Bioinformatics 3! V20 Kinetic Motifs" Mon, Jan 13, 2014"

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Bioinformatics 3! V20 Kinetic Motifs" Mon, Jan 13, 2014"

Modelling of Signalling Pathways" Curr. Op. Cell Biol. 15 (2003) 221" 1) How do the magnitudes of signal output and signal duration depend on the " kinetic properties of pathway components?" (2) Can high signal amplification be coupled with fast signaling?" (3) How are signaling pathways designed to ensure that they are safely off in the absence " of stimulation, yet display high signal amplification following receptor activation?" (4) How can different agonists stimulate the same pathway in distinct ways to " elicit a sustained or a transient response, which can have dramatically different consequences?" Bioinformatics 3 WS 13/14" V 20 " 2"

Linear Response" E.g., protein synthesis and degradation (see lecture V10)" S S = signal (e.g., concentration of mrna)" R = response (e.g., concentration of a protein)" R At steady state (which implies S = const):" =>" RSS linearly dependent on S" RSS! 2 1 0 0 1 2 S! k0 = 1, k1 = k2 = 2" Bioinformatics 3 WS 13/14" V 20 " 3"

R phosphorylation/dephosphorylation" S RP forward : R is converted to phosphorylated form RP" backward : RP can be dephosphorylated again to R" S + R => RP" RP => R + T" with Rtot = R + RP" phosphorylated form" T Find steady state for RP: linear until saturation" RPSS! 1 0.1 Output T proportional to RP level:" 0.01 0.01 0.1 1 10 100 S! Rtot = 1, S0 = 1" Bioinformatics 3 WS 13/14" V 20 " 4"

Enzyme: Michaelis-Menten-kinetics" S" kon" E" ES" koff" T" Reaction rate:" Steady state:" Total amount of enzyme is constant:" =>" turnover: " Bioinformatics 3 - WS 12/13" 5"

The MM-equation" Effective turnover according to MM: " Pro:" Cons:" analytical formula for turnover" curve can be easily interpreted: Vmax, KM" enzyme concentration can be ignored" less kinetic information" kon, koff, ET => Vmax, KM" Bioinformatics 3 - WS 12/13" 6"

Sigmoidal Characteristics with MM kinetics" S Same topology as before with Michaelis-Menten kinetics for phosphorylation and dephosphorylation." R RP T this means that S = Rt - RP! KM = R0! Quadratic equation for RP" => sigmoidal characteristics " (threshold behavior)" often found in signalling cascades" RPSS! 10 8 6 4 2 0 0 1 2 3 S! Rt = 10, R0 = RP0 = 1, k1 = k2 = 1" Bioinformatics 3 WS 13/14" V 20 " 7"

Graded Response" 10 RSS! 2 1 RPSS! 1 0.1 RPSS! 8 6 4 0 0 1 2 S! 0.01 0.01 0.1 1 10 100 S! 2 0 0 1 2 3 S Linear, hyperbolic, and sigmoidal characteristic give the same steady state response independent of the previous history" => no hysteresis" BUT: In fast time-dependent scenarios," delay may lead to a modified response " Bioinformatics 3 WS 13/14" V 20 " 8"

Time-dependent Sigmoidal Response" S Direct implementation:" R RP T Parameters: k1 = 1 (mol s) 1, k2 = 1 s 1, R0 = RP0 = 1 mol" Initial conditions: R = 10 mol, RP = 0" Time courses for " S = 1, 1.5, and 2," RP(0) = 0:" RP(t)" equilibrium is reached" faster for " stronger signal" t" Bioinformatics 3 WS 13/14" V 20 " 9"

Adaption - sniffer " Linear response modulated by a second species X" S X R Steady state: Rss independent of S" R changes transiently when S changes, " then goes back to its basal level." found in smell, vision, chemotaxis, " 2 1 S! X! Note: response strength!r depends on rate of change of S." => non-monotonous relation for R(S)" 0 R! 0 1 2 3 4 5 S! k1 = 30, k2 = 40, k3 = k4 = 5" Bioinformatics 3 WS 13/14" V 20 " 10"

Positive Feedback" Feedback via R and EP" => high levels of R will stay" "one-way switch" via bifurcation" Found in processes that are "final":" frog oocyte maturation, apoptosis, " Bioinformatics 3 WS 13/14" V 20 " 11"

Mutual Inhibition - Toggle Switch" Sigmoidal "threshold" in E <=> EP leads to bistable response (hysteresis): toggle switch! Converts continuous external stimulus into " two well defined stable states:" lac operon in bacteria" activation of M-phase promoting factor in frog eggs" Bioinformatics 3 WS 13/14" V 20 " 12"

Negative Feedback" S controls the "demand" for R" => homeostasis" found in biochemical pathways," no transient changes in R for steps in S" (cf. "sniffer")" Bioinformatics 3 WS 13/14" V 20 " 13"

Negative Feedback with Delay" Cyclic activation X => YP => RP => X" => Oscillations (in a range of S)" Proposed mechanism for circadian clocks" Bioinformatics 3 WS 13/14" V 20 " 14"

Circadian Clocks" CK1: casein kinase Rev-erb, ROR: retinoic acidrelated orphan nuclear receptors Cdg: clock-controlled gene(s) Ko & Takahashi Hum Mol Genet 15, R271 (2006) Bioinformatics 3 WS 13/14" V 20 " 15"

Substrate-Depletion Oscillations" R is produced in an autocatalytic reaction from X, finally depleting X " Similar to Lotka-Volterra system (autocatalysis for X, too):" Bioinformatics 3 WS 13/14" V 20 " 16"

The Cell Cycle" DNA separation" (mitosis)" Cell division" (cytokinesis)" DNA replication" cell growth" G1-phase" S-phase" When to take the next step???" Bioinformatics 3 WS 13/14" V 20 " 17"

Cell Cycle Control" Bioinformatics 3 WS 13/14" V 20 " 18"

Cell Cycle Control System" cdc = " "cell division cycle"" Tyson et al, Curr. Op. Cell Biol. 15 (2003) 221" Bioinformatics 3 WS 13/14" V 20 " 19"

Feedback loops control cell cycle" Bioinformatics 3 WS 13/14" V 20 " 20"

G1 => S Toggle Switch" Mutual inhibition between Cdk1-CycB and CKI" (cyclin kinase inhibitor)" Tyson et al, Curr. Op. Cell Biol. 15 (2003) 221" Bioinformatics 3 WS 13/14" V 20 " 21"

Mutual Inhibition"???" Assume: CycB:Cdk1:CKI is stable <=> dissociation is very slow" => same topology" <=> same bistable " behavior (?)" Bioinformatics 3 WS 13/14" V 20 " 22"

Rate Equations: Toggle Switch" R2" A" X" R1" R4" R3" Stoichiometric matrix" "(C)" = catalyst" R1" R2" R3" R4" A" 1" S" (C)" R" 1" 1" (C)" E" (C)" 1" 1" EP" 1" 1" X" 1" Bioinformatics 3 WS 13/14" V 20 " 23"

Rate Equations: G1/S Module" R5" R6" R1" R2" R3" R4" R1" R2" R3" R4" R5" R6" CycB" 1" Cdk1" 1" CycB:Cdk1" 1" 1" (C)" 1" CKI" 1" 1" 1" 1" CKI:P3" 1" 1" CKI:P3" 1" CycB:Cdk1:CKI" 1" -1" Bioinformatics 3 WS 13/14" V 20 " 24"

Comparison: Matrices" R2" A" X" R1" R4" R3" R5" R6" R1" R2" R3" R4" R1" R2" R3" R4" A" 1" S" (C)" R" 1" 1" (C)" E" (C)" 1" 1" EP" 1" 1" X" 1" R1" R2" R3" R4" R5" R6" CycB" 1" Cdk1" 1" CycB:Cdk1" 1" 1" (C)" 1" CKI" 1" 1" 1" 1" CKI:P3" 1" 1" CKI:P3" 1" CycB:Cdk1:CKI" 1" -1" Difference: catalysts vs. substrates" Bioinformatics 3 WS 13/14" V 20 " 25"

Comparison: Equations" R2" A" X" R1" R4" R3" R6" R1" R2" R3" R5" R4" Rename species => same rate equations => same behavior" Bioinformatics 3 WS 13/14" V 20 " 26"

Predicted Behavior: G1 => S" Signal: cell growth = concentration of CycB, Cdk1" Response: activity (concentration) of CycB:Cdk1" Toggle switch:" => above critical cell size CycB:Cdk1 activity will switch on" Tyson et al, Curr. Op. Cell Biol. 15 (2003) 221" Bioinformatics 3 WS 13/14" V 20 " 27"

G2 => M" Toggle switch:" mutual activation between " CycB:Cdk1 and Cdc25 " (phosphatase that activates " the dimer)" mutual inhibition between " CycB:Cdk1 and Wee1 " (kinase that inactivates the dimer)" =>"when the cell grows further during the second gap phase G2, the activity of CycB:Cdk1 will increase by a further step! Tyson et al, Curr. Op. Cell Biol. 15 (2003) 221" Bioinformatics 3 WS 13/14" V 20 " 28"

M => G1" Negative feedback loop" oscillator" i) CycB:Cdk1 activates anaphase " promoting complex (APC)" ii) APC activates Cdc20" iii) Cdc20 degrades CycB" Behavior:" at a critical cell size " CycB:Cdk1 activity increases and decreases again" => at low CycB:Cdk1 level, the G1/S toggle switches off again," => cell cycle completed" Tyson et al, Curr. Op. Cell Biol. 15 (2003) 221" Bioinformatics 3 WS 13/14" V 20 " 29"

Overall Behavior" Cell divides at size 1.46" => daughters start " growing from " size 0.73" => switches to " replication at " size 1.25" G1/S toggle => bistability" M/G1 oscillator" G2/M toggle => bistability" Tyson et al, Curr. Op. Cell Biol. 15 (2003) 221" Bioinformatics 3 WS 13/14" V 20 " 30"

Preventing Cross-Talk" Many enzymes are used " in multiple pathways" => how can different signals cross " the same kinase?" => different temporal signature" (slow vs. transient)" => Dynamic modelling!" Bioinformatics 3 WS 13/14" V 20 " 31"

Summary" Today:! Behavior of cell cycle control circuitry from its modules:" two toggle switches + one oscillator" => map biological system onto motif via" stoichiometric matrices" rate equations" Bioinformatics 3 WS 13/14" V 20 " 32"

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