Systems Biology I: Bistability

1. Systems Biology I: Bistability Macromolecules Jonathan Weissman

2. Systems Biology How does complex biological behavior emerge from the organization of proteins into pathways and networks? • Common properties: • Bistability • convert continuous stimulus into discrete response • Hysteresis • “memory” of stimulus long after it is withdrawn

3. Outline for this lecture: Use simple graphical method to describe conditions that lead to bistability Discuss two biological examples of bistability: Xenopus oocyte maturation - MAPK Lac operon Go through experiments that demonstrate system is bistable Understand what the origin of bistability is Describe the physiological consequences of bistability

4. Cellular responses to stimuli: switches versus dimmers

5. stimulus inactivation Michaelian system - no feedback Assume S, I far from saturation At steady state: System is monostable Perturb [A*/Atot], return to ss

6. Michaelian system - no feedback, cont. increase S At steady state: Response levels off because the larger S gets, the less inactive A there is for the kinase to act on, and the more A* there is for the p’tase

7. Michaelian system with linear feedback e.g. A* increases activity of S or phosphorylates A in trans Extremes: With no [A*] feedback will be 0 When [A*]/[Atot]=1 and [A]=0 so feedback also equals 0 In between: Will be maximum when [A*]=[A]

8. Michaelian system with linear feedback, cont. Consider simple case where k1S is small so basal rate is negligible

9. Michaelian system with linear feedback, cont. Two steady states: strong feedback stable ON state but unstable OFF state One steady state: weak feedback stable OFF state but no ON state

10. How can we stabilize the OFF state? 1. Make feedback sigmoidal function of A* • three steady-states, one unstable (threshold) and two stable • at threshold, if decrease A*, back reaction is faster than • forward reaction and system is driven to OFF state • at threshold, if increase A*, forward reaction is faster than • back reaction and system is driven to ON state

11. Making feedback sigmoidal function of A*, cont. i. cooperativity e.g. A* activates S and takes n molecules of A* to activate S ii. zero-order ultrasensitivity Zero-order conditions First-order conditions

12. Making feedback sigmoidal function of A*, cont. ii. zero-order ultrasensitivity, cont. Opposing reactions with the [substrate] >> Km for the modifying enzymes First-order kinase A A* phosphatase First-order: changing p’tase by 1.5x has small effect on steady state Zero-order Zero-order: changing p’tase by 1.5x changes ss from >90% A* to >90% A

13. Making feedback sigmoidal function of A*, cont. ii. zero-order ultrasensitivity, cont. • small changes in enzyme activity lead to large changes • in modified protein, steady state iii. inhibitor ultrasensitivity • low abundance, high affinity inhibitor of S • once inhibitor is saturated, S will be effective at causing • increases in [A*] (same as S-P below) - inhibitor: 1/9 EC50 causes 10% response 90% response at 9 x EC50 81-fold change in kinase 10 to 90% + inhibitor: 10/9 units kinase causes 10% response 90% response at 10 units kinase 9-fold change in kinase 10 to 90%

14. How can we stabilize the OFF state? 2. Saturate back reaction with A* before feedback saturates • back reaction saturates as A* accumulates • back reaction can more than keep up with first bit of feedback, • but then is overwhelmed as feedback continues to rise

15. How can we stabilize the OFF state? 1. Make feedback a sigmoidal function of A* i. cooperativity ii. zero-order ultrasensitivity iii. inhibitor ultrasensitivity 2. Saturate back reaction with A* before feedback saturates Systems are bistable only for a limited range of kinetic parameters

16. Switching between the OFF and ON states • continuously increase feedback-independent stimulus S • bistable system converts continuous change in S into discontinuous • change in output (A*) increase S - increase slope of basal rate

17. Switching between the OFF and ON states What happens when we lower the stimulus? OFF state reappears when S is lowered to 3, but no driving force to leave ON state HYSTERESIS/IRREVERSIBILITY

18. Hysteresis and irreversibility Hysteresis Path from ON to OFF is different than that from OFF to ON Any bistable system will exhibit some degree of hysteresis Irreversibility System stays in ON state indefinitely after S is removed Occurs when feedback is strong Decreases chattering between ON and OFF states when S is near threshold Mechanism for biochemical memory - unless positive feedback is broken system will remain in ON state - can remember a stimulus long after it is removed

19. immature mature progesterone G2 arrested metaphase arrest, meiosis II How does this system turn a continuously varying stimulus (progesterone) into an all-or- none response? Example 1: Xenopus oocyte maturation meiosis I GVBD MAPK cascade

20. Xenopus oocyte maturation, cont. Measure response of oocytes to different [progesterone] by measuring MAPK phosphorylation (activation) Response of population - treat oocytes with give [progesterone], make extract, measure MAPK phosphorylation and tabulate % activation Response is graded - Michaelian!

21. Xenopus oocyte maturation, cont. How do we interpret these observations? OR [progesterone] [progesterone] Answer: Look at the response of individuals

22. Xenopus oocyte maturation, cont. Response is all-or-none - no intermediate levels of MAPK activation BISTABLE Where does this behavior come from? Clue: Microinjection of activated Mos gives same result (bistability), indicating it comes from pathway downstream of Mos (MAPK cascade)

23. Xenopus oocyte maturation, cont. What are the functional consequences of bistability for this system? Small change in stimulus near threshold throws switch At low stimulus buffered a bit from change No intermediate states

24. Xenopus oocyte maturation, cont. Can quantitate the sensitivity of the response - for a given change in stimulus, how much change In output (MAPK phosphorylation) results Michaelian - requires 81-fold change in [ligand] to drive system from 10% to 90% on Ultrasensitive - requires <81-fold change in [ligand] to drive system from 10% to 90% on Subsensitive - requires >81-fold change in [ligand] to drive system from 10% to 90% on

25. Xenopus oocyte maturation, cont. Hill coefficient - measure of sensitivity Michaelian: nH=1 Ultrasensitive: nH>1 Subsensitive: nH<1 Relationship exists between Hill coefficient and frequency of occurrence of intermediate states Higher Hill coefficient - fewer intermediate states Counted 190 oocytes - lower bound on nH is 42

26. Xenopus oocyte maturation, cont. What is the origin of the bistability? REMEMBER: Bistability arises from positive feedback and a mechanism to stabilize the off state 1. Multistep ultrasensitivity - stabilizing the off state Two phosphorylation events required for MAPK and MAPKK activation Activating kinase must dissociate in between phosphorylation events (to load ATP) Rate will vary as [upstream kinase]2 Two steps - effects are multiplicative

27. Xenopus oocyte maturation, cont. 1. Multistep ultrasensitivity - stabilizing the off state Michaelian Multistep ultrasensitivity • forward rate (slope) varies as [kinase]2 • 1 unit of kinase gives 50% S-P; double kinase and rate increases 4-fold • S-P must increase to higher level than in Michaelian case for rates • to balance and reach new steady state (80% vs. 67%) • leads to sigmoidal stimulus-response curve

28. Xenopus oocyte maturation, cont. 1. Multistep ultrasensitivity, cont. - stabilizing the off state Measure dependence of MAPK activation on Mos input in vitro in oocyte extracts nH ~ 5 ~2.5 fold change in MAPKKK changes MAPK from 10% to 90% activity

29. + Xenopus oocyte maturation, cont. 2. Zero-order ultrasensitivity - stabilizing the off state • no clear data that reactions in MAPK cascade are operating • in zero-order conditions, but concentrations and kinetic • properties that have been measured are consistent with this • idea • small change in activity leads to large change in ss position 3. Positive feedback • protein synthesis-dependent feedback from active MAPK • to Mos

30. Xenopus oocyte maturation, cont. Is the biochemistry underlying oocyte maturation irreversible? • Is the [progesterone] required to activate MAPK and Cdc2 • different from the [progesterone] required to maintain activities? Induction: incubate with progesterone, wait until maturation plateaus Maintenance: incubate with 600 nM progesterone, wait until GVBD plateaus, wash for 10 hr, incubate with different [progesterone] Maturation is irreversible - “memory” of progesterone

31. Xenopus oocyte maturation, cont. • based on what we learned about bistability, postulate it is the • strength of the feedback that gives rise to irreversibility • predict that if feedback is disrupted, system should lose • irreversibility or “memory” +E2=MAPK pathway activated +E2, wash=MAPK pathway activated then 16 hr wash Disrupt feedback with CHX, Mos antisense “Memory” requires positive feedback

32. Xenopus oocyte maturation, cont. • also predict that disrupting positive feedback should alter • bistability - make less ultrasensitive • quantitate response of individual oocytes to microinjected Mos • in presence and absence of CHX • observe oocytes with intermediate amounts of phosphorylation - loss of • bistability

33. Xenopus oocyte maturation, cont. • ultrasensitivity of MAPK cascade plus positive feedback generates • bistability • Michaelian MAPK with feedback - unstable OFF state • ultrasensitive MAPK with feedback - stable OFF state, filters out small • stimuli

34. Lac operon • beta-galactosidase is formed by bacterial cells grown in the • presence of lactose - beta-gal is necessary for metabolism • of lactose • known that non-metabolizable galactosides (e.g. TMG; • thiomethyl-galactoside) induce beta-gal formation • add high [TMG], see induction of beta-gal at maximal • induction rate - under these conditions cells respond • uniformly • at lower [TMG], see dose-dependent rate of induction of • beta-gal • cells that have been exposed to a high [TMG] and then shifted • to lower [TMG] (maintenance concentrations) continue • to synthesize beta-gal at the maximum rate Phenotypic change following transient signal - memory of inducer!

35. Lac operon, cont. Cells growing in [TMG] that gives intermediate level of beta-gal synthesis (e.g. 30%) Is the Lac system bistable? Dilute to maintenance [TMG] to give ~1 bacterium/10 tubes • 10% of the tubes developed bacterial populations • 30% of the cultures from single bacteria had maximal beta-gal • levels; 70% had only small amounts Population at intermediate [TMG] consists of cells that are fully induced and those that are uninduced - BISTABLE

36. TMG TMG LacI LacY LacZ Lac operon, cont. LacI = Lac repressor LacY = Lac permease LacZ = beta-galactosidase • autocatalytic positive feedback (double negative) • if there is non-linearity in response, might expect • bistability in TMG, LacI activity, LacY and LacZ expression

37. Lac operon, cont. Could come from TMG binding LacI, relationship between active LacI and LacY production… Need k0 parameter because if there is no permease the first molecule of TMG cannot enter the cell, independent of the external concentration - either operon is not totally repressed or TMG can slowly diffuse

38. [TMG] [TMG] Lac operon, cont. Three steady-states: ss1, 3 stable ss2 unstable Bistable

39. Lac operon, cont. Can see bistability and hysteresis in single cell experiments Take cells expressing Lac promoter-GFP and grow in different [TMG] - either initially uninduced or induced [maintenance] start induced start uninduced Uninduced then grown 20 hr in 18 mM TMG Bistability and hysteresis

40. Lac operon, cont. When inducer is added, permease synthesis will be initiated at a rate determined by inducer in medium At low [inducer] rate of permease synthesis may be so low that probability of making a permease molecule during lifetime of bacterium is small Once bacterium has permease, [inducer] inside cell will increase, which will increase probability that second molecule of permease will be formed Two permeases further increases rate of permease - autocatalytic rise to maximal permease Once have maximal permease, bacterium and progeny will be induced indefinitely since [inducer] inside is above maintenance concentration Maintenance can be explained if the number of permease molecules is large relative to threshold, there is high probability that each daughter cell will receive sufficient permease to insure induction Transfer to less than maintenance - observe exponential decrease in activity, equivalent to constant chance of becoming uninduced - partitioning between daughter cells - some will not get enough to insure induction

41. Flipping the switch: induction at intermediate lac concentration occurs by complete dissociation of the tetrameric lac repressor (A) A high concentration of intracellular inducer can force dissociation of the repressor from its operators, (B) At low or intermediate concentrations of intracellular inducer, partial dissociation from one operator by the tetrameric LacI repressor is followed by a fast rebinding. Consequently, no more than one transcript is generated during such a brief dissociation event. However, the tetrameric repressor can dissociate from both operators stochastically and then be sequestered by the inducer so that it cannot rebind, leading to a large burst of expression. (C) A time-lapse sequence captures a phenotype-switching event. In the presence of low inducer, one such cell switches phenotype to express many LacY-YFP molecules (yellow fluorescence overlay) whereas the other daughter cell does not