Modeling signal transduction Phototransduction from frogs to flies
Eye as an evolutionary challenge To suppose that the eye, with all its inimitable contrivances, could have been formed by natural selection, seems, I freely confess, absurd in the highest possible degree. Yet reason tells me, C. Darwin, The Origin of Species: Darwin goes on to describe how eye may have evolved through accumulation of gradual improvements A number of different designs exist: e.g. vertebrate, molluskan or jellyfish camera eyes or insect compound eye The eye may have evolved independently 20 times!! (read Cells, Embryos and Evolution by Gerhart&Kirschner)
Eyes are present in most metazoan phyla: how did they evolve? Copepod's 2 lens telescope Scallop Trilobite fossil 500 million years House Fly Black ant Octopus Cuttlefish
The grand challenge: To understand the evolutionary processes that underlie the appearance of a complex organ (an eye). To what extent is the similarity between different eyes (e.g. vertebrate and mollusk) is due to common ancestry or is the result of evolutionary convergence due to physical constraints? What can we learn from the similarities and differences in the architecture/anatomy, development and molecular machinery of eyes (or light sensitive cells) in different species? BUT before we can address the question of evolution we need first to learn how it works
More broadly: Molecular pathway(s) of phototransduction are similar to many other signaling pathways: olfaction, taste, etc Comparative Systems Biology
Modeling molecular mechanisms of photo-transduction Case studies: 1) vertebrate and 2) insect Phototransduction as a model signaling system
Vertebrate Rods and Cones
Vertebrate photoreceptor cell Rod Outer Segment (2000 Discs) 100μm hv Rhodopsin Na + Na +, Ca 2+ Discs Light reduces the dark current into the cell
Intracellular Voltage in Rods and Cones Turtle Rod: a flash response family shown on different time scales Turtle Cone
Measuring currents
Patch clamp
Single Photon Response
Patch clamp recordings
In the dark a standing current circulates through the rod. Electrophysiology of Rods Na, Ca Na, Ca cgmp cgmp Ca,K Na Ca,K Na K K K Na K K ATP driven Na/K pump K K Na K K Light shuts off the influx of current into the outer segment, while K continues to exit the inner segment causing the cell to hyperpolarize. Na,Ca channels of outer segment need cgmp to stay open
Light detector protein: Rhodopsin Rhodopsin undergoes light-induced conformational change chromophore, 11-cis retinal + opsin, a membrane protein with 7 transmembrane segments
cis/trans retinal transition
Light-induced conformational transition cytoplasmic side
Rhodopsin is a G-Protein coupled receptor
Seven-Helix G-protein- Coupled Receptors form a large class (5% C. elegans Genome!) β 2 adrenergic receptor Rhodopsin cytoplasmic end
Rhodopsin is a G-Protein coupled receptor Rhodopsin about 10 9 rhodopsin molecules and about 10 8 G-protein molecules per rod outer segment (ROS) Rh* light photoactivated rhodopsin (Rh*) forms in about 1 ms and serially activates 100 to 1000 Transducin molecules per second Transducin is a heterotrimeric G protein specific to vision Tαβγ GDP Tα + Tβγ GTP
G- proteins α β γ α subunit: 35-45 kd β subunit: 35-40 kd γ subunit: 6-12 kd guanine nucleotide binding site on α subunit At least 15 different genes for α subunit and several different genes for β and γ subunits
extracellular cell membrane G protein coupled receptor (GPCR) GDP α γ β Resting state: (G protein off) GDP α Steps in activation receptor activated by action of external signal γ β 1. Binding of activated receptor to G protein opens guanine nucleotide binding pocket on α subunit
2. GDP -- GTP exchange at nucleotide binding site activates the G protein GDP 3. α GTP γ β GTP α * γ β The α and βγ subunits dissociate from activated GPCR GTP α * γ β Activated α subunit stimulates effector proteins: enzymes or ion channels
Rhodopsin light Rh* Tαβγ-GDP Tα -GTP + Tβγ PDE PDE* Effector cgmp GMP CNG Channels: OPEN CLOSED
Where did cgmp come from? Guanylate Cyclase GTP cgmp + PPi GMP Phosphodiesterase
G Protein Effectors Include Phosphodiesterase (PDE) hydrolyzes cyclic nucleotide; e.g. cgmp GMP Enzymes: Adenylyl cyclase Phospholipase C synthesizes camp from ATP hydrolyzes PIP 2 to produce IP 3 and diacylglycerol (DAG) Ion channels: e.g. K, Ca and Na channels
Shut-off Rhodopsin light Rh* Next question: How are the activated intermediates shut off? Tαβγ-GDP Tα -GTP + Tβγ PDE PDE* cgmp GMP CNG Channels: OPEN CLOSED
Rhodopsin inactivation
Transducin is inactivated by the α intrinsic GTPase activity which hydrolyzes GTP to GDP GTP α * γ β In Time GDP α + P i γ β Tα and βγ re-associate Accelerated by PDE* GDP α γ β Tα-GDP dissociates from PDE* which re-inhibits PDE*
The intrinsic GTPase activity of the α subunit is regulated by a GAP (GTPase accelerating protein) RGS-9 GTP α * γ β Tα * shut off is accelerated by action of RGS-9 Regulator of G-protein signaling GDP + α P i γ β
Recovery to the resting state requires resynthesis of the cgmp that had been lost to hydrolysis. This is accelerated by low Ca (feedback signal!) that stimulates Guanylate Cyclase GTP cgmp + PPi
Ca- the second 2 nd messenger Na, Ca Na, Ca cgmp cgmp Ca,K Na Ca,K Na channel closure shuts off Ca influx, while efflux by Na:Ca,K exchange continues and internal Ca declines. The fall in [Ca] is the [Ca] feedback signal. K K Na K K Na K K K K
Negative feedback Ca 2+ Regulation of Guanylate Cyclase
Signaling cascade Converts a microscopic stimulus activation of a single molecule -into a macroscopic response Alberts et al, Mol Bio of the Cell
Rhodopsin light Rh* Phototransduction Cascade as an enzymatic amplifier 1st Stage of amplification: 200-1000 G * per Rh* G αβγ - GDP G* α - GTP + G βγ Phosphodiesterase (PDE) PDE* 2nd Stage amplification: each PDE* hydrolyzes ~ 100 cgmp molecules. GTP GC* cgmp GMP Total gain: 2 x 10 5 10 6 cgmp / Rh* CNG Channels: OPEN CLOSED channel closure generates electrical signal
Olfaction: mucus film olfactory cilium tight junction supporting cell olfactory knob receptor dendrite cell body basement membrane axon
Olfactory receptor R Odor ligand R* Olfactory receptor cascade G αβγ - GDP G* α - GTP + G βγ AC* AC Adenylate cyclase ATP camp PDE* AMP CNG Channels: OPEN DEPOLARIZATION OF THE CELL
Rhodopsin light Invertebrate Phototransduction Cascade Rh* G q - GDP G q α - GTP + G q βγ Phospholipase C PLC* ( phosphoinositol 3,4 bisphosphate ) PIP2 IP3 & DAG? Trp Channels: CLOSED OPEN
Enzymatic amplifier modules GDP Rh* G* GTP PDE* 1 st stage: G-protein (Transducin) activation and deactivation GTP G GDP P i cgmp 2 nd stage: cgmp hydrolysis and synthesis GC GTP GMP PDE* Note: [GTP] / [GDP] & [GMP] acts a metabolic power supply
More examples of amp modules GDP G* GTP ADP S P GEF GAP Kinase Phosphotase G GDP P GTP i S ATP Small GTPases: Ras, Rho, Rab, Rap, Reb, Vasodilation Nitric Oxide Receptor Guanylate Cyclase GTP cgmp GMP PDE5 P i Viagra
General push-pull amplifier circuit a X c * E act E de-act Power supply : a+b c maintains high [c]/[a] c X a b d dt [ X*] = k[ X][ Eact ] k'[ X*][ E ] Steady state: [ X *] = de act k[ Eact ] ke [ ] k'[ E ] [ X ] tot act + de act Note: [X*]/[X] = e -βδe because the system is held out of equilibrium by fixed [c]/[a] maintained by metabolism
Amplifier gain and time constant Small change in [X*] induced by a small change in [E act ]: d δ[ X*] + τ 1 δ[ X*] = k[ Xtot ] δ[ Eact ] dt Linear response (in the Fourier domain): δ[ X*]( ω) δ[ E ]( ω) act τkx [ ] = + iωτ Static gain g 1 Time constant = τ k[ X] τ = k[ Eact ] + k'[ E ] de act Note: g ~ τ the gain-bandwidth theorem!!
Linear analysis of vertebrate phototransduction Rh* deactivation + 2 amplifier modules with negative feedback via [Ca ++ ] Good approximation to weak flash (single photon) response
Linear analysis of the cascade d 1 1 δg* = τ GδG* + τ GgGδRh* dt d 1 1 δ[ cgmp] = τ cgmpδ[ cgmp] τ cgmpgcgmpδg * dt Assuming stoichiometric processes of PDE* and Ch* activation are fast : δ PDE* ~ δ G* δ Ch* ~ δ cgmp* δch*~ δ[ cgmp]( ω) = g g G cgmp δrh *( ω) ( 1+ iωτ )( 1+ iωτ ) G cgmp
Hard and Soft parameters Kinetic constants/affinities -- hard parameters change on evolutionary time scale Enzyme concentrations -- soft parameters that can be regulated by the cell. e.g. g = τ k[ X] τ = k[ Eact ] + k'[ E ] de act Golden rule of biological networks: anything worth regulating is regulated
General behavior δx *( ω) g1... gn = δy *( ω) ( 1+ iωτ )...( 1+ iωτ ) Impulse response in the time domain: 1 n n δx*( t) { g t 1... gn δy *( 0 ) = τ1.. τ n g... t/ τ Max 1 g n e at short times at times times For: τ =... = τ = τ 1 n n δx*( t) δ *( 0) ~ t/ g t e n Y τ τ With n=3 - good fit to single-photon response
Case of feedback d τ G δg* = δg* + ggδrh* dt d τ cgmp δ[ cgmp] = δ[ cgmp] gcgmpδg * dt d τ Ca δ[ Ca] = δ[ Ca] + gcaδ[ cgmp] dt + g F δ[ca] feedback via δch* δcgmp( ω) δrh *( ω) = g g ( 1+ iωτ ) G cgmp Ca ( 1+ iωτ )[( 1+ iωτ )( 1+ iωτ ) g g ] G cgmp Ca Ca F
Consequences of negative feedback δcgmp( ω) = δrh *( ω) Reduction of static gain: g g ( 1+ iωτ ) G cgmp Ca ( 1+ iωτ )[( 1+ iωτ )( 1+ iωτ ) g g ] G cgmp Ca Ca F gg G cgmp g g G cgmp ( 1 g g ) Ca F Accelerated recovery: Ringing : gcagf > ( τ Ca τ cgmp ) 4τ τ Ca cgmp 2
Signal and Noise: How much gain is enough? Single photon signal : δι 2 pa Ι Dark 60 pa } δι /Ι Dark 3% What s the dominant source of background noise? CV 2 Thermal fluctuations? δ δ 2 V CVDark V = kbt = V Dark kt B 2 CV Dark ~ 10 6 ROS capacitance C ~ 20pF Negligible!
Reaction shot noise d dt X * = Γ ( X,..) ( X *,..) + ( t + Γ η ) # of molecules < η() t η( 0) >= ( Γ + Γ ) δ() t + Langevin noise (i.e. Gaussian, White) E.g. if Γ - = 0 consider ΔX* produced over time Δt z < ΔX* >= dtγ + z < ( ΔX*) 2 > < ΔX* > 2 =< [ dtη( t)] 2 >=< ΔX* > Poisson process
Channel opening noise d dt Ch* = ([ cgmp]) Ch 1 γ τ Ch * + η( t) Ch Ch D * =< Ch*> = τ Ch γ ([cgmp] D )Ch Tot Channel flicker noise: 2 < ( δch*) >=< Ch >= Ch < ( δch*) > < Ch > 2 1/ 2 * * Dark 1 1 = ~ = 4 Ch 10 * * D 1% Note: this Poisson law holds generally for mass action < 3% signal Plus fluctuations of δ[cgmp]: 2 * 2 < ( δch*) >= Ch + f ( τ / τ ) < ( δ[ cgmp] ) > D cgmp Ch
cgmp fluctuations Note: voltage response is coherent over the whole rod outer segment, hence must consider the whole volume V ros ~ 10 4 μm 3 #cgmp = [cgmp] V ros ~ 10μM 10 4 μm 3 ~ 10 7 Negligible fluctuations
Locality of single photon response 100μm cgmp depletion hv Na +, Ca 2+ G* and PDE* activity 3 2 1 l ~ D τ ~ 10 μm s. 5s ~ 20μm cgmp cgmp cgmp 2 1 l ~ 10μm s. 5s ~ 2μm G*
Single photon response variability Baylor-Riecke: coefficient of variation < [ ΔI < ΔI > ] > p p < ΔI > p 2 1/ 2 ~ 025.
What is the largest source of response variability? Spontaneous activation G -> G*?? < 10-7 s -1 Negligible even with 10 8 G molecules! Variability of Rh* on - time Δt?? ΔG* ~ kδt 1 st order Poisson process: < ( Δt) > < Δt > < Δt > 2 2 <Δt> = τ Rh* = 2 1 Baylor& Reicke measured: < 2 > < > 2 ( ΔIp) ΔIp ~. 05 2 < ΔI > p Poisson process of order 20!!!
Multistep deactivation of Rh*
Meta-Rhodopsin shut-off: Rh Kinase is turned on by binding to Rh* Rhodopsin Kinase Arrestin Arrestin is a 48kD accessory protein ATP Rh* Rh*-PO 4 Rh-PO 4 -Arrestin (active) (inactive)
Summary: What we have learned: GPCR / cyclic nucleotide cascade Enzymatic amplifier module and linear response Noise analysis Tomorrow from frog to fly and from linear to non-linear
Acknowledgements Anirvan Sengupta, (Rutgers) Peter Detwiler (U. Washington) Sharad Ramanathan (CGR/Lucent)