V14 Dynamic Cellular Processes

1. V14 Dynamic Cellular Processes John Tyson Bela Novak Bioinformatics III

2. Positive feedback: Mutual activation E: a protein involved with R EP: phosphorylated form of E Here, R activates E by phosphorylation, and EP enhances the synthesis of R. Tyson et al., Curr.Opin.Cell.Biol. 15, 221 (2003) Bioinformatics III

3. mutual activation: one-way switch As S increases, the response is low until S exceeds a critical value Scrit at which point the response increases abruptly to a high value. Then, if S decreases, the response stays high.  between 0 and Scrit, the control system is „bistable“ – it has two stable steady-state response values (on the upper and lower branches, the solid lines) separated by an unstable steady state (on the intermediate branch, the dashed line). This is called a one-parameter bifurcation. Tyson et al., Curr.Opin.Cell.Biol. 15, 221 (2003) Bioinformatics III

4. mutual inhibition Here, R inhibits E, and E promotes the degradation of R. Tyson et al., Curr.Opin.Cell.Biol. 15, 221 (2003) Bioinformatics III

5. mutual inhibition: toggle switch This bifurcation is called toggle switch („Kippschalter“): if S is decreased enough, the switch will go back to the off-state. For intermediate stimulus strengh (Scrit1 < S < Scrit2), the response of the system can be either small or large, depending on how S was changed. This is often called „hysteresis“. Examples: lac operon in bacteria, activation of M-phase promoting factor in frog egg extracts, and the autocatalytic conversion of normal prion protein to its pathogenic form. Tyson et al., Curr.Opin.Cell.Biol. 15, 221 (2003) Bioinformatics III

6. Negative feedback: homeostasis In negative feedback, the response counteracts the effect of the stimulus. Here, the response element R inhibits the enzyme E catalyzing its synthesis. Therefore, the rate of production of R is a sigmoidal decreasing function of S. Negative feedback in a two-component system X  R | X can also exhibit damped oscillations to a stable steady state but not sustained oscillations. Tyson et al., Curr.Opin.Cell.Biol. 15, 221 (2003) Bioinformatics III

7. Negative feedback: oscillatory response Sustained oscillations require at least 3 components: X  Y  R |X Left: example for a negative-feedback control loop. There are two ways to close the negative feedback loop: (1) RP inhibits the synthesis of X (2) RP activates the degradation of X. Tyson et al., Curr.Opin.Cell.Biol. 15, 221 (2003) Bioinformatics III

8. Negative feedback: oscillatory response Feedback loop leads to oscillations of X (black), YP (red), and RP (blue). Within the range Scrit1 < S < Scrit2, the steady-state response RP,ssis unstable. Within this range, RP(t) oscillates between RPmin and RPmax. Again, Scrit1and Scrit2are bifurcation points. The oscillations arise by a generic mechanism called „Hopf bifurcation“. Negative feedback has ben proposed as a basis for oscillations in protein synthesis, MPF activity, MAPK signaling pathways, and circadian rhythms. Tyson et al., Curr.Pin.Cell.Biol. 15, 221 (2003) Bioinformatics III

9. Positive and negative feedback: Activator-inhibitor oscillations R is created in an autocatalytic process, and then promotes the production of an inhibitor X, which speeds up R removal. The classic example of such a system is cyclic AMP production in the slime mold. External cAMP binds to a surface receptor, which stimulates adenylate cyclase to produce and excrete more cAMP. At the same time, cAMP-binding pushes the receptor into an inactive form. After cAMP falls off, the inactive form slowly recovers its ability to bind cAMP and stimulate adenylate cyclase again. Tyson et al., Curr.Pin.Cell.Biol. 15, 221 (2003) Bioinformatics III

10. Substrate-depletion oscillations X is converted into R in an autocatalytic process. Suppose at first, X is abundant and R is scarce. As R builds up, the production of R accelerates until there is an explosive conversion of the entire pool of X into R. Then, the autocatalytic reaction shuts off for lack of substrate, X. R is degraded, and X must build up again. This is the mechanism of MPF oscillations in frog egg extract. Tyson et al., Curr.Pin.Cell.Biol. 15, 221 (2003) Bioinformatics III

11. Complex networks All the signal-response elements just described, buzzers, sniffers, toggles and blinkers, usually appear as components of more complex networks. Example: wiring diagram for the Cdk network regulating DNA synthesis and mitosis. The network involving proteins that regulate the activity of Cdk1-cyclin B heterodimers consists of 3 modules that oversee the - G1/S - G2/M, and - M/G1 transitions of the cell cycle. Tyson et al., Curr.Pin.Cell.Biol. 15, 221 (2003) Bioinformatics III

12. Cell cycle control system Tyson et al., Curr.Opin.Cell.Biol. 15, 221 (2003) Bioinformatics III

13. cell-cycle machinery The signalling dynamics can become multi-stable when two or more bistable cycles form a cascade, such as a MAPK cascade. The biological outcome of multistability is the ability to control multiple irreversible transitions, for instance, sequential transitions in the cell cycle. Central components of the cell-cycle machinery are cyclin-dependent kinases (such as CDK1/ CDC2), the sequential activation and inactivation of which govern cell-cycle transitions. The activity of CDK1/CDC2 is low (off) in the G1 phase and has to be high (on) for entry into mitosis (M phase). Tyson et al., Curr.Opin.Cell.Biol. 15, 221 (2003) Bioinformatics III

14. Cell cycle control system The G1/S module is a toggle switch, based on mutual inhibition between Cdk1-cyclin B and CKI, a stoichiometric cyclin-dependent kinase inhibitor. signal: synthesis of Cdk1:CycB response: Cdk1/CycB Tyson et al., Curr.Pin.Cell.Biol. 15, 221 (2003) Bioinformatics III

15. Cell cycle control system The G2/M module is a second toggle switch, based on mutual activation between Cdk1-cyclinB and Cdc25 (a phosphotase that activates the dimer) and mutual inhibition between Cdk1-cyclin B and Wee1 (a kinase that inactivates the dimer). Tyson et al., Curr.Pin.Cell.Biol. 15, 221 (2003) Bioinformatics III

16. Cell cycle control system The M/G1 module is an oscillator, based on a negative-feedback loop: Cdk1-cyclin B activates the anaphase-promoting complex (APC), which activates Cdc20, which degrades cyclin B. The „signal“ that drives cell proliferation is cell growth: a newborn cell cannot leave G1 and enter the DNA synthesis/division process (S/G2/M) until it grows to a critical size. Tyson et al., Curr.Pin.Cell.Biol. 15, 221 (2003) Bioinformatics III

17. Cell cycle control system The signal-response curve is a plot of steady-state activity of Cdk1-cyclin B as a function of cell size. Progress through the cell cycle is viewed as a sequence of bifurcations. A very small newborn cell is attracted to the stable G1 steady state. As it grows, it eventually passes the saddle-point bifurcation SN3 where the G1 steady state disappears. The cell makes an irreversible transition into S/G2 until it grows so large that the S/G2 steady state disappears, giving way to an infinite period oscillation (SN/IP). Cyclin-B-dependent kinase activity soars, driving the cell into mitosis, and then plummets, as cyclin B is degraded by APC–Cdc20. The drop in Cdk1–cyclin B activity is the signal for the cell to divide, causing cell size to be halved from 1.46 to 0.73, and the control system is returned to its starting point, in the domain of attraction of the G1 steady state. Tyson et al., Curr.Pin.Cell.Biol. 15, 221 (2003) Bioinformatics III

18. cell-cycle machinery Hysteresis and bistability were recently shown to occur in the activation/ inactivation of CDK1/CDC2, an observation that confirmed a theoretical prediction by Novak and Tyson 10 years ago. Bistability in the CDK1/CDC2 cycle arises from positive and double-negative feedback loops in the reactions. CDK1/CDC2 activates its activator (the phosphatase CDC25) and inactivates its inhibitors (the kinases Wee1 and Myt1). Negative feedback from the anaphase-promoting complex (APC) turns the CDK1/CDC2 bistable switch into a relaxation oscillator that drives the cell cycle. Intriguingly, CDC25 and Wee1 can be phosphorylated on multiple sites and can therefore potentially exhibit bistability, which implies that the entire CDK/cyclin system can display multiple steady states — this prediction is awaiting experimental verification. Sequential bifurcations of multiple steady states provide more flexibility in the control of the cell fate and allow for several checkpoints in the cell cycle. Bioinformatics III

19. V17 Modelling signalling cascades B.N. Kholodenko, Nature Rev. Mol. Cell. Biol. 7, 165 (2006) Cells respond to external stimuli using a limited number of signalling pathways that are activated by plasmamembrane receptors, such as G protein-coupled receptors (GPCRs) and receptor tyrosine kinases (RTKs). These pathways do not simply transmit, but they also process, encode and integrate internal and external signals. Distinct spatio-temporal activation profiles of the same repertoire of signalling proteins may´result in different gene-expression patterns and diverse physiological responses  pivotal cellular decisions, such as cytoskeletal reorganization, cell-cycle checkpoints and cell death (apoptosis), depend on the precise temporal control and relative spatial distribution of activated signal transducers. Bioinformatics III

20. receptor tyrosine kinases RTK-mediated signalling pathways have a central role in the regulation of embryogenesis, cell survival, motility, proliferation, differentiation, glucose metabolism and apoptosis. Malfunction of RTK signalling is a leading cause of important human diseases involving e.g. developmental defects, cancer, chronic inflammatory syndromes and diabetes. Upon stimulation, RTKs undergo dimerization (e.g. the epidermal growth factor receptor. EGFR) or allosteric transitions (insulin receptor) that result in the activation of the intrinsic tyrosine-kinase activity. Subsequent phosphorylation of multiple tyrosine residues on the receptor transmits a biochemical signal to numerous cytoplasmic proteins, thereby triggering their mobilization to the cell surface. The resulting cellular responses occur through complex biochemical circuits of protein–protein interactions and covalent-modification cascades. Bioinformatics III

21. receptor tyrosine kinases Earlier concept: discrete linear pathways that relate extracellular signals to the expression of specific concepts. New concept: interconnected signalling networks. Several triggers use the same pathway in different fashions to achieve different output signals. How? E.g. PC12 cell-line stimulation with epidermal growth factor (EGF) and nerve growth factor (NGF). Both stimulate the MAPK cascade. EGF induces transient MAPK activation which results in cell proliferation. NGF creates a sustained MAPK activation that changes the cell fate and induces cell differentiation. Bioinformatics III

22. Cycle and cascade motifs A universal motif that is found in cellular networks is the cycle that is formed by two or more interconvertible forms of a signalling protein. This protein is modified by two opposing enzymes. These are a kinase and a phosphatase for phospho proteins, and a guanine nucleotide exchange factor (GEF) and a GTPase-activating protein (GAP) for small G proteins. Bioinformatics III

23. Feedback loops induce complex dynamics Feedback is one of the most fundamental concepts in biological control. An increase in the number of interconnecting cycles in a cascade or positive feedback further increases the sensitivity of the target to the input signal. Positive feedback amplifies the signal, whereas negative feedback attenuates it. However, feedback loops not only change steady-state responses, but also favour the occurrence of instabilities. When a steady state becomes unstable, a system can jump to another stable state, start to oscillate or exhibit chaotic behaviour. Positive feedback can cause bistability. Furthermore, positive feedback, alone or in combination with negative feedback, can trigger oscillations; for example, the Ca2+ oscillations that arise from Ca2+-induced Ca2+ release and the cell-cycle oscillations. Such positive-feedback oscillations generally do not have sinusoidal shapes and are referred to as relaxation oscillations, operating in a pulsatory manner: a part of a dynamic system is bistable, and there is a slow process that periodically forces the system to jump between ‘off ’ and ‘on’ states, generating oscillations. Bioinformatics III

24. complex dynamics Complex dynamic properties have traditionally been associated with cascades of cycles. Yet, even single cycles can exhibit complex dynamics, such as bistability and relaxation oscillations (see previous slide). A simple one-site modification cycle can turn into a bistable switch by four different regulatory mechanisms, in which one of the protein forms stimulates its own production or inhibits its consumption, thereby creating a destabilizing control loop. An extra (stabilizing) feedback loop that affects the rate of synthesis or degradation of a converting enzyme can render this bistable switch into a relaxation oscillator (32 distinct feedback designs result that can give rise to oscillations). Bioinformatics III

25. receptor tyrosine kinases Feedback designs that can turn a universal signalling cycle into a bistable switch and relaxation oscillator. A simple cycle can turn bistable in 4 distinct ways: either a protein M or its phosphorylated form Mp stimulates its own production (positive feedback) by product activation or substrate inhibition of the kinase (Kin) or phosphatase (Phos) reactions. Each of the 4 rows of feedback designs corresponds to a different bistable switch, provided that the kinase and the phosphatase abundances are assumed constant and only a single feedback (within the M cycle) is present. Sixteen relaxation-oscillation designs are generated by extra negative feedback brought about by negative or positive regulation of the synthesis or degradation rates of the kinase protein or phosphatase protein by M or Mp. Designs a*–h* are mirror images of designs a–h. Although synthesis and degradation reactions are shown for both the kinase and the phosphatase proteins, the protein concentration that is not controlled by feedback from the M cycle is considered constant, therefore it results in only two differential equations for each diagram. All the feedback regulations are described by simple Michaelis–Menten-type equations. Bioinformatics III

26. receptor tyrosine kinases Bioinformatics III

27. Signal Transduction (II) Study receptor-stimulated kinase/phosphotase signaling cascades as a model case of signal transduction networks. - amplitude of the signal output - rate and duration of signaling Bioinformatics III

28. Signal Transduction (II) To simplify the analysis, we first consider a simple linear signaling cascade in which stimulation of a receptor leads to the consecutive activation of several downstream protein kinases (Figure 1). The signal output of this pathway is the phosphorylation of the last kinase which, in turn, can elicit a cellular response (e.g., activation of a transcription factor). Signaling is terminated by phosphatases, which dephosphorylate the kinases, by inactivation of the receptor, which can involve receptor dephosphorylation, internalization of the receptor ligand complex, and/or degradation of the receptor or ligand. This general scheme is representative of many signaling pathways. E.g., growth factors such as EGF, PDGF, or NGF stimulate a receptor tyrosine kinase (RTK), which leads to the activation of three or four consecutivedownstream kinases (e.g., Raf, MEK, ERK, and RSK). Growth factor signals are terminated by protein-tyrosine phosphatases, RTK endocytosis and degradation, protein serine-threonine phosphatases, and dual-specificity and tyrosine-specific MAP kinase phosphatases. The same type scheme can model pathways that include lipid kinases, such as PI3K, whose reaction products help to activate downstream kinases such as PDK1 and Akt. Bioinformatics III

29. Linear Signalling Cascades Describe each phosphorylation step as a reaction between the phosphorylated form Xi-1 of kinase i – 1 and the non-phosphorylated form Xi of a downstream kinase i. Phosphorylation rate: second-order rate constant (2 proteins involved): ~ It is assumed that the concentration of each kinase-substrate complex is small compared with the total concentration of the reaction partners. Assuming that the concentration of active phosphatase is constant, dephosphorylation can be modeled as a first order reaction: Bioinformatics III

30. Linear Signalling Cascades For all but the first activated kinase in the pathway, the concentration of each activated kinase i as a function of time, Xi(t) is: Define as the total concentration of kinase i and as a pseudo-first order tate constant. The above equation becomes For the first kinase (X1), activation occurs via the stimulated receptor, and inactivation is mediated by phosphatase 1. Therefore, we have instead Bioinformatics III

31. Linear Signalling Cascades Assume that all pathway components are inactive at the start and they undergo rapid stimulation by setting the concentration of active receptor at t = 0 to R. Model receptor inactivation by 3 key questions are: (1) How fast does the signal arrive at its destination? (2) How long does the signal last? (3) How strong is the signal? Bioinformatics III

32. Signalling time The signalling time i is the average time to activate kinase i. Ii, the integrated response of Xiis the total amount of active kinase i generated during the signaling period. Ii corresponds to the area under the curve of Xi versus time. Ti / Ii is an average, analogous to the mean value of a statistical distribution. Bioinformatics III

33. Signal duration The signal duration is given by i gives a measure of how extended the signaling response is around the mean time. The signaling amplitude Si is given by In a geometric representation, Si is the height of a rectangle whose length is 2i and whose area equals the area under the curve Xi(t). Bioinformatics III

34. Weakly activated pathways A pathway is termed „weakly activated“ if all its component kinases are phosphorylated to a low degree (Xi << Ci). This may occur when the concentration of activated receptor is low, when the receptor is rapidly inactivated, and/or when the kinases are present at high concentrations. and the key parameters can be calculated explicitly. E.g. S depends on the kinetic properties of all pathway components. High signal amplitudes are obtained with fast kinases and slow phosphatases. Bioinformatics III

35. Weakly activated pathways The signaling time and duration do not depend on the kinase rate constants. Thus, in a weakly activated pathway, kinases regulate only signal amplitude, not signaling time or duration. In contrast, phosphatases affect all of these parameters, and in the same direction. Bioinformatics III

36. Amplification and dampening At any step in a signaling cascade, a signal can be amplified (Si > Si-1), dampened (Si < Si-1), or remain constant. Amplification at step i will occur if Amplification at step i requires that the phosphate rate constant i for a given reaction is small compared to the kinase rate constant i. Amplification at step i also depends on the signal duration at the preceding step (i-1). When the signal duration was long, amplification can be achieved even when the phosphatase rate constant at step i is high (but still smaller than i). Bioinformatics III

37. Amplification and dampening Bioinformatics III

38. Summary • Kinetic modelling of signal transduction networks by systems of coupled ordinary differential equations: • challenge consists of deriving the appropriate sets of equations • solving their time-dependent behavior is routine when done numerically, • may be very challenging (or impossible) if done analytically. • Other approaches for „data-driven“ modelling of signal-transduction networks: • clustering • principal component analysis • partial least squares regression • See e.g. Janes & Yaffe, Nat. Rev. Mol. Cell. Biol. 7, 820 (2006) Bioinformatics III