downregulation and Reset to Basal State

Effector 1

Effector 2

Minutes

GDP

RGSSeconds

Receptor

GTP

Signal Termination, Downregulation and Reset to Basal State

Effector 1

Minutes

GDP

RGSSeconds

G-ReceptorKinase (GRK)

Receptor

GTP

Signal Termination and Reset to Basal State

G-ReceptorKinase (GRK)

P P P

Receptor

P P P

Inactive

Minutes

GDP

RGSSeconds

Arrestin

Receptor

DephosphorylationAnd rebinding ofG 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.

Integral Feedback ControlAnalogous 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: dRP/dt = VP

max - VKmax(A)/(KK+A) (where A is

the concentration of activated receptors, KK is the KM of the GRK for activated receptors, VP

max is the maximal activity of the phosphatase and VKmax is the maximal

activity of the kinase, GRK ). Thus, the activity at steady state will be: Ast= KKVP

max/(VKmax-VP

max) This is the set point (y0 in the model above). y is defined as the difference between the activity at time t (y1) and the activity at steady state (y0). Thus, at steady state, y = 0.

Increased ligand binding acutely increases u and elevates y1 to a value above y0, 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, x0 (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) = x0 + ydt

Notice that y can be + or - depending on whether ligand decreases or increases.Thus dx/dt = y = k(u-x) - y0

At steady state, dx/dt=y=0 and y1=y0 Notice that since k and y0 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) = y0.

0

t

Kin

ase

Kin

ase

P-Tyr

Tyr-P

Kin

ase

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.

SH

2PI3K

Tyr-P P-Tyr

Regulation of protein-Tyr kinases

Kin

ase

Kin

ase

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.

SH

2

SHP2

P-Tyr

Tyr-P

Tyr-P P-Tyr

Tyr 1158

Tyr 1162

Tyr 1163

ATPPocket

INSULIN RECEPTOR CATALTIC DOMAIN (INACTIVE)

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.

Activated Insulin Receptor

Peptide substrate

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:

Ast = KM-SHP2VKinmax/(VSHP2

max - VKinmax)

This simplified system does not reset to the same steady state as prior to receptor stimulation since VKin

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.

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.

Ras-GDP Ras-GTP

GEF (SOS)

GDP/GTP Exchange Factor (GEF) activate: analogous to GPCR

Effector

GAPGTPase 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.

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-bindingproteins

Protein phosphorylation to create docking site

Generation of lipidsecond messengers

PI3K

GDP-Ras

SH2RasGEF

PI-4,5-P2

AKT

PH

PI-3,4,5-P3

Membrane

GTP-Ras

Membrane

Tyr P-Tyr

Membrane

Large AmplificationStochiometric Small Amplification

R28

1

34

5

1

3

Plasma MembraneSarraste

The PH domain of BTK binds the head group of PI-3,4,5-P3 and crystallizes as a dimer with the two binding pockets on the same surface. However, in solution, it behaves as a monomer.

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

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

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